FLUID ACTUATION FOR IMAGING COMPATIBLE DEVICES

FLUID ACTUATION FOR IMAGING COMPATIBLE DEVICES

A Thesis

Presented to

the Faculty of the Department of Mechanical Engineering

University of Houston

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

in Aerospace Engineering

by

William Rifenburgh

December 2013


______________________

William M. Rifenburgh

Approved:

Committee Members:

Dr. Suresh K. Khator, Associate Dean, Cullen College of Engineering

_____________________________

Chair of the Committee, Dr. Karolos M. Grigoriadis, Professor, Mechanical Engineering

_____________________________

Dr. Jagannatha R. Rao, Associate Professor, Mechanical Engineering

_____________________________

Dr. Marc Garbey, Professor, Computer Science _____________________________

Dr. Karolos M. Grigoriadis Professor and Chair, Aerospace Engineering

iv

Acknowledgements

This thesis is the culmination of three years of work in two different

countries. I want to acknowledge all of those I have met along the way that

played a role, however small or large, in guiding me to this point. Starting from

day one, I would like to thank Mrs. Trina Johnson. Without her help, I would not

have become a graduate student at the University of Houston. I would like to

thank Dr. Karolos Grigoriadis, who agreed to be my advisor and my guide into

the world of control systems engineering. I would like to thank the Alliance for

Graduate Education and the Professoriate (AGEP) for accepting me into their

fellowship program. I would like to thank Dr. Nikolaos Tsekos, for my time in his

lab and Dr. Marc Garbey, for introducing me into the Atlantis Program that

brought me to Université de Strasbourg and France. I would like to thank

Professor Bernard Bayle, for accepting me as his student there. I would like to

thank everyone at the Institut de Recherche contre les Cancers de l’Appareil

Digestif (IRCAD) that helped me with my experimental system, especially

Professor Olivier Piccin. Special thanks go out to Dr. Jannagatha Rao, for

graciously agreeing to be a member of my defense committee. Last but not least,

I want to give a very special thanks to my parents who supported me every step

of the way.

v


An Abstract

of a

A Thesis

Presented to

the Faculty of the Department of Mechanical Engineering

University of Houston

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

in Aerospace Engineering

by

William Rifenburgh

December 2013

vi

Abstract

The use of robots in imaging devices is becoming more prominent with the

development of image guided surgery robots and imaging related research

requiring mechanical actuation. Many such robotic systems exist today but

unfortunately cause imaging distortion and artifacts due to the presence of

actuators and control electronics that are incompatible with the imaging devices

used. One solution to this problem is the use of fluid actuators. Fluid actuators

can be made entirely of polymers that are fully compatible with both MRI and CT

scanning. In the course of this work, the modeling, identification and control of

hydraulic and pneumatic linear piston-cylinder actuators was investigated and a

performance comparison of the two types of actuation in various medical robotics

applications was made. The results show that hydraulic systems are better suited

for precise positioning tasks and haptic force-feedback teleoperation and

pneumatic systems are better suited for applications requiring compliant motion.

