Hindawi Publishing CorporationJournal of RoboticsVolume 2013 Article ID 256364 14 pageshttpdxdoiorg1011552013256364

Research ArticleA Comparison between Two Force-Position Controllers withGravity Compensation Simulated on a Humanoid Arm

Giovanni Gerardo Muscolo1 Kenji Hashimoto2 Atsuo Takanishi23 and Paolo Dario4

1 RampD Department Creative Design Laboratory Humanot srl via Modigliani 7-59100 Prato Italy2 Department of Modern Mechanical Engineering Waseda University 17 Kikui-cho Shinjuku-ku Tokyo 162-0044 Japan3Humanoid Robotics Institute Waseda University 2-2 Wakamatsu-cho Shinjuku-ku Tokyo 162-8480 Japan4The BioRobotics Institute Scuola Superiore SantrsquoAnna Viale Rinaldo Piaggio 34 56025 Pontedera Italy

Correspondence should be addressed to Giovanni Gerardo Muscolo gmuscleghotmailcom

Received 31 October 2012 Revised 29 January 2013 Accepted 29 January 2013

Academic Editor Huosheng Hu

Copyright copy 2013 Giovanni Gerardo Muscolo et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The authors propose a comparison between two force-position controllers with gravity compensation simulated on the DEXTERbioinspired robotic arm The two controllers are both constituted by an internal proportional-derivative (PD) closed-loop for theposition control The force control of the two systems is composed of an external proportional (P) closed-loop for one system (Psystem) and an external proportional-integrative (PI) closed-loop for the other system (PI system)The simulation tests performedwith the two systems on a planar representation of theDEXTER an eight-DOF bioinspired arm showed that by varying the stiffnessof the environment with a correct setting of parameters both systems ensure the achievement of the desired force regime and withgreat precision the desired positionThe two controllers do not have large differences in performance when interacting with a lowerstiffness environment In case of an environment with greater rigidity the PI system is more stableThe subsequent implementationof these control systems on the DEXTER robotic bioinspired arm gives guidance on the design and control optimisation of the armsof the humanoid robot named SABIAN

1 Introduction

The manipulation control [1] presents difficulties especiallyin the variation of the compliance with the environment [2]For the safety of persons that surround the manipulator avariation of the stiffness of the humanoid robotic arms isnecessary

A real contact is a distributed phenomenon whichinvolves the local elastic properties of both the manipulatorand the environment Many methodologies allow modifyingthe stiffness of the manipulator in relation to the task Thecompliance inside theDC servo actuators is usually generatedby mechanical systems such as linear or torsional springs Inthese types of studies a hardware modification is developed

The actuators with variable stiffness are increasingly usedin the field of humanoid robotics [3] an example of thisapplication on humanoid robot iCub is presented in [4]A different kind of application of variable stiffness which

uses pneumatic or hydraulic systems as compliance elementformed by the fluid is presented in [5] In [6] a control forregulation tasks of robot manipulators with flexible links isproposed

In this paper in order to modify the compliance ofthe manipulator the authors modified only the softwareparameters

Considering 119870119860as the environment stiffness matrix and

by increasing or decreasing its value it is possible to modifythe compliance of all external part of the arm Increasing thevalue of119870

119860allows the manipulator to reach a given position

thus the arm encounters an obstacle that may not physicallyexist but in reality exerts a contact force which opposes themotion of the robotic arm and causes its arrest

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compensa-tion simulated on a bioinspired manipulator of eight DOFsnamed DEXTER (Figure 1 and Tables 1 2 3 4 and 5) [2 6]

2 Journal of Robotics

Figure 1 DEXTER bioinspired robotics arm

Table 1 DEXTER characteristics

Characteristics DEXTERDimensions (mm) width-length-height 400-400-950Weight (kg) (payload) 40 (2)Workspace (mm-∘) 1200-350∘

Velocity (ms) 02DOF Total 8

The next steps will be the implementation of these systemsinto the DEXTER robotic arm with the ultimate aim ofcontrol and design of the two arms of the humanoid robotSABIAN (Figure 5) [7 8]

The two proposed controllers are both constituted byan internal proportional-derivative (PD) closed-loop for theposition control The force controller of the two systems iscomposed of an external proportional (P) closed-loop for onesystem (P system) and an external proportional-integrative(PI) closed-loop for the other system (PI system)

This paper is composed of three parts The first partdescribes the dimensional characteristics of theDEXTER andthe SABIANrobots In the secondpart the two force-positioncontrollers are proposed and discussed In the third part theanalysis of simulational data and future applications based onthese results are proposed

2 Materials and Methods

21 DEXTER Bioinspired Robotics Arm The DEXTER arm(Figure 1) has eight DOFs with eight rotational joints [26] The joints are implemented by many electric DC servomotors located in the first link The motors transmit torquethrough a cables and pulleys system The motor-reducer forthe coupling 0 is integrated in themobile base while the joint1 is mounted on the link 0 The motors of the other joints areall in the link 1

The advantage of this type of mechanical structure is toimprove the dynamic performance of the robot because thereis a reduction of the masses in motion The disadvantageis related to the complexity of the mechanical transmissionsystem

Table 2 Motor data sheet

Axis Type of DC motor Nominal voltage(V)

Torque constant(mNmA)

0 PMI S9M4HI 24 84101 PMI S9M4HI 24 84102 3557 024 CR 24 42903 3557 024 CR 24 42904 3557 024 CR 24 42905 3557 024 CR 24 42906 3557 024 CS 24 41007 3557 024 CS 24 4100

Table 3 Drivers

Axis Type of driverContinuouscurrent(A)

Peakcurrent(A)

119866119894= 119868peakMaxInput

(AV)

0 Elmo ISA 1080 5 10 11 Elmo ISA 1080 5 10 12 Elmo ISA 1080 4 12 123 Elmo ISA 1080 4 12 124 Elmo ISA 1080 4 12 125 Elmo ISA 1080 4 12 126 Elmo ISA 1080 2 6 067 Elmo ISA 1080 2 6 06

Table 4 Denavit-Hartenberg parameters

Joint 119886119894(mm) 119889

119894(mm) 120572

119894(rad) 120579

119894(rad)

1 0 0 1205872 1205791

2 144 450 minus1205872 1205792

3 0 0 1205872 1205793

4 minus100 350 minus1205872 1205794

5 0 0 1205872 1205795

6 minus24 250 minus1205872 1205796

7 0 0 1205872 1205797

8 100 0 0 1205798

Table 5 Center of mass of the links

119903119909(mm) 119903

119910(mm) 119903

119911(mm) m (kg)

Link 0 0 692 2772 9429Link 1 minus13935 17449 4608 12051Link 2 0 minus611 3459 1627Link 3 9072 13377 minus024 2488Link 4 001 minus372 2030 0818Link 5 minus2401 14105 011 0541Link 6 minus005 236 678 0266Link 7 1035 181 3326 0095

In Tables 1 2 3 4 and 5 the physical dimensions themotor data sheet the drivers the parameters of Denavit-Hartenberg and the coordinates of the centers of mass of thelinks are respectively represented

Journal of Robotics 3

Link 7 axis 0

Link 6 axis 0

Link 5 axis 0

Link 1 axis 1

Link 3 axis 2

Link 4 axis 0

Link 2 axis 0

Link 3 axis 0

Figure 2 DEXTER robotic arm axis joints and links position

In Figures 2 and 3 the scheme of the manipulator isshown

TheDEXTERmanipulator system includes the functionalblocks of the Figure 4 The manipulation is constituted coor-dinating the joint movement of the arm with the movementof the hand mounted on the force sensor

