A NEW TRUCK PROTOTYPE FOR TRANSPORTINGFLEXIBLE MANIPULATORS

Daniel Feliu-Talegon(1), Juan Carlos Cambera(1), Andres San-Millan(2), Vicente Feliu-Batlle(3)1 Instituto de Investigaciones Energeticas y Aplicaciones Industriales, University of Castilla-La Mancha.

2 Institute of Mechanical Engineering, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland.3 Escuela Tecnica Superior de Ingenieros Industriales, University of Castilla-La Mancha.

Emails: JuanCarlos.Cambera@alu.uclm.es, Daniel.Feliu@uclm.es, andres.sanmillanrodriguez@epfl.ch, Vicente.Feliu@uclm.es.

Abstract

This work is concerned with the mechanical design

and the description of the different components of

a novel mobile base for a flexible mobile manipu-

lator. A flexible mobile manipulator is normally

composed of multiple flexible links mounted on a

mobile platform. This work is focused on the de-

scription of the mobile platform. The mobile plat-

form of this work has two different configurations

in order to carry out different tasks. Also, some

hypothesis and experimental results are shown in

this work as a first step to be able to obtain a kine-

matic model of the system later.

Keywords: Kinematic model, orientation, pos-ture, linear actuators, DC motors, identification.

1 INTRODUCTION

Compared to conventional robots, flexible linkmanipulators have the advantages of lower cost,larger work volume (they have longer links),higher operational speed, greater payload-to-manipulator-weight ratio, smaller actuators, lowerenergy consumption, better maneuverability, bet-ter transportability and safer operation due to re-duced inertia. For these numerous advantages,extensive use of flexible manipulators in variousrobotic applications has made it as one of theresearch interests for many researchers over theworld over the last few decades. Because energyconsumption in motors is directly proportional tothe mass and size of robot elements, long and lightrobot links are commonly used but which have adeformation that cannot be ignored. Some reviewsof flexible robots can be found in [1] and [3].

There are many existing applications that take ad-vantages of using lightweight links: in interven-tion robots, for hazardous waste cleanup, bombdisposal and refighting, maintenance of danger-ous things (e.g hot electric power lines), miningrobots, etc. Many of these applications use a mo-bile platform in order to transport the flexible ma-nipulators.

Mobile manipulators have recently received con-

siderable attention and a wide range of applica-tions have been explored. In most cases, a mobilerobot needs some manipulation capability in or-der to be useful. For that reason, manipulatorsare mounted on mobile platforms.

These manipulators have usually power on boardwith limited energy due to the difficulty to storea great amount of energy in batteries. In thisway, they reasonably make necessary the incor-poration of light links in order to decrease the en-ergy consumption. Another important advantageof using flexible manipulators is that due to theirlightweight features, longer links can be designedin order to extend the workspace of the manipula-tors allowing them to reach targets that were, ini-tially, outside of the manipulator workspace. Anextensive literature survey on mobile manipulatorsystem can be found in [2] .

However the greatest disadvantage of these ma-nipulators is the vibration problem due to lowstiffness. This disadvantage makes very difficultthe description of dynamics models and the de-sign of control laws. Nevertheless, the importanceand usefulness of these systems have engaged re-searchers worldwide in the investigation of thesekind of systems. However, among different worksthat are carried out for mobile robotic arms, veryfew researches are dealt with the problem of mod-eling and control of mobile flexible manipulators(see [5] and [4]).

In this work, a new mechanical device able totransport a flexible robot, is presented. Its mainfeatures are: a) transport the flexible robot; b) in-crease the stability of the system when it reachesa specific target.

This article is organized as follows. Section 2 de-scribes the mechanical design and the componentsof the system presented in this work. A controlscheme for the linear actuators of the system isdescribed in Section 3. Some experimental resultsare shown in Section 4. Finally some conclusionson the results are presented in Section 5.

Actas de las XXXIX Jornadas de Automática, Badajoz, 5-7 de Septiembre de 2018

356

2 MECHANICAL DESIGN

The system presented in this work is consideredto be the mobile base of a flexible mobile manipu-lator. The platform consists of a rectangular basewith four legs and four wheels (see Figure 1). Thesystem described in this work is based in two dif-ferent configurations in order to carry out two dif-ferent tasks. The first configuration is when thesystem has the legs up and they are not in contactwith the ground. In this configuration, the legs arenot used and the system is used to transport theflexible manipulator from one place to another.The second configuration is when the system hasthe legs in contact with the field and in this casethe wheels are not used. In this case, the systemis used to control the orientation and the postureof the base of the flexible manipulator. Anotherfunction of this second configuration, is to increasethe static stability of the system because when themobile base reaches a particular target, the flex-ible manipulator which is on the mobile base isgoing to start moving.

c2l lc1c3l

Figure 1: Front view of the experimental platform.