vii

Table of Contents

Acknowledgements…………………………………………………………………..iv

Abstract…………………………………………………………………………………vi

Table of Contents…………………………………………………………………….vii

List of Figures…………………………………………………………………………ix

List of Tables…………………………………………………………...……………..xii

1. Introduction………………………………………………………….………..….…1

2. Background……....……………...……………………………….……….….…....3

3. Data Acquistion and Control Electronics……………………………………..4

4. Hydraulic Actuation………………………………………………………….……6

4.1. The Hydraulic System………………………………………………….……...7

4.2. Modeling & Parameter Identification…………………………………….…..7

4.2.1. Ball-Screw Mechanism………………………………………………..10

4.2.2. Hydrostatic System……………………………………………………18

4.2.3. Final System model…………………………………………………...23

4.3. Control System Design………………………………………………….……24

4.4. Results…………………………………………………………………………28

5. Pneumatic Actuation……………………………………………………….……39

5.1. The Pneumatic System………………………………………………………39

5.2. Modeling & Parameter Identification…………………………………….….41

5.2.1. The Piston-Cylinder……………………………………………………41

5.2.2. The Proportional Valves………………………………………………43

5.2.3. The Transmission Lines……………………………………………....45

viii

5.3. Control System Design………………………………………………….……46

5.4. Results…………………………………………………………………………48

6. Discussion…………………………………………………………………….…..58

7. Conclusions………………………………………………………………...…….60

7.1. Summary……………………………………………………………………….60

7.2. Future Work……………………………………………………………………60

8. References……………………………………………………………….………..62

9. Appendix…………………………………………………………………….…….66

ix

List of Figures

Figure 1 – CT-Bot (left) and CT-Bot Kinematic Model (right)………………………3

Figure 2 – Hydraulic Actuation Test bed Schematic………………………………...7

Figure 3 – The Haptic Interface………………………………………………………..8

Figure 4 – The Actual Hydraulic System……………………………………………..8

Figure 5 – Exploded View of Ball-Screw Mechanism……………………………...11

Figure 6 – Bearings within the ball-nut………………………………………………11

Figure 7 – Ball-Screw System Force Diagram……………………………………..12

Figure 8 – Power Screw Force Diagram [4]………………………………………...14

Figure 9 – Ball-screw Threading……………………………………………………..15

Figure 10 – Input Torque………………………………………………………...……17

Figure 11 – Position Outputs………………………………………………………....17

Figure 12 – Velocity Outputs…………………………………………………………17

Figure 13 – Transmission line mechanical equivalent [5]…………………………18

Figure 14 – Hydrostatic system mechanical equivalent…………………………...19

Figure 15 – Hammerstein model……………………………………………………..20

Figure 16 – Simplified Hydrostatic system model………………………………….20

Figure 17 – Hydrostatic system identification experimental setup……………….21

Figure 18 – Identified dead zone (Newtons vs. Newtons)………………………...22

Figure 19 – One of three trial run output comparisons…………………………….23

Figure 20 – Control System with plant in green box……………………………….25

Figure 21 – Classical control system problem……………………………………...25

Figure 22 – 0.5 mm Step…………………………………………………………..….28

Figure 23 – Triangle wave input tracking……………………………………………29

Figure 24 – Triangle wave input tracking error……………………………………..29

Figures 25 – Triangle wave position tracking with secured master actuator…....30

x

Figures 26 – Triangle wave tracking error with secured master actuator……….30

Figures 27 – Sine wave position tracking without friction compensation………..31

Figures 28 – Sine wave tracking error without friction compensation…………...31

Figures 29 – Sine wave position tracking with friction compensation………...….32

Figures 30 – Sine wave tracking error with friction compensation……………….32

Figure 31 – Tissue puncture simulation test bed…………………………………..33

Figure 32 – Pre-puncture needle insertion model………………………………….33

Figure 33 – Post-puncture needle insertion model………………………………...34

Figure 34 – Teleoperated Needle Insertion Position Tracking……………………34

Figure 35 – Environment force during teleoperated needle insertion……………35

Figure 36 – Position tracking error during teleoperated needle insertion………..35

Figure 37 – Position tracking during ramp needle insertion………………………36

Figure 38 – Environment force during ramp needle insertion…………………….37

Figure 39 – Position tracking error during teleoperated needle insertion………..37

Figure 40 – Pneumatic System Schematic…………………………………………39

Figure 41 – The Pneumatic System…………………………………………………40

Figure 42 – Pneumatic actuator identification setup……………………………….42

Figure 43 – Coulomb & viscous force versus velocity……………………………..43

Figure 44 – Pressure proportional valve diagram [7]………………………………44

Figure 45 – Impedance Control System…………………………………………….46

Figure 46 – Desired actuator behavior………………………………………………47

Figure 47 – 1mm Step Response at default settings………………………………49

Figure 48 – 20 mm step response at default settings……………………………..50

Figure 49 – Slow ramp triangle wave input tracking……………………………….50

Figure 50 – Slow ramp triangle wave input tracking error…………………………51

Figure 51 – Teleoperated needle insertion position tracking …………………….51

Figure 52- Teleoperated needle insertion force feedback………………………...52

xi

Figure 53 – Teleoperated needle insertion tracking error………………………....52

Figure 54 – Ramp needle insertion, default settings………………………………53

Figure 55 – Ramp needle insertion force, default settings………………………..53

Figure 56 – Ramp needle insertion tracking error, default settings………………54

Figure 57 - Ramp needle insertion, P_sum=4 bar…………………………………54

Figure 58 – Ramp needle insertion force, P_sum=4 bar………………………….55

Figure 59 – Ramp needle insertion tracking error, P_sum=4 bar………………...55

Figure 60 - Ramp needle insertion, k=1000 N/m…………………………………..56

Figure 61 – Ramp needle insertion force, k=1000 N/m……………………………56

Figure 62 – Ramp needle insertion tracking error, k=1000 N/m………………….57

xii

List of Tables

Table 1 – Hydraulic System Components……………………………………………9

Table 2 – Ball-Screw System Nomenclature……………………………………….13

Table 3 – Ball-Screw Parameter estimates…………………………………………16

Table 4 – Pneumatic system components……………………………………….....41

1

1. Introduction

The use of robots in imaging devices is becoming more prominent with the

development of image guided surgery robots and imaging related research

requiring mechanical actuation. Many such robotic systems exist today but

unfortunately cause imaging distortion and artifacts due to the presence of

actuators and control electronics in their systems that are incompatible with the

imaging devices used. One solution to this problem is the use of fluid actuators.

Fluid actuators can be made entirely of polymers that are fully compatible with

both MRI and CT scanning. In the course of this work, macro-scale, hydraulic

and pneumatic linear piston-cylinder actuators were investigated.

Pneumatic actuators in particular also offer the advantage of natural

compliance. Natural compliance can be a desirable characteristic in actuators for

haptic force feedback systems because the actuators function as natural

impedances and can be used in impedance control schemes. This compliance is

due to the compressibility of air which can also offer disadvantageous effects

such as significant time delay.

Hydraulic actuators exhibit stiff and heavily dampened motion. The

characteristics of hydraulic actuators offer less significant time delay and more

robust positioning with respect to external forces. Hydraulic systems are more

well-known for their high power-to-weight ratios than their pneumatic

counterparts, though the hydraulic system investigated in this work is a low

pressure hydrostatic system.

2

This written work includes a memoire of experiments conducted to

evaluate the performance of fluid actuators. Of particular interest is their

performance within haptic feedback systems. The results will primarily be

considered for their potential use in robot-assisted needle insertion for

interventional radiology, but not strictly limited to. It is hoped this work will aid in

the selection of actuators to be implemented in the next generation prototype of

CT-Bot of the AVR-ICube research group and other robotic systems.

This report will begin with a brief overview possible applications of fluid

actuation and what performance criteria will be used to evaluate the experimental

systems. Afterwards, two sections, each describing the modeling, parameter

identification, control system design, and experimental results of a test bed

system will be presented for the hydraulic and pneumatic cases respectively. A

discussion comparing the results of the systems and suggestions for future work

will conclude this report.

3

2. Background

The AVR group at the ICube lab is involved in prototyping several surgical

devices that could make use of imaging compatible fluid actuators as well as

imaging projects that could make use of imaging compatible manipulators. Of

importance to the design of such devices is the ability of actuators to perform

positioning and force tracking either separately or simultaneously.

Positioning performance can be critical in surgical robotics. Perhaps the

most critical positioning performance expected will be that which is required by

CT-Bot (figure 1).

Figure 1 – CT-Bot (left) and CT-Bot Kinematic Model (right) [1].