22 SABIAN Humanoid Robot SABIAN [7 8] (Figure 5)has two 7-DOF legs a 2-DOF waist and a 2-DOF trunkEach actuator system of the joint consists of a DC motora harmonic drive gear a lug belt and two pulleys Thisdouble speed reduction mechanism allows a high reductionratio and also a joint axis to be set apart from the motoraxisThis mechanism provides designs for a human-like jointmechanism without a considerable projection Figure 5(a) isa photograph of SABIANThe height of the robot is 1480mmand the weight is 407 kg without batteries SABIAN is theItalian version of the WABIAN-2 robot [8] (see Figure 6)SABIAN does not have arms and the head is a version of theICUB head [4]

23WABIAN-2rsquos Arm Characteristics ThearmofWABIAN-2 has 7 DOFs and Figure 7 shows the 3D-CAD model Thearms were designed based on a concept that the arms of therobot can hold the robotrsquos weight while it leans on a walk-assist machine as shown in [9] Since the robot can lean on awalk-assist machine most of its weight will be distributed onboth its forearms

In general a forcetorque sensor is mounted on a robotrsquoswrist in order to enable it to grasp push or pull somethingusing a hand as an end-effector But because one of the designconcepts ofWABIAN-2 is a robot that can lean against awalk-assist machine a 6-axis forcetorque sensor is mounted oneach upper arm which enables the robot to measure externalforces acted on the forearm

In order to realize a humanoid robot with great dex-terity not only in locomotion as in WABIAN-2 but also inmanipulation as in DEXTER it is necessary to redesign theWABIAN-2rsquos arm and implement it on the SABIAN robot

24 WABIAN-2rsquos Arm Control Architecture A conventionalposition controller is used for WABIAN-2rsquos arms The six-dimensional hand trajectories are given and each joint angleis calculated by solving the inverse kinematics and the resultis the 120599

119901value as input in Figure 8 The DC motor is driven

bymotor drivers (Model no TD12770-48W05) developed byTOKUSHU DENSO Co Ltd which enables speed controlusing an electrical governor without a tachogenerator witha 100 kHz PWM The maximum output current range ofTD12770-48W05 is greater than 15A at 48V The currentmonitor port mounted on the motor drivers is utilizedin energy consumption experiments Figure 9 shows thephotograph of themotor driverThe 119909

119889is the fixed ideal value

of the hand position

3 Analysis of Control Schemes

31 DEXTER Bioinspired Robotics Arm Control ArchitectureThematrix 119870

119903of the reduction of the DEXTER robotmotion

is given by

119870119903= 1198701015840

119903119860 (1)

where 119860 is the matrix of the speed reduction related to themechanical transmission system 1198701015840

119903represents the diagonal

matrix of the reduction coefficients Consider119860

=

[[[[[[

[

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 minus4375 0 0 0 0 0

0 0 1162 minus3375 0 0 0 0

0 0 0583 0 3424 0 0 0

0 0 0483 0 minus1005 2882 0 0

0 0 0894 0 minus0638 0 minus1106 0

0 0 0894 0 minus0638 0 minus1106 minus1557

]]]]]]

]

1198701015840

119903=

[[[[[[[[[[

[

282 0 0 0 0 0 0 0

0 141 0 0 0 0 0 0

0 0 66 0 0 0 0 0

0 0 0 66 0 0 0 0

0 0 0 0 43 0 0 0

0 0 0 0 0 43 0 0

0 0 0 0 0 0 66 0

0 0 0 0 0 0 0 43

]]]]]]]]]]

]

(2)

The reduction system is constituted by redactors inproximity of each jointThe generic element119870

119903119894119895of thematrix

119870119903expresses the ratio of proportionality between the rotation

of the joint 119895 and the rotation of the rotor 119894 The relationshipbetween the torque vector of the motors to the torque vectorof the joints is given by

120591 = 119870119879

119903120591119898 (3)

This relationship allows to implement the conversionblock 120591 rarr 120591

119898and to directly move the motors The size of

119870119903matrix is 7 times 7 for the elimination of the first row and first

column relating to the joint 0 which is controlled by a PIDcontroller The standard PID controller used is expressed bythe control law

119879119899= 119870119875119864119899+ 119870119863(119864119899minus 119864119899minus1

)

+ 119870119868119878119899+ 119870119880119880119899+ 64119870

119885119885119899+ 119870119874

(4)

4 Journal of Robotics

12057911205792

1205793

12057941205795

1205796

1205797

1205798

1198831

1198832 = 1198833

1198834 = 1198835

1198850

1198852

1198853

1198854

1198855

1198856

1198858

1198830 = 1198851

1198857 = 1198836

1198838

1198837

Figure 3 DEXTER DOF configuration

User interface

Supervisor

High-level controllerof the arm

High-level controllerof the hand

Low-level controllerof the arm

Low-level controllerof the hand

Actuators of the arm Actuators of the hand

HandArm

Figure 4 Functional architecture of the DEXTER manipulatorsystem

119879119899represents the analog voltage control of the generic motor

output from the PIDwith a value ranging fromminus10V to+10V119870119875 119870119863 and 119870

119868are respectively the gains proportional

derivative and integral 119864119899represents the position error

to the joints determined in each sampling instant 119878119899is

the integrated error and in particular conditions can beexpressed as 119878

119899= 119878119899minus1

+ 119864119899 119880119899and 119885

119899are the speed and the

acceleration of the feed-forward terms119870119880and119870

119885introduce

the speed and the acceleration of the feed-forward terms119870119874

is a static offset used to compensate the small variations in theoutput voltage due to the119863119860 converters or also to the offsetof the amplifiers After notifying the movement commandsto the PID the first of the 8 motors is implemented with avoltage value equal to 119879

119899 Figures 10 and 11 respectively show

(a) (b)

Figure 5 SABIAN humanoid robot

the functional architecture of the subsystem of the arm andthe functional scheme of the PID controller

Figure 12 shows the PID controller of the joint 0 Figure 13shows the solution used to bypass the PID control of the joint0

The control law used for the analysis of the position of the1ndash7 joints is given by

120591 = 119870119875 minus 119870119863 + 119892 (119902) (5)

where 120591 is the torque vector 119870119875and 119870

119863 are respectively

the proportional and derivative matrices 119892(119902) is the gravitycompensation and 119902

119889is the vector of the desired joint

position = 119902119889minus 119902 is the error The relation (5) calculates

the value of the torque 120591 but not of the speed 119889119902 Thus it

is necessary to bypass the PID control to be able to controldirectly the actuators (Figure 13)

Journal of Robotics 5

Active joint Passive joint

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

P PitchR RollY Yaw

Roll

PitchYaw119874

119885

119883

119884

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

Pitch Roll Yaw

PitchYaw119874

119885

119884

(a)

1480

119885

119883119884

(b)

Figure 6 WABIAN-2 humanoid robot

DC motor

Harmonic driveServo driver

6-axis FT sensor

Figure 7 WABIAN-2rsquos arm

From (5) we obtain

120591119898= (119870119879

119903)minus1

120591

120591119898= 119870119905119894119898

119894119898= 119866119894V119898

119894119898= 119870119905

minus1120591119898

V119898= 119866119894

minus1119894119898

(6)

where 119870119905is the diagonal matrix of motor torque constant

derived from data-sheet of the 7 motors (Table 2) 119866119894is the

gain matrix of the power drivers 119894119898and V119898are respectively

the parameters of the currents and voltages in input to thepower drivers The technical specifications of the systemimplementation of the 8 joints are shown in Tables 2 3 4and 5

The software procedure achieves a conversion of thecontrol voltage from volt (V

119898) to increments (V

119898 inc)The used relations are

= 119909119889minus 119909 (7)

and if 119889= 0

119909 = minus119869119860(119902) (8)

where 119869119860(119902) is the Jacobianmatrix which allows to rewrite (6)

in [1] as

120591 = 119869119879

119860(119902)119870119875 minus 119869119879

119860(119902)119870119863119869119860(119902) + 119892 (119902) (9)