Therefore, the legs provide a solid base for thesystem. Their purpose is to improve the stabilityof the system during the operation of the flexiblemanipulator which is on the mobile base. Theyprovide a solid platform for the flexible manipula-tor safe operation and efficient use. If the flexiblemanipulator has to be used, it is important to fullyextend all of the legs and get the tires of the wheelsoff the ground.

The wheels do not offer the stability needed for thesystem, so the system needs the legs to prevent thesystem from leaning too much to one side or theother, or even overturn. This is the main purposeof adding four legs to our mobile platform. In thelast decades, mobile cranes have used similar ap-proaches in order to improve their stability. Theyuse support devices called outriggers (see Figure2). The outriggers normally use hydraulics to liftthe entire crane, whereas our prototype uses linearactuator inside a mechanism that can be consid-ered a four-link mechanism. The outriggers are

only one mechanism used to balance the craneduring lifting operations The legs prevent the sys-tem from tipping forward and backward duringoperation.

Outriggers

Figure 2: Mobile Crane. (image extractedfrom: http://www.arnold.af.mil/News/Article-Display/Article/1192160/new-crane-purchased-to-support-national-defense-mission/)

Each leg is actuated by a linear actuator whichhas the function to change the configuration ofthe system. Looking at Figure 3, we can see thatmodifying the extension of the linear actuator, thedistance between the support point of the leg, PD,and the point which joins the leg and the base ofthe truck, PE , changes.

4l

l5

l 2

l6

l 7

l3

PD

PE

Linear actuator

Figure 3: Scheme of a leg of the system.

In the Figure 3, it can be seen that each leg is afour-bar linkage which consists of four rigid barsin the plane connected by revolute joints. For an-alytical purposes, four bar linkages are treated asplanar mechanisms. However, in practice, imple-mentation of a four bar linkage could be spatial(non-planar). The four-bar linkage is the simplestand, often, the most useful mechanism. A varietyof useful mechanisms can be formed from a four-link mechanism through slight variations, such aschanging the character of the pairs, proportionsof links, etc. As it was mentioned previously, the

357

objective of the four-bar linkage used in this workis to be able to modify the difference of height be-tween PD and PE modifying the length of the lin-ear actuator which is located in the middle of thefour-bar system. Therefore, combining the move-ment of the four legs, we are able to modify theheight and the posture (orientation) of the base ofthe system.

Figures 1 and 4 depict different views of the sys-tem and the rest of variables which define the fea-tures of the system. The values of these variablescan be seen in Table 1.

lc1

lc2

β

Figure 4: Top view of the experimental platform.

The parameters of the systems are:

Table 1: Parameters of the system

Parameters Value

lc1 400 mmlc2 170 mmlc3 113 mml2, l3 80 mml4, l5 440 mml6 165 mml7 205 mmα 61 ◦

β 49 ◦

2.1 COMPONENTS OF THE SYSTEM

This section describes the components of the sys-tem:

One real-time high-performance embeddedcontroller: it is an advanced reconfigurable con-trol and acquisition system. it includes a reconfig-

urable Field Programmable Gate Array (FPGA)chassis and it runs Labview Real-Time for controland analysis.

One Module I/O Digitals (NI-9403 ): Thismodule is used to acquire the signal from the ac-celerometer, the encoders of the linear actuatorsand the twelve limit switches.

One Module Voltage (NI-9264 ): This moduleis used to send the control voltage signal to the twomotor drivers in order to control the voltage in thelinear actuators.

Four linear actuators: Linear actuators areelectric devices able to convert rotational motionof a DC motor into linear pull/push movements.The actuators con50(14) are versatile, high effi-ciency, 12/24V DC industrial motors with plan-etary gears with small overall dimensions and avery high relation of reduction gear. They aremade of powder-coated steel, providing a sturdydesign that protects the motor and electric cir-cuits. They are used to control the extension ofthe legs of the system (see Figure 3).