CT-Bot is a patient mounted, CT image-guided robot that first aligns its needle

with a pre-planned needle path axis under computer control and then inserts its

needle into a patient under haptic feedback teleoperation command from a

surgeon. The axis alignment procedure requires precise positioning with

negligible tracking rate. As long as the actuators can eventually reach the desired

position and maintain it while sustaining external forces that may occur

4

throughout a surgical procedure, the actuators’ performance could be considered

satisfactory. The insertion procedure however requires both precision and

responsive position tracking because it is crucial to provide a surgeon with

accurate kinesthetic feedback. The latest prototype of the CT-Bot teleoperated

needle insertion system uses a three-channel scheme in which position

commands are sent to the slave device and position and force feedback data is

returned to the master interface [1].

To assess the performance of position tracking of an actuator a ramp

signal will be input into the system and the resulting error will indicate the quality

of tracking. Step inputs will be used to evaluate rise time and steady state error

precision. Position tracking under the influence of external forces will be

examined as well. Teleoperation of the actuators in haptic force feedback

systems will be used to command the actuators to interact with an environment

force simulation robot to simulate needle insertion.

5

3. Data Acquisition and Control Electronics

The data acquisition and control electronics used throughout the entire

project were Beckhoff EtherCAT modules. The modules have architecture akin to

that of modular Programmable Logic Controllers (PLCs). The Beckhoff modules

may be programmed using PLC code, C++ or Simulink Models using their

accompanying software known as TwinCAT 3. TwinCAT 3 functions as a

Microsoft Visual Studio Shell and controls Beckhoff modules from a computer

connected to a PLC module bus via Ethernet cable. Simulink models were used

to create control systems for all experiments in this project. Simulink models can

be used to control ‘silently’ much like a script or in ‘external mode’ where

Simulink model runs open. In this mode, oscilloscope blocks can be used to

record and display data and parameters such as gain block gains can be

modified, all in real-time.

At the time of the conduction of all experiments of this project, TwinCAT 3

was still under development and not commercially available for purchase. A trial

beta version of TwinCAT 3 was used. This trial beta version had many limitations

including:

5 max inputs in any one .mdl file

5 max outputs in any one .mdl file

1000 data point recording limit

100 block limit per .mdl file

6

The 1000 data point limit forced use of 100 Hz sampling frequency in all

experiments for 10 seconds of data. The ODE solver for all Simulink models

used in control was the default Fixed-Step Discrete solver of Simulink. Simulink

models used to control the experimental apparatus are available in the appendix.

7

4. Hydraulic Actuation

4.1 The Hydraulic System

The Hydraulic system is series combination of a ball-screw mechanism

and two identical, hydrostatically connected linear piston-cylinder actuators (see

figure 2).

Figure 2 – Hydraulic Actuation Test bed Schematic

The ball-screw shaft is rotated by a servomotor with a planetary gear system at

its output shaft (not shown). Motion of the ball-screw mechanisms cart moves the

piston of the master hydraulic actuator which results in equal and opposite

motion of the slave actuator. Note that the term “master actuator,” should not be

confused with the haptic interface actuator. The haptic interface, usually known

as a “master,” in teleoperation systems research, is actuated by another

servomotor in combination with a capstan and lever mechanism that converts

8

rotational motion into linear motion. The haptic interface is the same device used

in [1] and is pictured in figure 3 in its present state.

Figure 3 – The Haptic Interface.

The slave end-effector is equipped with a force sensor and a position sensor and

the servomotor that drives the ball-screw mechanism is also equipped with an

encoder.

Figure 4 – The Actual Hydraulic System.

9

The section of the system contained in the box labeled “Slave End-Effector,” in

figure 2 is the part of the system that would be within an imaging device. Though

it should be made of polymers, it is metallic for the experiments.

This hydrostatic system is favored over conventional hydraulic systems

because it doesn’t require a bulky pump and complicated valve actuation. The

ball-screw mechanism offers the system precision and high force to overcome

damping forces present within the hydrostatic system. The friction torque caused

by the ball-screw mechanism is significantly reduced due to the use of ball-

bearings. However the friction torque still affects positioning and is difficult to

model as will be shown in the next section. The following is a table of the

components and relevant specifications.

Table 1 – Hydraulic System Components.

Component(s) Model & Specifications Ball-screw Motor Encoder

Maxon HEDL 5540 Optical Encoder, 2000 counts/rev

Servoamplifier Maxon ADS 50/5, 4-Q-DC Servoamplifier Servomotor + Gear Maxon DC Motor 118746 with 4.4 gear ratio planetary

gear Ball-Screw Mechanism Misumi LX2001C 150mm stroke, lead=1mm/rev Hydraulic Cylinders SMC Dual Action 50mm Stroke Cylinders

CDQSXB20-50D Force Sensor Scaime K1563 50N Load Cell Displacement Sensor ETI Systems 55mm 5 kΩ Potentiometer 0.7%

Linearity Tubing SMC 2.5mm Inner diam. 4mm OD Hard Polyurethane

Tube Control Electronics Beckhoff EtherCAT Modules running TwinCAT 3

software at 100Hz

10

4.2 Modeling & Parameter Identification

At first glance, the hydraulic system in its entirety makes for a complicated

system to model and identify. To simplify the identification process, the ball-

screw mechanism and the fluid system were identified separately. This prevents

minor hard non-linearities, such as backlash in the connection between the two

subsystems, from compounding model complexity. The backlash present

between the two systems was largely due to the lower grade assembly of the

hydraulic test bed. Rapid prototyping 3D printed plastic and wood components

were used in its construction and backlash can easily be eliminated using higher

grade fabrication materials and methods. This backlash has a minor but

noticeable effect in the systems positioning precision and is further discussed in

the results.

4.2.1 The Ball-Screw Mechanism

Modeling

The ball-screw is a mechanism that axially translates a guide-rail mounted

cart (78 in figure 5) using a rotating screw shaft (28). This shaft is rotated by a

DC motor (14). The ball-nut (32) contains ball bearings to reduce the friction

between itself and the shaft.

Though the use of bearings dramatically reduces friction, it complicates

the modeling of the friction torque enacted on the screw shaft by the ball-nut.