The interaction force can be controlled in an indirectmanner by acting on the 119909

119889reference variable of the posi-

tion controller of the manipulator the interaction betweenmanipulator and the environment is directly influenced bythe characteristics of the compliance of the environment andof the manipulator The measure of the force is corrupted bynoise for which the derivative control cannot be used

In Figures 14 and 15 two examples of force controlschemes respectively with position and velocity internalclosed-loop as in [1] are shown 119872

119889is a generic diagonal

positive matrix used for the impedence controlIndicating with 119891

119889the desired constant force with 119862

119865

a diagonal matrix whose elements characterize the actions

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 Journal of Robotics

Figure 1 DEXTER bioinspired robotics arm

Table 1 DEXTER characteristics

Characteristics DEXTERDimensions (mm) width-length-height 400-400-950Weight (kg) (payload) 40 (2)Workspace (mm-∘) 1200-350∘

Velocity (ms) 02DOF Total 8

The next steps will be the implementation of these systemsinto the DEXTER robotic arm with the ultimate aim ofcontrol and design of the two arms of the humanoid robotSABIAN (Figure 5) [7 8]

The two proposed controllers are both constituted byan internal proportional-derivative (PD) closed-loop for theposition control The force controller of the two systems iscomposed of an external proportional (P) closed-loop for onesystem (P system) and an external proportional-integrative(PI) closed-loop for the other system (PI system)

This paper is composed of three parts The first partdescribes the dimensional characteristics of theDEXTER andthe SABIANrobots In the secondpart the two force-positioncontrollers are proposed and discussed In the third part theanalysis of simulational data and future applications based onthese results are proposed

2 Materials and Methods

21 DEXTER Bioinspired Robotics Arm The DEXTER arm(Figure 1) has eight DOFs with eight rotational joints [26] The joints are implemented by many electric DC servomotors located in the first link The motors transmit torquethrough a cables and pulleys system The motor-reducer forthe coupling 0 is integrated in themobile base while the joint1 is mounted on the link 0 The motors of the other joints areall in the link 1

The advantage of this type of mechanical structure is toimprove the dynamic performance of the robot because thereis a reduction of the masses in motion The disadvantageis related to the complexity of the mechanical transmissionsystem

Table 2 Motor data sheet

Axis Type of DC motor Nominal voltage(V)

Torque constant(mNmA)

0 PMI S9M4HI 24 84101 PMI S9M4HI 24 84102 3557 024 CR 24 42903 3557 024 CR 24 42904 3557 024 CR 24 42905 3557 024 CR 24 42906 3557 024 CS 24 41007 3557 024 CS 24 4100

Table 3 Drivers

Axis Type of driverContinuouscurrent(A)

Peakcurrent(A)

119866119894= 119868peakMaxInput

(AV)

0 Elmo ISA 1080 5 10 11 Elmo ISA 1080 5 10 12 Elmo ISA 1080 4 12 123 Elmo ISA 1080 4 12 124 Elmo ISA 1080 4 12 125 Elmo ISA 1080 4 12 126 Elmo ISA 1080 2 6 067 Elmo ISA 1080 2 6 06

Table 4 Denavit-Hartenberg parameters

Joint 119886119894(mm) 119889

119894(mm) 120572

119894(rad) 120579

119894(rad)

1 0 0 1205872 1205791

2 144 450 minus1205872 1205792

3 0 0 1205872 1205793

4 minus100 350 minus1205872 1205794

5 0 0 1205872 1205795

6 minus24 250 minus1205872 1205796

7 0 0 1205872 1205797

8 100 0 0 1205798

Table 5 Center of mass of the links

119903119909(mm) 119903

119910(mm) 119903

119911(mm) m (kg)

Link 0 0 692 2772 9429Link 1 minus13935 17449 4608 12051Link 2 0 minus611 3459 1627Link 3 9072 13377 minus024 2488Link 4 001 minus372 2030 0818Link 5 minus2401 14105 011 0541Link 6 minus005 236 678 0266Link 7 1035 181 3326 0095

In Tables 1 2 3 4 and 5 the physical dimensions themotor data sheet the drivers the parameters of Denavit-Hartenberg and the coordinates of the centers of mass of thelinks are respectively represented

Journal of Robotics 3

Link 7 axis 0

Link 6 axis 0

Link 5 axis 0

Link 1 axis 1

Link 3 axis 2

Link 4 axis 0

Link 2 axis 0

Link 3 axis 0

Figure 2 DEXTER robotic arm axis joints and links position

In Figures 2 and 3 the scheme of the manipulator isshown

TheDEXTERmanipulator system includes the functionalblocks of the Figure 4 The manipulation is constituted coor-dinating the joint movement of the arm with the movementof the hand mounted on the force sensor

22 SABIAN Humanoid Robot SABIAN [7 8] (Figure 5)has two 7-DOF legs a 2-DOF waist and a 2-DOF trunkEach actuator system of the joint consists of a DC motora harmonic drive gear a lug belt and two pulleys Thisdouble speed reduction mechanism allows a high reductionratio and also a joint axis to be set apart from the motoraxisThis mechanism provides designs for a human-like jointmechanism without a considerable projection Figure 5(a) isa photograph of SABIANThe height of the robot is 1480mmand the weight is 407 kg without batteries SABIAN is theItalian version of the WABIAN-2 robot [8] (see Figure 6)SABIAN does not have arms and the head is a version of theICUB head [4]

23WABIAN-2rsquos Arm Characteristics ThearmofWABIAN-2 has 7 DOFs and Figure 7 shows the 3D-CAD model Thearms were designed based on a concept that the arms of therobot can hold the robotrsquos weight while it leans on a walk-assist machine as shown in [9] Since the robot can lean on awalk-assist machine most of its weight will be distributed onboth its forearms

In general a forcetorque sensor is mounted on a robotrsquoswrist in order to enable it to grasp push or pull somethingusing a hand as an end-effector But because one of the designconcepts ofWABIAN-2 is a robot that can lean against awalk-assist machine a 6-axis forcetorque sensor is mounted oneach upper arm which enables the robot to measure externalforces acted on the forearm

In order to realize a humanoid robot with great dex-terity not only in locomotion as in WABIAN-2 but also inmanipulation as in DEXTER it is necessary to redesign theWABIAN-2rsquos arm and implement it on the SABIAN robot

24 WABIAN-2rsquos Arm Control Architecture A conventionalposition controller is used for WABIAN-2rsquos arms The six-dimensional hand trajectories are given and each joint angleis calculated by solving the inverse kinematics and the resultis the 120599

119901value as input in Figure 8 The DC motor is driven

bymotor drivers (Model no TD12770-48W05) developed byTOKUSHU DENSO Co Ltd which enables speed controlusing an electrical governor without a tachogenerator witha 100 kHz PWM The maximum output current range ofTD12770-48W05 is greater than 15A at 48V The currentmonitor port mounted on the motor drivers is utilizedin energy consumption experiments Figure 9 shows thephotograph of themotor driverThe 119909

119889is the fixed ideal value

of the hand position

3 Analysis of Control Schemes

31 DEXTER Bioinspired Robotics Arm Control ArchitectureThematrix 119870

119903of the reduction of the DEXTER robotmotion

is given by

119870119903= 1198701015840

119903119860 (1)

where 119860 is the matrix of the speed reduction related to themechanical transmission system 1198701015840

119903represents the diagonal

matrix of the reduction coefficients Consider119860

=

[[[[[[

[

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 minus4375 0 0 0 0 0

0 0 1162 minus3375 0 0 0 0

0 0 0583 0 3424 0 0 0

0 0 0483 0 minus1005 2882 0 0

0 0 0894 0 minus0638 0 minus1106 0

0 0 0894 0 minus0638 0 minus1106 minus1557

]]]]]]

]