Two motor drivers: The Sabertooth 2x25 V2are very versatile, efficient and easy to use dualmotor drivers. The Sabertooth can supply twoDC brushed motors with up to 25A each one. Inour platform, each Sabertooth allows us to controltwo linear actuators with analog voltage, indepen-dently. Therefore, they will be used to control theposition and the direction of the linear actuators.

Four linear actuator encoders: Each linearactuator has an encoder which measures the dis-placement of the linear actuators of the system.These sensors allow us to control the position andthe speed of the linear actuators.

Four Maxon DC motors set: Each set is com-posed of Maxon DC motor which are high-qualitymotors fitted with powerful permanent magnets.Planetary reduction gears (n = 26) and incremen-tal high precision encoders with high signal res-olution are mounted exclusively on motors withthrough shafts for resonance reasons. They areused to control the rotational movement of thewheels of the system.

Four Positioning controllers (EPOS2 24/5):They are small-sized smart motion controllers.Due to the flexible and high efficient power stage,the EPOS 24/5 drives brushed DC motors withdigital encoder as well as brushless EC motorswith digital Hall sensors and encoders. They inte-grate position, velocity and current controls whichallow the user to develop sophisticated positioningapplications. Each of these controllers is used tomove one of the Maxon DC motors.

358

Twelve limit switches: These switches includeelectrical contacts with which to energize and de-energize a circuit. Four switches are located in or-der to detect the maximum extension of each legand the other four switches are located in order todetect the maximum shrinkage of each leg. Theseeight switches are used in order to avoid the dam-age of the system when it surpasses its mechanicallimits. Apart from that, the system has other fourswitches in order to detect when the leg is in con-tact with the field. This will be very important atthe time the stabilization process is used.

One inertial sensor: The sensor is calledADIS16448 and it is a complete inertial systemthat includes a triaxial gyroscope, a triaxial ac-celerometer and a triaxial magnetometer. Thesensor has been placed in the central part of thebase of the truck in order to measure the orienta-tion of the base of the platform.

NI cRIO-9076

NI-9403NI-9264

2 motor drivers

4 linear actuators 4 maxon DC motor sets

Inertial sensor

4 positioning controllers

Figure 5: Components of the platform.

3 CONTROL OF THE LINEAR

ACTUATORS

The definition of a mathematical model when thelegs are in contact with the ground is of utmost im-portance in order to obtain advanced controllersthat improve the control of the orientation andthe posture of the base of the truck. The idea isto develop a simplified model based on a kinematicmodel of the system that relates the extension ofthe linear actuator with the orientation and pos-ture of the system. This can be justified becausethe prototype when the legs are in contact withthe ground moves at a slow speed. Therefore, theaccelerations of the whole system are very small in

the stabilization phase which implies that inertialforces are very small in comparison with gravityforces. As a first step to develop the kinematicmodel of the system, we have to design controllersto control the extension of the linear actuators.

3.1 LINEAR ACTUATOR DYNAMICS

The dynamic model of a typical DC motor is avery well known second-order equation. As it wasexplained previously, a linear actuator is a de-vice that converts the rotational movement of aDC motor into linear movements. Therefore, theequation that describes the dynamics of a linearactuator can be expressed as:

Γ = KmV = Jlx+ νlx+ Γnlc , (1)

where Γ is the motor torque and it is assumed tobe proportional to the control voltage signal V ,Km is the constant that relates the motor torqueswith the control voltages, Jl and νl are the equiva-lent inertia and the viscous friction of the system,Γnlc is the Coulomb friction of the motor and x

is the linear position of the system. Therefore,the transfer function of the system considering theCoulomb Friction as a disturbance that will becanceled for the controller can be expressed as:

x

V=

Km

Jl

s(s+ νl

Jl

), (2)

3.2 IDENTIFICATION OF THESYSTEM

The identification process of the dynamics of thelinear actuators was done for two different cases:a) when the leg is not in contact with the ground,therefore, the system does not have to move anyload and b) when the system is in contact with theground and it has the load of the mobile platformdistributed among the four legs. In each case, tensteps with different amplitudes were used as inputto the system. In Figures 6 and 7, the appliedvoltage of the system and the extension of the lin-ear actuator are shown, respectively, for the casea). In Figures 8 and 9, the applied voltage of thesystem and the position of the linear actuator areshown, respectively, for the case b).