Adding to the complexity is the friction within the bearings at the ends of the

screw shaft when the shaft receives axial loads. The existence of an accurate

mathematical model that is simple enough for a practical control systems design

11

is a topic of current research [2],[3]. In short, the friction torque induced by the

ball-screw’s multiple bearings is largely dependent upon the rotation speed of the

shaft, a change in movement direction, and external forces acting on the ball nut.

To identify the models proposed by [2], would require slow motion measurements

Figure 5 – Exploded View of Ball-Screw Mechanism.

Figure 6 – Bearings within the ball-nut.

with slow varying external forces at different speeds in a process deemed too

time consuming and also not possible given the data collecting constraints of the

TwinCAT 3 trial software used. It was ultimately decided that a portion of bearing

12

rolling friction torque would be treated as a disturbance whilst the remaining

portion shall be attempted to be characterized by classical coulomb and viscous

friction terms. The external force dependent portion of the friction torque will be

henceforth included into a term known as disturbance .

Figure 7 – Ball-Screw System Force Diagram.

The ball-screw motor system can then be modeled using the following equation,

, (1)

where

. (2)

Table 2 describes the nomenclature of equations 1 and 2 and figure 7. It should

be noted that all possible sources of friction are ball bearings and the use of

and is an attempt to characterize the behavior of bearing friction in the

absence of external forces into classical dynamics approximations. Because the

cart will be moving slowly a viscous term for its movement was neglected. It was

soon after noticed that the mass of the cart and the guide rail friction was

13

negligibly small as well so they were eliminated from the cart’s dynamics, thus

resulting in the presented form of equation 2.

Table 2 – Ball-Screw Motor System Nomenclature.

Parameter Description

Torque of the motor which commanded directly using current control mode of with the servo-amplifier of the DC motor.

Equivalent system inertia excluding cart.

Equivalent viscous friction excluding cart.

Equivalent coulomb friction excluding cart.

The angle of the motor shaft.

The gear ratio of the planetary gear system

The lead of the screw shaft, i.e., the translation for every screw shaft revolution.

The sum of the forces acting on the cart that is attached to the ball-nut.

The mass of the ball-nut, its bearings, and the cart.

The friction between the cart and its guide rails.

Any external force acting axially on the cart.

Screw shaft geometric constant relating the dynamics of the cart and the ball-screw.

In power screw theory, the problem of determining the screw torque required to

move a nut can be likened to that of finding the force required to move an object

on a ramp. In figure 8, is the diameter at which forces from the nut act on the

screw shaft. Plane projection of the side view of the screw shaft for one

revolution results in the right hand side image of figure 8.

14

Figure 8 – Power Screw Force Diagram [4].

The variable in the figure 8 is in the case of the ball screw and is a

coefficient of friction that when multiplied by the normal force, cos , gives

the friction force. The sum of the force in the horizontal and vertical directions is

given by

∑ 0 and (3)

∑ sin cos 0, (4)

where is the force required to move the ball-nut [4]. In the modeling of the ball-

screw, the friction terms of 3 and 4 have been grouped into the disturbance term

because of the complex rolling bearing friction. From equation 3, all that

remains unaccounted is the term sin . Thus the coefficient is intended to

model this portion of required force to move the nut and is described by

equation 5,

, (5)

where is multiplied to convert required force into a required torque and to

account for the gear ratio of the planetary gear system. The vertical forces in

15

equation 4 result in an axial force on the screw shaft, thus varying friction within

the bearings that support it. To restate, this type of force dependent friction has

been grouped into disturbance term . It should be noted that is just an

approximation based upon an idealized square threading of the screw shaft. In

reality, the threading looks like the images in figure 9.

Figure 9 – Ball-screw Threading.

The shape of the threading can slightly influence the diameter and only

slightly lessen normal force depending on the average position of the ball

bearings.

Parameter Identification

An estimate of the equivalent inertia is given by equation 6,

. (6)

The motor shaft, screw shaft and gear system inertias were all available in

manufacturer documentation. Parameter was determined using manufacturer

documentation with equation 5. Terms and were left to be determined by

experiment.

Determining and was performed by comparing time responses of

the actual system to time responses of a simulink model (see appendix) of the

16

system in response to the same inputs. A range of estimates for and were

used in the model and the parameter estimates that resulted in the lowest root

mean square (RMS) error in motor shaft angular position and velocity were

judged to be the most accurate. Acceleration RMS error was considered

unsuitable in judging as the recorded acceleration of the actual system was

derived from second order discrete differentiation and was too noisy. These

experiments were done initially done without the hydrostatic system attached so

that would be zero and the presence of disturbance would be

minimized. The resulting dynamic model of the system is given by equation 7,

. (7)

Table 3 presents the final estimates of the parameters.

Table 3 – Ball-Screw Parameter Estimates. Parameter Estimated Value Derivation

11.71 g cm Analytical

0.056 mm Analytical

≅ 0Nm srad

Time Response Curve-fitting

2.9 mNm Time Response Curve-fitting 1.9 mNm Time Response Curve-fitting 2.0 mNm Time Response Curve-fitting 1.6 mNm Time Response Curve-fitting

The coulomb friction was found to be asymmetric thus resulting in the

identification of four coefficients. Part of this asymmetry may also be due to a

small offset in the servo-amplifier’s tuning. Figures 10-12 shows a time response

comparison of chirp signal - one of the four simulation trials used for the

parameter identification. Between different trials, the kinetic friction coefficients

17

had the largest impact on simulation position output accuracy and varied

between the best RMS fit results of each trial. The parameter values of and

found in table 3 are averages of the estimates returned by each of the trials.

Figure 10 – Input Torque.

Figure 11 – Position Outputs.

Figure 12 – Velocity Outputs.

Fortunately the accuracy of the coulomb friction coefficients will not be critical in

creating and tuning the controller for reasons discussed in the control section.