1198701015840

119903=

[[[[[[[[[[

[

282 0 0 0 0 0 0 0

0 141 0 0 0 0 0 0

0 0 66 0 0 0 0 0

0 0 0 66 0 0 0 0

0 0 0 0 43 0 0 0

0 0 0 0 0 43 0 0

0 0 0 0 0 0 66 0

0 0 0 0 0 0 0 43

]]]]]]]]]]

]

(2)

The reduction system is constituted by redactors inproximity of each jointThe generic element119870

119903119894119895of thematrix

119870119903expresses the ratio of proportionality between the rotation

of the joint 119895 and the rotation of the rotor 119894 The relationshipbetween the torque vector of the motors to the torque vectorof the joints is given by

120591 = 119870119879

119903120591119898 (3)

This relationship allows to implement the conversionblock 120591 rarr 120591

119898and to directly move the motors The size of

119870119903matrix is 7 times 7 for the elimination of the first row and first

column relating to the joint 0 which is controlled by a PIDcontroller The standard PID controller used is expressed bythe control law

119879119899= 119870119875119864119899+ 119870119863(119864119899minus 119864119899minus1

)

+ 119870119868119878119899+ 119870119880119880119899+ 64119870

119885119885119899+ 119870119874

(4)

4 Journal of Robotics

12057911205792

1205793

12057941205795

1205796

1205797

1205798

1198831

1198832 = 1198833

1198834 = 1198835

1198850

1198852

1198853

1198854

1198855

1198856

1198858

1198830 = 1198851

1198857 = 1198836

1198838

1198837

Figure 3 DEXTER DOF configuration

User interface

Supervisor

High-level controllerof the arm

High-level controllerof the hand

Low-level controllerof the arm

Low-level controllerof the hand

Actuators of the arm Actuators of the hand

HandArm

Figure 4 Functional architecture of the DEXTER manipulatorsystem

119879119899represents the analog voltage control of the generic motor

output from the PIDwith a value ranging fromminus10V to+10V119870119875 119870119863 and 119870

119868are respectively the gains proportional

derivative and integral 119864119899represents the position error

to the joints determined in each sampling instant 119878119899is

the integrated error and in particular conditions can beexpressed as 119878

119899= 119878119899minus1

+ 119864119899 119880119899and 119885

119899are the speed and the

acceleration of the feed-forward terms119870119880and119870

119885introduce

the speed and the acceleration of the feed-forward terms119870119874

is a static offset used to compensate the small variations in theoutput voltage due to the119863119860 converters or also to the offsetof the amplifiers After notifying the movement commandsto the PID the first of the 8 motors is implemented with avoltage value equal to 119879

119899 Figures 10 and 11 respectively show

(a) (b)

Figure 5 SABIAN humanoid robot

the functional architecture of the subsystem of the arm andthe functional scheme of the PID controller

Figure 12 shows the PID controller of the joint 0 Figure 13shows the solution used to bypass the PID control of the joint0

The control law used for the analysis of the position of the1ndash7 joints is given by

120591 = 119870119875 minus 119870119863 + 119892 (119902) (5)

where 120591 is the torque vector 119870119875and 119870

119863 are respectively

the proportional and derivative matrices 119892(119902) is the gravitycompensation and 119902

119889is the vector of the desired joint

position = 119902119889minus 119902 is the error The relation (5) calculates

the value of the torque 120591 but not of the speed 119889119902 Thus it

is necessary to bypass the PID control to be able to controldirectly the actuators (Figure 13)

Journal of Robotics 5

Active joint Passive joint

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

P PitchR RollY Yaw

Roll

PitchYaw119874

119885

119883

119884

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

Pitch Roll Yaw

PitchYaw119874

119885

119884

(a)

1480

119885

119883119884

(b)

Figure 6 WABIAN-2 humanoid robot

DC motor

Harmonic driveServo driver

6-axis FT sensor

Figure 7 WABIAN-2rsquos arm

From (5) we obtain

120591119898= (119870119879

119903)minus1

120591

120591119898= 119870119905119894119898

119894119898= 119866119894V119898

119894119898= 119870119905

minus1120591119898

V119898= 119866119894

minus1119894119898

(6)

where 119870119905is the diagonal matrix of motor torque constant

derived from data-sheet of the 7 motors (Table 2) 119866119894is the

gain matrix of the power drivers 119894119898and V119898are respectively

the parameters of the currents and voltages in input to thepower drivers The technical specifications of the systemimplementation of the 8 joints are shown in Tables 2 3 4and 5

The software procedure achieves a conversion of thecontrol voltage from volt (V

119898) to increments (V

119898 inc)The used relations are

= 119909119889minus 119909 (7)

and if 119889= 0

119909 = minus119869119860(119902) (8)

where 119869119860(119902) is the Jacobianmatrix which allows to rewrite (6)

in [1] as

120591 = 119869119879

119860(119902)119870119875 minus 119869119879

119860(119902)119870119863119869119860(119902) + 119892 (119902) (9)

The interaction force can be controlled in an indirectmanner by acting on the 119909

119889reference variable of the posi-

tion controller of the manipulator the interaction betweenmanipulator and the environment is directly influenced bythe characteristics of the compliance of the environment andof the manipulator The measure of the force is corrupted bynoise for which the derivative control cannot be used

In Figures 14 and 15 two examples of force controlschemes respectively with position and velocity internalclosed-loop as in [1] are shown 119872

119889is a generic diagonal

positive matrix used for the impedence controlIndicating with 119891

119889the desired constant force with 119862

119865

a diagonal matrix whose elements characterize the actions

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

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DistributedSensor Networks

International Journal of

Journal of Robotics 3

Link 7 axis 0

Link 6 axis 0

Link 5 axis 0

Link 1 axis 1

Link 3 axis 2

Link 4 axis 0

Link 2 axis 0

Link 3 axis 0

Figure 2 DEXTER robotic arm axis joints and links position

In Figures 2 and 3 the scheme of the manipulator isshown

TheDEXTERmanipulator system includes the functionalblocks of the Figure 4 The manipulation is constituted coor-dinating the joint movement of the arm with the movementof the hand mounted on the force sensor

22 SABIAN Humanoid Robot SABIAN [7 8] (Figure 5)has two 7-DOF legs a 2-DOF waist and a 2-DOF trunkEach actuator system of the joint consists of a DC motora harmonic drive gear a lug belt and two pulleys Thisdouble speed reduction mechanism allows a high reductionratio and also a joint axis to be set apart from the motoraxisThis mechanism provides designs for a human-like jointmechanism without a considerable projection Figure 5(a) isa photograph of SABIANThe height of the robot is 1480mmand the weight is 407 kg without batteries SABIAN is theItalian version of the WABIAN-2 robot [8] (see Figure 6)SABIAN does not have arms and the head is a version of theICUB head [4]

23WABIAN-2rsquos Arm Characteristics ThearmofWABIAN-2 has 7 DOFs and Figure 7 shows the 3D-CAD model Thearms were designed based on a concept that the arms of therobot can hold the robotrsquos weight while it leans on a walk-assist machine as shown in [9] Since the robot can lean on awalk-assist machine most of its weight will be distributed onboth its forearms

In general a forcetorque sensor is mounted on a robotrsquoswrist in order to enable it to grasp push or pull somethingusing a hand as an end-effector But because one of the designconcepts ofWABIAN-2 is a robot that can lean against awalk-assist machine a 6-axis forcetorque sensor is mounted oneach upper arm which enables the robot to measure externalforces acted on the forearm

In order to realize a humanoid robot with great dex-terity not only in locomotion as in WABIAN-2 but also inmanipulation as in DEXTER it is necessary to redesign theWABIAN-2rsquos arm and implement it on the SABIAN robot

24 WABIAN-2rsquos Arm Control Architecture A conventionalposition controller is used for WABIAN-2rsquos arms The six-dimensional hand trajectories are given and each joint angleis calculated by solving the inverse kinematics and the resultis the 120599