359

0 10 20 30 40 50 60 70 80 90 100

Time (s)

-3

-2

-1

0

1

2

3

Re

fere

nce

(V

)

1

2

3

4

5

6

7

8

9

10

Figure 6: Applied voltage in case a).

0 10 20 30 40 50 60 70 80 90 100

Time (s)

-0.08

-0.06

-0.04

-0.02

0

x (

mm

)

Figure 7: Extension of the linear actuator in casea)

0 10 20 30 40 50 60

Time (s)

-3

-2

-1

0

1

2

3

Re

fere

nce

(V

)

1

2

3

4

5

6

7

8

9

10

Figure 8: Applied voltage in case b).

0 10 20 30 40 50 60

Time (s)

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

x (

mm

)

Figure 9: Extension of the linear actuator in caseb)

From the previous figures, it can be concluded thatthe transfer function that relates the control sig-nal (V ) and the linear position of the actuator (x)for both cases, can be approximated by the ex-pression:

G(s) =x(s)

V (s)=K

s; (3)

It can be noticed that equation (2) tends to equa-tion (3) if νl

Jl

is much higher than 1.

In Figure 10, the relation between the control sig-nal and the velocity of the system can be shownfor both cases.

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Reference (V)

-0.04

-0.02

0

0.02

0.04

0.06

v (

mm

/s)

Without load

With load

Figure 10: Relation between the control signal andthe velocity.

The constant K of the transfer function (3) foreach step and for both experiments can be seen inFigure 15:

2 3 4 5 6 7 8 9 10

n

0.008

0.009

0.01

0.011

0.012

0.013

K

Without load

With load

Figure 11: Estimation of the parameter K of thetransfer function (3) .

The results show that the system has a similarbehavior if the system has load or not. This phe-nomenon happens because the linear actuator hasa very high reduction gear, therefore, the addi-tional torque required to move a load has veryslight influence in the dynamics of the system. Fi-nally, it is obtained a nominal value of K = 0.01with a maximum variation of 15% for both experi-ments. This value was obtained doing the mean ofK of the ten steps in both experiments. The samestudy was done for the other three legs obtainingsimilar results. Therefore, it was considered thatthe dynamics of the four legs of the system canbe described using the transfer function (3) witha value of K = 0.01.

360

3.3 DESIGN OF THE CONTROLLERS

In our control system, we feed back measurementsof the linear actuator positions x.

x∗ xVR(s) K/s

Figure 12: Control scheme.

We propose a controller with the form:

R(s) =Kp +Kvs

s; (4)

Operating the characteristic polynomial (denom-inator of the closed-loop tranfer function) of thesystem and equalizing to a second order transferfunction:

H(s) = 1 +Kp +Kvs

s

K

s= 0; (5)

s2 +KpKvs+KpKv = s2 + 2ps+ p2; (6)

where p is the absolute value of the position of thepoles of the closed-loop transfer function. There-fore, from equation (6), we have two parametersand two equations.

4 EXPERIMENTAL RESULTS

This section shows some experimental results ofusing the proposed controllers of the linear ac-tuators when the system is in contact with theground in order to: a) demonstrate the efficiencyof the proposed controllers for the linear actuatorsof the system and b) show how the orientation ofthe base of the truck changes when the four linearactuators move using a combined trajectory withthe proposed control position. Figure 13 shows aphotograph of the prototype.

Figure 13: Experimental platform.

The method of describing the orientation of theframes used in this work will be the well-knownroll (φ), pitch (θ) and yaw (ψ) angles about fixedaxes. This is the rotation about X by φ (roll),rotation about Y by θ (pitch) and about Z by ψ(yaw). The derivation of the equivalent rotationmatrix I

JRrpy is straightforward because all rota-tions occur about axes of the reference frame:

IJRrpy = Rz(ψ)Ry(θ)Rx(φ) (7)

Rz(ψ) =

cosψ − sinψ 0sinψ cosψ 00 0 1

;

Ry(θ) =

cos θ 0 sin θ0 1 0− sin θ 0 cos θ

;

Rx(φ) =

1 0 00 cosφ − sinφ0 sinφ cosφ

;

The different frames of the system can be defined(see Figure 14) as:

BX

Z B

YB

X A

ZA

Y A

ZC

X C

Y C

Figure 14: Experimental platform.

• Frame {A}: is the fixed frame of the system,its Z axis is parallel to the gravity force but

361

with opposite direction. This frame will beconsidered as the reference frame.