0 1 2 3 4 5 6 7 8 9 10-4

-2

0

2

4Input Torque

Time (s)

Tor

que

(mN

-m)

0 1 2 3 4 5 6 7 8 9 10-100

-50

0

50

100

150

200

250Position Comparison

Time (s)

Mot

or S

haft A

ngle

(ra

d)

Simulation

Actual

0 1 2 3 4 5 6 7 8 9 10-300

-200

-100

0

100

200

300

400Velocity Comparison

Time (s)

Mot

or S

haft S

peed

(ra

d/s)

18

4.2.2 Hydrostatic System

Modeling

The hydrostatic system was initially modeled according to the work found

in [5]. The paper describes a hydraulic actuation system that uses a hydrostatic

fluid circuit in combination with an electric motor. Because the application of this

actuator was for actuation within an MRI sca nner, the authors had to take

transmission line time delay into account. The electric motors used had to be

several meters away from the MRI machine thus introducing the need for long

pipes. The dynamics of a long pipe, according to [5], could be modeled with the

mechanical equivalent shown in figure 13.

Figure 13 – Transmission line mechanical equivalent [5].

The mass of figure 13 models the mass of the fluid moving through a pipe.

The surface on which this mass slides represents the inner wall friction of the

pipes which is a function of Reynolds number of the moving water and surface

roughness of the pipes. Reynolds number was found to be in both laminar and

turbulent regions in the system. The springs model the slight compressibility of

hydraulic fluid and the dampers model the damping from the orifice flow of fluid

from an actuator’s chamber into the pipes and other small sources of flow

constriction such as bends in the transmission lines. Figure 14 shows a

19

mechanical equivalent of the hydrostatic system. .

Figure 14 – Hydrostatic system mechanical equivalent.

The two additional larger masses act as the masses of the piston of each

actuator, master and slave. The friction surfaces under the piston masses act as

sliding friction of a piston against the inside of its chamber. The rack and pinion

systems represent the fluid volume transfer relationship between an actuator’s

chamber and the pipe. It should be noted that the racks and pinions are

massless and their gear ratios are equivalent to the ratio of cross sectional areas

of an actuator’s piston and the transmission line pipe.

The complexity of the mechanical equivalent creates a challenging

identification problem. Fortunately, the authors found that the system can be well

approximated with a linear second order system with time delay. The authors

also found that if the transmission lines were short enough, the time delay could

be eliminated. Knowing that the hydraulic system’s transmission lines were

relatively short (2.36 m) a Hammerstein-Weiner model (figure 15) of a dead zone

input nonlinearity in series with a linear second order system was chosen as the

model for the parameter identification.

20

Parameter Identification

Figure 15 – Hammerstein model.

Hammerstein-Weiner model identification is available with the MATLAB

System Identification Toolbox and solves for parameters by automatically

selecting an optimal solving method from an arsenal of line-search based and

least-squares estimation based algorithms. The model expected to be identified

is depicted in figure 16, where is a mass that represents the inertia of both

pistons and of water rapidly accelerating in the pipes.

Figure 16 – Simplified Hydrostatic system model.

The assumption was made that the water in the system behaved stiffly enough

so that the master and slave pistons could be considered to move in unison. The

damper models damping from the high friction orifice flow at the inlets and

outlets of the actuators and through the transmission lines. is the sliding

friction of both pistons within their chambers. The resulting equation of motion for

the hydrodynamic system becomes

21

. (8)

The dead zone input nonlinearity of the Hammerstein-Wiener model

approximates . Figure 17 shows the system identification experiment setup

used to collect input and output data.

Figure 17 – Hydrostatic system identification experimental setup.

The force sensor was attached to the piston of the master actuator and

the displacement sensor potentiometer was attached to the slave. The master’s

piston was moved by hand while the force sensor data and position sensor data

were recorded as input and output respectively. Figure 17 features short

transmission lines for illustrative purposes, actual testing was done with 2.36 m

long lines. The identified dead zone (figure 18) for the sliding friction force input is

strongly biased in one direction.

The identified discrete transfer function of the second order system was

. ∙

. .. (9)

The transfer function matched experimental data with fit percentages 85%-95%

for the three trials (see figure 19). Using a Tustin transformation of the above

22

Figure 18 – Identified dead zone (Newtons vs. Newtons).

discrete transfer function into a continuous time transfer function, one has

≅ .

. . (10)

From which, one may derive that 53.7kg and 1720.5 ∙. Considering

the small size of the hydraulic system, the mass may seem absurdly high.

However, considering that millimeters in motion of the pistons results in meters of

motion of the water in the transmission lines, the water is relatively rapidly

accelerated, thus resulting in a large perception of a small mass. One should

note that the numerical approximation in equation item 10 contained negligibly

small higher order terms, common in numerical Tustin transformation

approximation, that were removed from the numerator. A negligibly small first

order term was removed from the denominator as well.

23

Figure 19 – One of three trial run output comparisons.

4.2.3 Final System Model

Equation 1 and equation 8 are combined to form the equation of motion of

the entire system,

. (11)

This equation assumes that and that the connection between the two

subsystems is rigid. Term is the force acting on the on the end-effector and

assumed to have perfect transmissibility to through the hydrostatic system. Term

was chosen to replace as the working state variable because the

potentiometer signal was to be used for the system.

The system is marked by unusual but favorable inertial behavior. As the

motor accelerates the position of the end-effector to a desired position, it must

overcome a large inertia presented by the hydrostatic system transmission lines,

the hydrostatic system’s damping, as well as a friction torque that is somehow

related to the resistance force enacted by the hydrostatic system on the cart.

1 2 3 4 5 6 7 8 9 10

-8

-7

-6

-5

-4

-3

-2

-1

0

x 10-3

Time (s)

Pos

ition

(m

)

94.76% Fit

Simulation

Actual

24

However upon reaching this target, this large inertia disappears almost

instantaneously as it is absorbed by the large damping of the hydrostatic system.

In the event of overshoot, this sudden change prevents the system from going

any further than a small distance as the inertia of the motor shaft and ball-screw

shaft are insignificant to all sources of friction and the disturbance D(t), which is

purely resistive in nature. In summary, the entire system requires great effort to

accelerate and nearly none to decelerate.