119901value as input in Figure 8 The DC motor is driven

bymotor drivers (Model no TD12770-48W05) developed byTOKUSHU DENSO Co Ltd which enables speed controlusing an electrical governor without a tachogenerator witha 100 kHz PWM The maximum output current range ofTD12770-48W05 is greater than 15A at 48V The currentmonitor port mounted on the motor drivers is utilizedin energy consumption experiments Figure 9 shows thephotograph of themotor driverThe 119909

119889is the fixed ideal value

of the hand position

3 Analysis of Control Schemes

31 DEXTER Bioinspired Robotics Arm Control ArchitectureThematrix 119870

119903of the reduction of the DEXTER robotmotion

is given by

119870119903= 1198701015840

119903119860 (1)

where 119860 is the matrix of the speed reduction related to themechanical transmission system 1198701015840

119903represents the diagonal

matrix of the reduction coefficients Consider119860

=

[[[[[[

[

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 minus4375 0 0 0 0 0

0 0 1162 minus3375 0 0 0 0

0 0 0583 0 3424 0 0 0

0 0 0483 0 minus1005 2882 0 0

0 0 0894 0 minus0638 0 minus1106 0

0 0 0894 0 minus0638 0 minus1106 minus1557

]]]]]]

]

1198701015840

119903=

[[[[[[[[[[

[

282 0 0 0 0 0 0 0

0 141 0 0 0 0 0 0

0 0 66 0 0 0 0 0

0 0 0 66 0 0 0 0

0 0 0 0 43 0 0 0

0 0 0 0 0 43 0 0

0 0 0 0 0 0 66 0

0 0 0 0 0 0 0 43

]]]]]]]]]]

]

(2)

The reduction system is constituted by redactors inproximity of each jointThe generic element119870

119903119894119895of thematrix

119870119903expresses the ratio of proportionality between the rotation

of the joint 119895 and the rotation of the rotor 119894 The relationshipbetween the torque vector of the motors to the torque vectorof the joints is given by

120591 = 119870119879

119903120591119898 (3)

This relationship allows to implement the conversionblock 120591 rarr 120591

119898and to directly move the motors The size of

119870119903matrix is 7 times 7 for the elimination of the first row and first

column relating to the joint 0 which is controlled by a PIDcontroller The standard PID controller used is expressed bythe control law

119879119899= 119870119875119864119899+ 119870119863(119864119899minus 119864119899minus1

)

+ 119870119868119878119899+ 119870119880119880119899+ 64119870

119885119885119899+ 119870119874

(4)

4 Journal of Robotics

12057911205792

1205793

12057941205795

1205796

1205797

1205798

1198831

1198832 = 1198833

1198834 = 1198835

1198850

1198852

1198853

1198854

1198855

1198856

1198858

1198830 = 1198851

1198857 = 1198836

1198838

1198837

Figure 3 DEXTER DOF configuration

User interface

Supervisor

High-level controllerof the arm

High-level controllerof the hand

Low-level controllerof the arm

Low-level controllerof the hand

Actuators of the arm Actuators of the hand

HandArm

Figure 4 Functional architecture of the DEXTER manipulatorsystem

119879119899represents the analog voltage control of the generic motor

output from the PIDwith a value ranging fromminus10V to+10V119870119875 119870119863 and 119870

119868are respectively the gains proportional

derivative and integral 119864119899represents the position error

to the joints determined in each sampling instant 119878119899is

the integrated error and in particular conditions can beexpressed as 119878

119899= 119878119899minus1

+ 119864119899 119880119899and 119885

119899are the speed and the

acceleration of the feed-forward terms119870119880and119870

119885introduce

the speed and the acceleration of the feed-forward terms119870119874

is a static offset used to compensate the small variations in theoutput voltage due to the119863119860 converters or also to the offsetof the amplifiers After notifying the movement commandsto the PID the first of the 8 motors is implemented with avoltage value equal to 119879

119899 Figures 10 and 11 respectively show

(a) (b)

Figure 5 SABIAN humanoid robot

the functional architecture of the subsystem of the arm andthe functional scheme of the PID controller

Figure 12 shows the PID controller of the joint 0 Figure 13shows the solution used to bypass the PID control of the joint0

The control law used for the analysis of the position of the1ndash7 joints is given by

120591 = 119870119875 minus 119870119863 + 119892 (119902) (5)

where 120591 is the torque vector 119870119875and 119870

119863 are respectively

the proportional and derivative matrices 119892(119902) is the gravitycompensation and 119902

119889is the vector of the desired joint

position = 119902119889minus 119902 is the error The relation (5) calculates

the value of the torque 120591 but not of the speed 119889119902 Thus it

is necessary to bypass the PID control to be able to controldirectly the actuators (Figure 13)

Journal of Robotics 5

Active joint Passive joint

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

P PitchR RollY Yaw

Roll

PitchYaw119874

119885

119883

119884

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

Pitch Roll Yaw

PitchYaw119874

119885

119884

(a)

1480

119885

119883119884

(b)

Figure 6 WABIAN-2 humanoid robot

DC motor

Harmonic driveServo driver

6-axis FT sensor

Figure 7 WABIAN-2rsquos arm

From (5) we obtain

120591119898= (119870119879

119903)minus1

120591

120591119898= 119870119905119894119898

119894119898= 119866119894V119898

119894119898= 119870119905

minus1120591119898

V119898= 119866119894

minus1119894119898

(6)

where 119870119905is the diagonal matrix of motor torque constant

derived from data-sheet of the 7 motors (Table 2) 119866119894is the

gain matrix of the power drivers 119894119898and V119898are respectively

the parameters of the currents and voltages in input to thepower drivers The technical specifications of the systemimplementation of the 8 joints are shown in Tables 2 3 4and 5

The software procedure achieves a conversion of thecontrol voltage from volt (V

119898) to increments (V

119898 inc)The used relations are

= 119909119889minus 119909 (7)

and if 119889= 0

119909 = minus119869119860(119902) (8)

where 119869119860(119902) is the Jacobianmatrix which allows to rewrite (6)

in [1] as

120591 = 119869119879

119860(119902)119870119875 minus 119869119879

119860(119902)119870119863119869119860(119902) + 119892 (119902) (9)

The interaction force can be controlled in an indirectmanner by acting on the 119909

119889reference variable of the posi-

tion controller of the manipulator the interaction betweenmanipulator and the environment is directly influenced bythe characteristics of the compliance of the environment andof the manipulator The measure of the force is corrupted bynoise for which the derivative control cannot be used

In Figures 14 and 15 two examples of force controlschemes respectively with position and velocity internalclosed-loop as in [1] are shown 119872

119889is a generic diagonal

positive matrix used for the impedence controlIndicating with 119891

119889the desired constant force with 119862

119865

a diagonal matrix whose elements characterize the actions

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

4 Journal of Robotics

12057911205792

1205793

12057941205795

1205796

1205797

1205798

1198831

1198832 = 1198833

1198834 = 1198835

1198850

1198852

1198853

1198854

1198855

1198856

1198858

1198830 = 1198851

1198857 = 1198836

1198838

1198837

Figure 3 DEXTER DOF configuration

User interface

Supervisor

High-level controllerof the arm

High-level controllerof the hand

Low-level controllerof the arm

Low-level controllerof the hand

Actuators of the arm Actuators of the hand

HandArm

Figure 4 Functional architecture of the DEXTER manipulatorsystem

119879119899represents the analog voltage control of the generic motor

output from the PIDwith a value ranging fromminus10V to+10V119870119875 119870119863 and 119870