• Frame {B}: is a fixed frame of the surfacewhere the system will be. Its Z axis is per-pendicular to this surface. The orientation ofthis frame respect to {A} is [φ0 θ0 ψ0]. It isassumed that during the stabilization processthis frame is constant.

• Frame {C}: is an inertial frame, its Z axis isperpendicular to the upper part of the baseof the truck. The orientation of this framerespect to {A} is [φ(t) θ(t) ψ(t)]. It is inter-esting to express the orientation of this framerespect to {A} because the inclination mea-surements of the sensor that will be used inthe system are related to frame {A}. Theorigin of this coordinate frame is in the geo-metric center of the base of the truck.

Figures 15 and 16 show the results of using thecontrol proposed in this work for the four parts.The poles of the controller were located in p =−10 for the four linear actuators obtaining fromequation (6) the following controller for the fourlinear actuators:

R(s) =2000s+ 10000

s; (8)

In Figure 15 the extension of the legs are shown,whereas in Figure 16 the two first components ofthe orientation of the base are shown. A camera-based optical tracking system was also used as anexternal sensor. This sensor consists of three in-frared cameras which measures the orientation ofthe system with very high precision. Notice that,the third component is zero because the systemdoes not rotate about the Z axis. In this Fig-ure, we can see how the orientation of the systemchanges with the different extension of the legs.

0 10 20 30 40 50 60 70 80 90 100

Time (s)

0.395

0.4

0.405

0.41

0.415

0.42

0.425

Lin

ea

r e

xte

nsio

n (

m)

Linear actuator 1

Linear actuator 2

Linear actuator 3

Linear actuator 4

Figure 15: Extension of the linear actuators.

0 10 20 30 40 50 60 70 80 90 100

Time (s)

-5

0

5

Orie

nta

tio

n (

º)

θ

φ

Figure 16: Orientation of the base of the platform.

Finally, Figure 17 shows a nearly perfect trackingof the extension of a linear actuator is achieved.

0 5 10 15 20

Time (s)

0.395

0.4

0.405

0.41

0.415

0.42x

*

x

Figure 17: Response of the extension of a linearactuator.

5 CONCLUSIONS

We have presented a new mobile platform for flex-ible mobile manipulators. Its main features arethat the system has legs and wheels in order tocarry out two different tasks: a) transport a flexi-ble manipulator from one place to another and b)increase the stability of the system being able topositionate the base of the platform with a spe-cific posture and orientation. Also, it is proposeda control scheme for the extension of the linearactuators. Some experimental results show the ef-ficiency of the proposed control scheme. It is im-portant to highlight the importance of obtaining aprecise model of the system in order to develop acontrol law for the posture and orientation of thesystem. The development of a kinematic model ofthe legs of the system in contact with the ground,that relates the extension of the actuators withthe orientation of the base of the platform, will bethe objective of our future research.

Acknowledgement

This research was sponsored in part by the Span-ish FPU14/02256 Program (Ministerio de Edu-cacion, Cultura y Deporte), in part by the Span-ish State Research Agency and in part by theEuropean Social Fund with the project DPI2016-

362

80547-R (AEI/FEDER, UE).

References

[1] Benosman, M., and Le Vey, G. Control offlexible manipulators: A survey. Robotica 22,5 (2004), 533–545.

[2] Bloch, A., Baillieul, J., Crouch, P.,

Marsden, J. E., Krishnaprasad, P. S.,

Murray, R., and Zenkov, D. Non-

holonomic mechanics and control, vol. 24.Springer, 2003.

[3] Dwivedy, S. K., and Eberhard, P. Dy-namic analysis of flexible manipulators, a liter-ature review. Mechanism and machine theory

41, 7 (2006), 749–777.

[4] Korayem, M. H., and Nohooji, H. R.

Trajectory optimization of flexible mobile ma-nipulators using open-loop optimal controlmethod. In International Conference on In-

telligent Robotics and Applications (2008),Springer, pp. 54–63.

[5] Kumar, A., Pathak, P. M., and Suka-

vanam, N. Trajectory control of a two dofrigid–flexible space robot by a virtual space ve-hicle. Robotics and Autonomous Systems 61,5 (2013), 473–482.

c© 2018 by the authors.Submitted for possibleopen access publication

under the terms and conditions of the CreativeCommons Attribution CC-BY-NC 3.0 license(http://creativecommons.org/licenses/by-nc/3.0/).

363