4.3 Control System Design

The system generally behaves as a classical second order linear system

with no capacitive elements (e.g., springs) and sliding friction nonlinearities so a

PD controller with a sliding friction compensator was chosen. The approach

taken to design the controller was to assume no environment force acting on the

system during the design phase and then to see if the system behaves tracks

position robustly enough with respect to environment forces in the testing phase.

In classical control systems design theory, position tracking capability of a

system can be analytically evaluated by determining the steady-state error

response of that system to a unit ramp [6]. Assuming the system’s sliding friction

is adequately compensated, the system reduces to that in figure 21. The closed-

loop transfer function of the system in figure 21 is

, (12)

where and are the proportional and derivative control gains respectively.

25

Figure 20 – Control System with plant in green box.

Figure 21 – Classical control system problem.

The reference-error transfer function is

. (13)

Setting the reference signal to a ramp: . The error becomes

. (14)

Using the steady-state theorem, the steady error resolves to a constant

lim → . (15)

Thus tuning as high as possible results minimizes the tracking error. But it

does so at the price of stability. Increasing the system’s damping preserves

stability.

26

The system’s damping coefficient is

. (16)

Thus increasing increases damping. It was soon after noticed that damping

could also be naturally increased by not compensating kinetic friction. Having

natural damping is beneficial because the derivate control portion of the control

system uses discrete differentiation of the error signal. Discrete differentiation is

problematic because of its noise and the derivative control itself causes instability

when the physical plant moves at high frequencies.

Static friction still needed compensation. If the system is commanded to

move from rest, the commanded position will need be a minimum distance away

from the original resting position before the proportional term of the PD controller

can command a torque strong enough to break static friction. Adding static

friction compensation eliminates this distance requirement. The static friction

compensator of the system is

∙ u | | , (17)

where u is a Heaviside function and is a velocity tolerance that encompasses

the noise of the end-effector velocity signal at actual zero velocity. Sensor signal

derivatives, (i.e., , , ) were obtained with discrete differentiator followed in

series by a Butterworth filter. The Butterworth filter was second order with a cut-

off frequency of 10Hz. While the Butterworth filter was effective at attenuating

high frequency noise, it also caused ringing in the velocity signal that was

noticeable after the end-effector quickly stops. This ringing was also taken into

account for the value of . The static friction in eq. 17 was

27

, 00, 0, 0

, (18)

where is the position error signal and and are the asymmetric values of

static friction in the positive and negative directions of the total system.

Controller Tuning

The tuning of the PD controller was done on a trial-error basis without

friction compensation. First, the term was slowly increased from 0 while

commanding slow, random continuous motions using the haptic master interface.

It was increased until the system began to oscillate, indicating the onset of

instability. was then slowly increased, also while inputting slow motion

commands, until stability returned.

After tuning the PD controller, the static friction compensator was tuned.

The friction values obtained from the parameter identification experiments were

used as initial estimations of what static friction would be in the combined

system. These friction values were then tuned while running the system. Slow

ramp motion commands were made to determine if the PD-controller-friction-

compensator combination had difficulty breaking static friction. Static-friction

compensation would be augmented until the minimum required breaking distance

was reduced to a minimal, sub-millimeter value. This process was done for both

movement directions. The simulink model of the control system is available in the

appendix.

28

4.4. Results

To assess the performance of the control system step inputs, ramp inputs, sine

waves and haptic teleoperation control were used under different conditions. A

0.5 mm step response with no environment force is shown in figure 22.

Figure 22 – 0.5 mm Step.

The step shows a max overshoot of approximately 0.3 mm and a steady-state

error of approximately 0.1 mm above target. Overshoot can be eliminated by

decreasing , at the expense of sub-millimeter tracking at even slow motions.

Figure 23 shows a slow ramping triangle wave input. The triangle wave’s speed

is approximately 5 mm/s.

The tracking error remains within 1 mm but does so with shaky movement.

This can be attributed to the spring-like deformation of the plastic component that

secures the master actuator to the wooden baseboard of the system. If the

master actuator is held firmly against the wooden base, the shaky behavior is

nearly eliminated as evident in figure 25 & 26.

0 1 2 3 4 5 6 7 8 9 10

6.4

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

7.3

0.5mm Step

Time (s)

Pos

ition

(m

m)

29

Figure 23 – Triangle wave input tracking.

Figure 24 – Triangle wave input tracking error.

0 1 2 3 4 5 6 7 8 9 1010

15

20

25

30

35

40Triangle Wave

Time (s)

Pos

ition

(m

m)

Position

Command

0 1 2 3 4 5 6 7 8 9 10-1.5

-1

-0.5

0

0.5

1Triangle tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

30

Figures 25 – Triangle wave position tracking with secured master actuator.

Figures 26 – Triangle wave tracking error with secured master actuator.

This is a minor problem and can be easily eliminated using stiffer

components. Note that this problem is not eliminated for other results shown in

this project report due to insufficient time required to machine metal replacement

parts. The remaining oscillations in figure 26 can be attributed to other non-

modeled stiffness issues such air bubbles in the hydrostatic system, the slight

compressibility of water, and the static friction compensator periodically switching

0 1 2 3 4 5 6 7 8 9 1010

15

20

25

30

35

40Triangle Wave 2

Time (s)

Pos

ition

(m

m)

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1Triangle tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

31

on and off with changes in velocity. To observe the effect of the static friction

compensator on the system, a low frequency sine wave was used with static

friction compensation off (figures 27 & 28) and with static friction compensation

on (figures 29 & 30).

In figure 27 a plateau is noticeable at the crests and troughs of the sine

output. Looking at the error of figure 28, the static fiction breaking distance for the

proportional controller alone is 0.5 to 0.7 mm. With friction compensation, the

plateaus are minimized and tracking error RMS is improved as shown in figures

29 & 30.

Figures 27 – Sine wave position tracking without friction compensation.