119868are respectively the gains proportional

derivative and integral 119864119899represents the position error

to the joints determined in each sampling instant 119878119899is

the integrated error and in particular conditions can beexpressed as 119878

119899= 119878119899minus1

+ 119864119899 119880119899and 119885

119899are the speed and the

acceleration of the feed-forward terms119870119880and119870

119885introduce

the speed and the acceleration of the feed-forward terms119870119874

is a static offset used to compensate the small variations in theoutput voltage due to the119863119860 converters or also to the offsetof the amplifiers After notifying the movement commandsto the PID the first of the 8 motors is implemented with avoltage value equal to 119879

119899 Figures 10 and 11 respectively show

(a) (b)

Figure 5 SABIAN humanoid robot

the functional architecture of the subsystem of the arm andthe functional scheme of the PID controller

Figure 12 shows the PID controller of the joint 0 Figure 13shows the solution used to bypass the PID control of the joint0

The control law used for the analysis of the position of the1ndash7 joints is given by

120591 = 119870119875 minus 119870119863 + 119892 (119902) (5)

where 120591 is the torque vector 119870119875and 119870

119863 are respectively

the proportional and derivative matrices 119892(119902) is the gravitycompensation and 119902

119889is the vector of the desired joint

position = 119902119889minus 119902 is the error The relation (5) calculates

the value of the torque 120591 but not of the speed 119889119902 Thus it

is necessary to bypass the PID control to be able to controldirectly the actuators (Figure 13)

Journal of Robotics 5

Active joint Passive joint

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

P PitchR RollY Yaw

Roll

PitchYaw119874

119885

119883

119884

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

Pitch Roll Yaw

PitchYaw119874

119885

119884

(a)

1480

119885

119883119884

(b)

Figure 6 WABIAN-2 humanoid robot

DC motor

Harmonic driveServo driver

6-axis FT sensor

Figure 7 WABIAN-2rsquos arm

From (5) we obtain

120591119898= (119870119879

119903)minus1

120591

120591119898= 119870119905119894119898

119894119898= 119866119894V119898

119894119898= 119870119905

minus1120591119898

V119898= 119866119894

minus1119894119898

(6)

where 119870119905is the diagonal matrix of motor torque constant

derived from data-sheet of the 7 motors (Table 2) 119866119894is the

gain matrix of the power drivers 119894119898and V119898are respectively

the parameters of the currents and voltages in input to thepower drivers The technical specifications of the systemimplementation of the 8 joints are shown in Tables 2 3 4and 5

The software procedure achieves a conversion of thecontrol voltage from volt (V

119898) to increments (V

119898 inc)The used relations are

= 119909119889minus 119909 (7)

and if 119889= 0

119909 = minus119869119860(119902) (8)

where 119869119860(119902) is the Jacobianmatrix which allows to rewrite (6)

in [1] as

120591 = 119869119879

119860(119902)119870119875 minus 119869119879

119860(119902)119870119863119869119860(119902) + 119892 (119902) (9)

The interaction force can be controlled in an indirectmanner by acting on the 119909

119889reference variable of the posi-

tion controller of the manipulator the interaction betweenmanipulator and the environment is directly influenced bythe characteristics of the compliance of the environment andof the manipulator The measure of the force is corrupted bynoise for which the derivative control cannot be used

In Figures 14 and 15 two examples of force controlschemes respectively with position and velocity internalclosed-loop as in [1] are shown 119872

119889is a generic diagonal

positive matrix used for the impedence controlIndicating with 119891

119889the desired constant force with 119862

119865

a diagonal matrix whose elements characterize the actions

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Robotics 5

Active joint Passive joint

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

P PitchR RollY Yaw

Roll

PitchYaw119874

119885

119883

119884

Neck

Shoulder

Elbow

Wrist

Waist

Hand Hip

Knee

Ankle

Trunk

Pitch Roll Yaw

PitchYaw119874

119885

119884

(a)

1480

119885

119883119884

(b)

Figure 6 WABIAN-2 humanoid robot

DC motor

Harmonic driveServo driver

6-axis FT sensor

Figure 7 WABIAN-2rsquos arm

From (5) we obtain

120591119898= (119870119879

119903)minus1

120591

120591119898= 119870119905119894119898

119894119898= 119866119894V119898

119894119898= 119870119905

minus1120591119898

V119898= 119866119894

minus1119894119898

(6)

where 119870119905is the diagonal matrix of motor torque constant

derived from data-sheet of the 7 motors (Table 2) 119866119894is the

gain matrix of the power drivers 119894119898and V119898are respectively

the parameters of the currents and voltages in input to thepower drivers The technical specifications of the systemimplementation of the 8 joints are shown in Tables 2 3 4and 5

The software procedure achieves a conversion of thecontrol voltage from volt (V

119898) to increments (V

119898 inc)The used relations are

= 119909119889minus 119909 (7)

and if 119889= 0

119909 = minus119869119860(119902) (8)

where 119869119860(119902) is the Jacobianmatrix which allows to rewrite (6)

in [1] as

120591 = 119869119879

119860(119902)119870119875 minus 119869119879

119860(119902)119870119863119869119860(119902) + 119892 (119902) (9)

The interaction force can be controlled in an indirectmanner by acting on the 119909

119889reference variable of the posi-

tion controller of the manipulator the interaction betweenmanipulator and the environment is directly influenced bythe characteristics of the compliance of the environment andof the manipulator The measure of the force is corrupted bynoise for which the derivative control cannot be used

In Figures 14 and 15 two examples of force controlschemes respectively with position and velocity internalclosed-loop as in [1] are shown 119872

119889is a generic diagonal

positive matrix used for the impedence controlIndicating with 119891

119889the desired constant force with 119862

119865

a diagonal matrix whose elements characterize the actions

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 Journal of Robotics

Position control

+

+ +minus

minus

minus

minus

Motor + servo driver

1119904 119909119889120579119901

1]+ 119904119879119891

1119877119886 + 119904119871119886

1119863 + 119904119869119898

119870119875 + 119904119870119863

119860

119861

119870119905

119870119890

119870119892

Figure 8 Position control scheme for WABIAN-2rsquos arm

Figure 9 Servo driver used for WABIAN-2rsquos arm (TD12770-48W05)

Compliance control

Actuators of the arm

Arm

120591

120591 rarr 120591119898

120591119898

Figure 10 Functional architecture of the subsystem of the arm

of control to exert along the directions of interest of theoperative space with 119909

119890the equilibrium position of the not

deformed environment with 119870119860the stiffness matrix of the

environment and with 119909119865a reference that should then be

put in relation with an error of force we have the followingrelationships as in [1]

119909119865= 119862119865(119891119889minus 119891)

= 119891119889minus 119891

(10)

The difference between the desired force and the forceactually developed by the manipulator gives the errorFigure 14 shows that if119862

119865is proportional119891 cannot be similar

to 119891119889because 119909

119890modifies the interaction force if 119862

119865also

expresses an integral action on the force components it ispossible to obtain 119891 = 119891

119889and at the same time to limit

the influence of 119909119890on 119891 Therefore an action proportional-

integral (PI) can be chosen for 119862119865

In Figure 16 an example is shown (as in [1]) of a force-position control It is a modification of Figure 14 with 119909

119889used

in input to the position loop

32 Force Controllers Two force-control schemes were con-structed as external closed-loop a first system in which theforce exerts a proportional-integral (PI System) controller(Figure 17) and a second system inwhich action developed bythe controller is a proportional type (System P) (Figure 18)

321 PI System Force Controller The block diagram of thissystem is shown in Figure 17 The action exerted by the forcecontroller is proportional-integral (PI) For controlling theposition of the joints the law (5) has been used

For the force control the following law was used

119883119865= 119870119865 + 119870

119868int 119889119905 (11)

The position transducer provides an electrical signalproportional to the angular displacement of link carriedby the robot The force sensor is used as the connectingmember to the wrist between the last arm of DEXTER andthe End-Effector Through the use of the exteroceptive andproprioceptive sensors it is possible to obtain the measuredvalues of 119902 and 119891 Using the control law of force (11) 119883