Figures 28 – Sinee wave tracking error without friction compensation.

0 1 2 3 4 5 6 7 8 9 105

10

15Low Freq Sine Wave

Time (s)

Pos

ition

(m

m)

Output

Input

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1Sine Wave Tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

32

The system was tested in haptic force feedback teleoperation with 1:1 force-

feedback ratio. The stroke of the haptic interface was twice as long as the stroke

of the end effector, i.e., 2 mm in the motion of the master device commands 1

mm of motion. The end-effector was commanded to interact with another device

that was intended to simulate a sudden puncture of tissue in needle insertion

(figure 31).

Figures 29 – Sine wave position tracking with friction compensation.

Figures 30 – Sine wave tracking error with friction compensation.

0 1 2 3 4 5 6 7 8 9 105

10

15Low Freq Sine Wave

Time (s)

Pos

ition

(m

m)

Output

Input

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1Sine Wave Tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

33

Figure 31 – Tissue puncture simulation test bed.

The tissue simulator, on the right side of figure 31, is a DC motor attached

to a linear motion mechanism. At its fully extended position, as in figure 31, it is

commanded to simulate the surface of a tissue using the dynamics of a spring-

damper (figure 32). After the simulator is pushed a certain distance, the

resistance force of this spring-damper is suddenly deactivated and replaced with

a weaker spring force proportional to the distance of insertion.

Figure 32 – Pre-puncture needle insertion model.

34

Figure 33 – Post-puncture needle insertion model.

The value of the pre-puncture stiffness and puncture distance was chosen

so that the peak resistance force would be approximately 5N. A force of 5N may

be an exaggeration for normal tissue behavior, but it serves as a worst case

scenario and provides insight into the system’s performance under relatively high

environment force. Figures 34-36 shows the results of an insertion trial.

Figure 34 – Teleoperated needle insertion position tracking.

0 1 2 3 4 5 6 7 8 9 1010

15

20

25

30

35

40

45Teleoperation Insertion

Time (s)

Pos

ition

(m

m)

Output

Input

35

Figure 35 – Environment force during teleoperated needle insertion.

Figure 36 – Position tracking error during teleoperated needle insertion.

The first bars in figures 34-36 indicate the time of contact with the surface

of the simulator and the second bars indicate the time of puncture. It is evident

0 1 2 3 4 5 6 7 8 9 10-6

-5

-4

-3

-2

-1

0Environment Force

Time (s)

For

ce (

N)

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5Teleoperation Tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

36

that the position tracking performs nearly the same with environment force as it

does without environment force, indicating robustness. After the approximate 5

Newton drop in environment force, the operator appears to command a 0.7 mm

sudden insertion for the end-effector. The end-effector soon follows and

overshoots by approximately 0.45 mm. This totals for 1.2 mm in sudden, post-

puncture insertion, not accounting for how real tissue may continue to shear itself

towards the needle. Despite how problematic this may seem, several solutions

exist to lessen the effects of and even avoid sudden puncture during actual

needle insertion and further research into this subject is outside the scope of this

report.

The fact that the position-tracking of the end-effector appears to be

minimally affected by environment force is a good sign. An automated needle

insertion experiment was conducted in which a ramp position command is used

to puncture the simulated tissue.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

10

15

20

25

30

35

40Ramp Insertion

Time (s)

Pos

ition

(m

m)

Output

Input

Figure 37 – Position tracking during ramp needle insertion.

37

Figure 38 – Environment force during ramp needle insertion.

Figure 39 – Position tracking error during teleoperated needle insertion.

According to this experiment, the sudden drop in force has little effect on the

tracking performance of the controller. This means that the most of the overshoot

that occurs in the haptic teleoperation experiment is largely due to the human

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-6

-5

-4

-3

-2

-1

0Environment Force

Time (s)

For

ce (

N)

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6Ramp Insertion Tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

38

operator. If the human operator can learn to firmly control the haptic interface

with large impedance, the operator can minimize overshoot greatly.

39

5. Pneumatic Actuation

5.1 The Pneumatic System

The pneumatic system uses the same model piston-cylinder actuator as

the hydraulic system in nearly the same configuration with the exception of slave

actuation.

Figure 40 – Pneumatic System Schematic.

A compressor and air filter combination supplies the system with up to 10 bar of

pressurized, clean, dry air. This pressurized air is fed to two voltage-pressure

proportional valves which control the pressure within each chamber of the

actuator. Each proportional valve has an internal outlet pressure sensor and

feedback control system, further described in the modeling section. Because it

was expected that the time-delay for air to travel through the transmission lines

from the valves would be significant, two additional pressure sensors are

40

attached to the transmission lines, near the ports of the actuator, in order to study

its effects. Figure 41 shows a picture of the actual pneumatic system.

Figure 41 – The Pneumatic System.

Pressure proportional valves were chosen initially because they were

kindly lent from colleagues at Montpellier but were later found to be ideal for

precision pressure control and are less noisy than on-off valves. Pressure

proportional valves are usually more expensive than on-off valves because they

require high precision machining and fabrication. Table 4 lists the make and

model of the components of the pneumatic system as well as some of their

relevant specifications.

41

Table 4 – Pneumatic system components, * = Same as in Hydraulic System.

Component(s) Model & Specifications Compressor Generic 10 Bar Compressor with pressure regulator Air Filter Generic Air filter/dryer also with pressure regulator Proportional Valves FESTO MPPES 3-way 1/8” adapter 0-10 Bar Gauge Pressure Sensors SMC PSE 560 0-1 MPa Gauge Pneumatic Cylinder* SMC Dual Action 50mm Stroke Cylinders

CDQSXB20-50D Force Sensor* Scaime K1563 50N Load Cell Displacement Sensor* ETI Systems 55mm 5 kΩ Potentiometer 0.7%

Linearity Transmission Line Tubing*

SMC 2.5mm Inner diam. 4mm OD Hard Polyurethane Tube

Supply Line Tubing SMC 8mm OD Hard Polyurethane Tube Control Electronics* Beckhoff EtherCAT Modules running TwinCAT 3

software at 100Hz

5.2 Modeling & Parameter Identification

Three components in the pneumatic system were modeled and identified

separately. They include the piston-cylinder, the proportional valves, and the

transmission lines.