119865is

obtained which allows to obtain in output the error in the

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Robotics 7

Controller

Memory

AD

8254

8254 Encoder

8 channels12 bit

Timer3ndash16 bit

IO

CPU

Input signals

1199020119894 1199020119891

PID Output signal(analogic)

Busdata

Figure 11 Functional scheme of the PID controller

C code PID Actuator Robot

Encoder

11990201199020119894

1199020119891119879119899119889119902[0]

Figure 12 Joint 0

C code PID Actuators Robot

Encoder

119902119907119898

119907119898120591 119904119908ℎ119908

119889119902

Figure 13 Joints 1ndash7

operational spaceΔ119883The joints error is obtained bymeansof inverse kinematics and the vector of torque to be suppliedto the actuators is obtained by using the law for the positioncontrol

322 P System Force Controller In this scheme (Figure 18)the force controller exerts a proportional (P) action As for thePI system the law (5) is used for the position control whilefor the force control the following has been used

119865= 119870119868 (12)

In contrast to the scheme of Figure 17 this secondsystem allows to derive the joints position error through

119891119889+ +

minus minus

+ +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889119870119875

Figure 14 Classical force controller with internal position closed-loop [1]

119891119889+

minus minus

+ + minus119870119865

119870119863

int int 119870119860 119891

119909119890

119872minus1119889

119870119875

Figure 15 Classical force controller with internal velocity closed-loop [1]

considerations on the speed and not on the positions in theoperational space

In the P system a single block of inverse kinematics ispresent and this helps to reduce errors that can arise as a resultof transformation from work space to the joints space

4 Analysis of Experimental Data

The behaviour of the two control systems of Figures 17and 18 was simulated using MatlabSimulink software InFigure 19(a) simulation of the PI System implemented in aplanar representation of the DEXTER arm (3 DOF) and withand without an obstacle is shown

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

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Active and Passive Electronic Components

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RotatingMachinery

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Journal ofEngineeringVolume 2014

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VLSI Design

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Shock and Vibration

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Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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DistributedSensor Networks

International Journal of

8 Journal of Robotics

119891119889+ +

minus minus

+ + +

minus

minus119862119865

119870119863

int int 119870119860 119891

119909119890119909119889

119872minus1119889119870119875

Figure 16 Classical force-position control scheme [1]

Table 6 Reference values of the PI System

119870119865

119870119868

119870119875

119870119863

119870119860

00005 008 106 6000 1000

Five gains (119870119865 119870119875 119870119868 119870119863 and 119870

119860) were established as

inputs to the simulation models The simulation graphs areshown from Figure 20 to Figure 27 In particular the force(N) value and the error position (m) value of the End-Effectorof the DEXTER are presented For each 119870 gain a maximuma minimum or an intermediate value has been assigned inorder to evaluate the behaviour of the system varying119870 gainsIn Tables 6 and 7 the reference 119870 values for the PI and Psystems are presented The reference 119870 values are referred tothe DEXTER robot during its movements

41 PI System Force Controller Figure 17 represents the blockdiagram of a forceposition control system that uses aproportional-integrative (PI) and a proportional-derivative(PD) controller respectively to measure the force and theposition of the End-Effector

Considering Figure 20 and varying119870119865 the measured (or

real) force presents a peak value of 15N while the ideal (ordesired) force has a value of 10N With the advancement ofthe simulation after a time of 2000ms the measured forceoscillates around the value of the ideal force

Bringing the value of 119870119865ranging from 00005 to 0005 a

smaller difference between the measured and the ideal forceis obtained with a consequent reduction of the amplitudesof oscillation after the 2000ms There are no substantialdifferences in the trends of the position and position errorof the End-Effector varying 119870

119865

Figure 21 is made to vary only 119870119868maintaining the other

values of Table 6 Decreasing this parameter from 008(Figure 20(a)) to 004 (Figure 21(a)) the difference betweenthe measured and ideal impulse force increases goes overthe threshold of 18N Assigning to 119870

119868a value equal to

012 (Figure 21(b)) the value of the difference between themeasured and the ideal force is no more than 35N

Decreasing the value of 119870119875 from 106 (Figure 20(a)) to

250000 (Figure 22(a)) a higher peak pulse is created Varying119870119875value from 106 (Figure 20(a)) to 107 (Figure 22(b)) the

maximum value of the measured force decreasesFigure 23 shows the trends of the error position

Analysing the graphs it is noted that the increase of 119870119875

decreases the error Differences in force position and posi-tion error were not noted in PI system varying 119870

119863gain

Table 7 Reference values of the P system

119870119875

119870119868

119870119863

119870119860

106 005 6000 1000

42 P System Force Controller Figure 18 represents the blockdiagram of a forceposition control system that uses a pro-portional (P) and a proportional-derivative (PD) controllerrespectively tomeasure the force and the position of the End-Effector

Using values of Table 7 and decreasing the value of 119870119868

from 005 to 002 an increment of the force in Figure 24is shown The measured force value is equal to 26N(Figure 24(a)) If 119870

119868is equal to the 008 value (Figure 24(c))

the peak of the measured force in the P system decreases as itwas decreased in the PI system

Figure 25 shows the measured and the ideal force of theEnd-Effector of the P system varying 119870

119875 If the 119870

119875value

decreases from 106 (Figure 24(b)) to 250000 (Figure 25(a))the measured peak value will be equal to 20N

As for the PI System in the P System the position errordecreases if 119870

119875is equal to 107 and the simulation graphs are

similar to the graphs of Figure 23A comparison between the simulation graphs of the two

systems (PI and P) (Figures from 20 to 25) shows that in theP system the peak value of the measured force is bigger withrespect to the other one

43 Comparison between PI and P Systems The EnvironmentInteraction In the last section graphs were obtained fromthe simulation of the two systems by changing119870

119865119870119875119870119868 and

119870119863gains In this section the behaviour of the two controllers

will be analysed by varying only the stiffness matrix value(119870119860)The authors considered 119870

119860as the environment stiffness

matrix and by increasing or decreasing its value it is possibleto modify the compliance of all external part of the armIncreasing the value of 119870

119860allows the manipulator to reach a

given position thus the arm encounters an obstacle that maynot physically exist but in reality exerts a contact force whichopposes the motion of the robotic arm and causes its arrest

In the graphs of Figures 26 and 27 the force the positionand the error position values respectively of the PI and Psystems are presented

Increasing the119870119860value from 1000 (Figure 20(a)) to 10000

(Figure 26(a)) a high pulse of force was generated as shownin Figure 26 When the manipulator is working in a higherstiffness environment the pulse of force that the End-Effectornotes is naturally higher

An increment of the real force from 18N (Figure 24(b))to 24N (Figure 27(a)) is noted in Figure 27(a) assuming a119870

119860

value equal to 5000The differences between the PI and P Systems are evident

by a comparison of Figures 26(a) and 27(a) In particularin Figure 26(a) the peak of the measured force is equal to18N but nomore oscillations were observed In Figure 27(a)the peak of the measured force is 24N and the forcevalue is variable before the 2000ms A comparison of these

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Robotics 9

minus minus minus

++

++

+119891119889

int

int

119891

119870119865

119892(119902)

119889119889119905 119870119863

11987917

119902

Encoder

Force sensor

DEXTERDA119869minus1 119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 17 PI System

minus minus minus

++

+ + +

+119891119889 int

119891119892(119902)

119889119889119905 119870119863119902

Encoder

DEXTER119869minus1

Force sensor

DA119870119875

119891inc minus 119891

119870119868

119902inc minus 119902

119879 minus 119881inc

Figure 18 P System

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(a)

2

18

16

14

12

1

08

06

04

02

00 05 1 15 2 25

119883-axis

119884-axis

(b)

Figure 19 Simulation of the PI System in a planar representation of the DEXTER arm (3DOF) with (a) and without (b) an obstacle 119909 = 186119910 = 15 is the initial position of the End-Effector 119909 = 235 119910 = 18 is the final position of the End-Effector 119909 = 22 is the position of theobstacle

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Robotics

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0001= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 0005= 008

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(c)

Figure 20 End-Effector force value (N) varying the 119870119865gain in the PI system (a)119870

119865= 00005 (b)119870

119865= 0001 (c) 119870

119865= 0005

20

18

16

14

12

10

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 004

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

Measured force

Ideal force

119891(N

)

119905 (ms)

119870119865119909 = 00005= 012

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119870119868119909

(b)

Figure 21 End-Effector force value (N) varying the 119870119868gain in the PI system (a)119870

119868= 004 (b)119870

119868= 012

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Robotics 11

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(a)

18

17

16

15

14

13

12

11

10

9

8500 1000 1500 2000 2500 3000 3500 4000

119891(N

)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

Measured force

Ideal force

119870119868119909

(b)

Figure 22 End-Effector force value (N) varying the 119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(a)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 = 107

119870119863119909 = 119870119863119910 = 6000119870119860119909 = 1000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

0

0 500 1000 1500 2000 2500 3000 3500 4000

119870119868119909

(b)

Figure 23 End-Effector error position value (m) varying the119870119875gain in the PI system (a)119870

119875= 250000 (b) 119870

119875= 107

graphs indicates that the P system is more influenced by theenvironment (varying 119870

119860) with respect to the PI system By

means of the analysis of Figures 26(b) 26(c) 27(b) and 27(c)it was noted that the increase or decrease of the 119870

119860value

influences only the trends of the force and not the positionof the End-Effector of the manipulator

5 Conclusions and Future Developments

In this paper the authors propose a comparison betweentwo force-position control systems with gravity compen-sation designed for an eight-DOF bioinspired roboticarm named DEXTER The two position controllers areboth proportional-derivative (PD) the two force controllersare one proportional (P system) and one proportional-integrative (PI system)

The simulation tests performed with the two systems ona planar representation of the DEXTER (3-DOF arm in theplane) show that by varying the stiffness of the environmentwith a correct setting of parameters both systems ensurethe achievement of the desired force regime and with greatprecision the desired position The two controllers do nothave large differences in performance when interacting witha lower stiffness environment In case of an environment withgreater rigidity the PI system is more stable

The next step of this work will be the implementationof these systems into the DEXTER robotics arm with theultimate aim of control and design of the two arms of thehumanoid robot SABIAN

In this paper the authors explained the differencesbetween the proposed method and other studies The pro-posed approach is oriented to execute a softwaremodificationof the compliance in humanoid robotics in opposition to

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Robotics

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

30

28

26

24

22

20

18

16

14

12

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119868119909 = 002

(a)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(b)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 008119870119868119909

(c)

Figure 24 End-Effector force value (N) varying the 119870119868gain in the P system (a) 119870

119868= 002 (b)119870

119868= 005 (c) 119870

119868= 008

119870119875119909 = 119870119875119910 = 250000119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005119870119868

(a)

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 1000

22

20

18

16

14

12

10

8Ideal force

Measured force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

= 005

119870119875119909 = 119870119875119910 = 107

119870119868

(b)

Figure 25 End-Effector force value (N) varying the119870119875gain in the P system (a) 119870

119875= 250000 (b) 119870

119875= 107

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Robotics 13

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

18

15

16

17

14

12

11

13

10

9

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119865119909 = 00005119870119868119909 = 008

(a)

119870119875119909 = 119870119875119910 = 106119870119863119909 = 119870119863119910 = 6000

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119870119865119909 = 00005

119884(m

)

119883 (m)

119870119860119909 = 10000

119870119868119909 = 008

(b)

119905 (ms)

119870119865119909 = 00005= 008

119870119875119909 = 119870119875119910 =119870119863119909 = 119870119863119910 = 6000119870119860119909 = 10000

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500 4000

106119870119868119909

(c)

Figure 26 Force (N) position (m) and error position (m) of PIsystem assuming that 119870

119860= 10000

24

18

20

22

16

12

14

10

8

Measured force

Ideal force

500 1000 1500 2000 2500 3000 3500 4000119905 (ms)

119891(N

)

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(a)

2

185

19

195

18

17

165

175

16

155

15

Measured trajectory

Ideal trajectory

18 19 2 21 22 23 24 25

119884(m

)

119883 (m)

Measured trajectory

Ideal trajecj

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000119870119868119909 = 005

(b)

119905 (ms)

119890 119909119890

119910(m

)

119890119909

119890119910

02

018

016

014

012

01

008

006

004

002

00 500 1000 1500 2000 2500 3000 3500

119890119910

4000

119870119875119909 = 119870119875119910 = 106

119870119863119909 = 119870119863119910 = 6000

119870119860119909 = 5000= 005119870119868

(c)

Figure 27 Force (N) position (m) and error position (m) of Psystem assuming that 119870

119860= 5000

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Journal of Robotics

the hardware modification of the compliance developed byother studies On the other hand a comparison between twoforce-position controllers could be used by the science andtechnology community

Acknowledgments

This research was conducted at the RobotAn Lab in theBioRobotics Institute of the Scuola Superiore SantrsquoAnna andwas partly supported by the Italian Ministry of ForeignAffairs supporting the RobotAn and the RoboCasa joint labsof the Scuola Superiore SantrsquoAnna and Waseda Universityas well as by the European Commission in the ICT STREPRoboSoM Project (Contract no 248366)

References

[1] L Sciavicco and B Siciliano Modelling and Control of RobotManipulators Springer London UK 2nd edition 2000

[2] L Zollo B Siciliano E Guglielmelli and P Dario ldquoA bio-inspired approach for regulating visco-elastic properties of arobot armrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation pp 3576ndash3581 Taipei TaiwanSeptember 2003

[3] G Tonietti R Schiavi and A Bicchi ldquoDesign and controlof a variable stiffness actuator for safe and fast physicalhumanrobot interactionrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 526ndash531Barcelona Spain April 2005

[4] N G Tsagarakis M Laffranchi B Vanderborght and D GCaldwell ldquoA compact soft actuator unit for small scale humanfriendly robotsrdquo in IEEE International Conference on Roboticsand Automation Kobe International Conference Center KobeJapan May 2009

[5] D G Caldwell G A Medrano-Cerda and M GoodwinldquoControl of pneumatic muscle actuatorsrdquo IEEE Control SystemsMagazine vol 15 no 1 pp 40ndash48 1995

[6] L Zollo B Siciliano A De Luca and E Guglielmelli ldquoPD con-trol with online gravity compensation for robots with flexiblelinksrdquo in Proceedings of the European Control Conference KosGreece July 2007

[7] G G Muscolo C T Recchiuto K Hashimoto C Laschi PDario and A Takanishi ldquoA method for the calculation of theeffective Center of Mass of humanoid robotsrdquo in Proceedingsof the 11th IEEE-RAS International Conference on HumanoidRobots (Humanoids rsquo11) pp 371ndash376 Bled Slovenia October2011

[8] G G Muscolo C T Recchiuto K Hashimoto P Dario and ATakanishi ldquoTowards an improvement of the SABIANhumanoidrobot from design to optimisationrdquo Journal of MechanicalEngineering and Automation Scientific amp Academic Publishingvol 2 no 4 pp 80ndash84 2012

[9] Y Ogura H Aikawa K Shimomura et al ldquoDevelopment of ahumanoid robot capable of leaning on awalk-assistmachinerdquo inProceedings of the 1st IEEERAS-EMBS International Conferenceon Biomedical Robotics and Biomechatronics (BioRob rsquo06) pp835ndash840 Pisa Italy February 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of