5.2.1 The Piston-Cylinder

Modeling & Identification

Three parameters that were not given by manufacturer documentation

required identification, they include the friction, viscous damping and piston mass

of the actuator. A basic modeling of the system was required for the identification

and chosen the same as that of the hydrostatic system’s mass-damper-surface

model. Unfortunately, since the mass of the one piston is very small, its

identification with curve-fitting or frequency methods was ineffective because

proper excitation of the system by hand movements was not possible. The

42

piston’s mass was instead estimated using its geometry and material density and

was found to be approximately 80 g. The mass of the attached load cell was 60

g, as found using a scale. This totals for 140 g for what shall henceforth be

referred to as “piston mass,” .

Figure 42 – Pneumatic actuator identification setup.

To identify the viscous damping and sliding friction, the slave actuator’s piston

was moved by hand with the position sensor and force sensor attached (see

figure 42). Force was plotted versus velocity recorded in figure 43.

By curve-fitting the viscous plus coulomb friction model to data, one finds

that 45 ∙ and that sliding friction could be modeled with eq. (19),

sgn , (19)

where 2.4N in both directions. Figure 43 includes data from three different

experiments with slow, medium and fast speed oscillations. The estimated model

is represented in magenta.

43

Figure 43 – Coulomb & viscous force versus velocity.

5.2.2 The Proportional Valves


Three pressure proportional valves were lent to us. One of which was

found to have an internal pressure sensor that was much more sensitive than the

other two. Since the other two agreed closely on pressure sensor measurements,

they were used for the project as balancing pressures within the chambers of the

actuator is crucial. Each of the proportional valves has an internal electro-

mechanical feedback control system [7].

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-25

-20

-15

-10

-5

0

5

10

15

20

25Coulomb+Viscous Friction Data

Velocity (m/s)

For

ce (

N)

fast

med

slow

44

Figure 44 – Pressure proportional valve diagram [7].

The valve is slowly actuated to vary the cross-sectional areas of the

pressure supply port, outlet port, and exhaust port. These cross-sectional areas

determine mass flow rate and thus outlet pressure with equations described in

[22]. The outlet pressure is feedback to a chamber under the plunger valve with

the aforementioned spring and is also monitored by an electronic pressure

sensor. The pressure signal, , of the electronic pressure sensor is feedback to

a control circuit that compares it to the voltage signal of desired pressure, , and

computes a voltage to command the electromagnet. The dynamics of the plunger

are summarized with in [7].

Several major problems are posed in identifying the dynamics of the

proportional valves. The largest of these problems is that control system with the

control circuitry is not provided by the manufacturers. The proportional valves

thus required black-box modeling. In [8], the authors found that they could

approximate their proportional valves with a first order system. However their

valves were piezo-actuated. After some trial and error, the proportional valves

45

were found to behave as second order systems. The transfer function in (20)

closely approximates both proportional valves,

. .

. ., (20)

where is desired pressure, as proportionally commanded with , and is

outlet pressure, according the internal pressure sensor voltage which is

accessible from the proportional valve electronics.

5.2.3 The Transmission Lines


The transmission lines used in the experiments are 5 m long, 2.5 mm

inner diameter, hard polyurethane pipe. According to [8], the transmission line

dynamics can be approximated by a first order equation with a time delay in

seconds that is the ratio of the length of the pipe to the speed of sound in a fluid,

. The first order transfer function accounts for the dynamics of pressure build up

within a chamber of an actuator. To identify this transfer function the pneumatic

actuator was fully extended in one direction and excited the pressure within the

fully opened chamber and its transmission line using one proportional valve. The

transfer function describing the transmission line from outlet pressure at the

proportional valve , to the pressure at the chamber , as measured by an

external SMC PSE pressure sensor at the port of the actuator chamber is

. .

.. . (21)

A time delay of 0.0147 seconds results from the ratio of of the system, which

is not very significant in comparison to the 0.01 second sampling time used to

46

control the system. The slow dynamic of chamber pressurization appears

presents a larger problem.

5.3 Control System Design

The impedance control positioning as studied in [9] was chosen as the

control method for the pneumatic system because of its versatility. This type of

control enabled testing of the pneumatic system’s position tracking capability as

well as its compliant behavior under different settings. The basic structure of the

control system is in figure 45.

Figure 45 – Impedance Control System. The first block, calculates the force necessary to exert on the piston of the

actuator, . It calculates this force based on a desired impedance for the

actuator end-effector. This impedance is described by spring-mass-damper with

stiffness , mass , and damping that the control designer chooses. The

actuator moves according to its position relative the commanded position, .

Figure 46 illustrates the desired behavior.

The block labeled “Desired Pressure,” calculates the desired pressure,

and , of each chamber based on the equations in (22),

and , (22)

47

Figure 46 – Desired actuator behavior.

where the variables are defined as the following:

– The surface area of the piston in the chamber that pushes the piston

out of the cylinder.

– The surface area of the piston in the chamber that pushes the piston

inside.

– The cross-sectional area of the piston rod

– Atmospheric pressure, 101325 Pa

– The set sum of pressures in chambers and .

The set sum of pressures , is what determines the natural compliance of

the actuator i.e., the inverse of its natural impedance. During impedance control

of the system, the impedance controller attempts to simulate the impedance of

the spring-mass-damper in figure 46, while the natural impedance is what

genuinely felt by anyone that exerts a sudden force on the system, as in the case

of tissue puncture. The setting of natural impedance has an effect on the

48

system’s actual compliance that depends on how well the impedance controller

performs its objective.

The “Pressure Control,” block computes the appropriate command signals to

send to the proportional valves. The authors’ of [9] use sliding mode control in

their study because they had direct control over their valve orifice areas and had

their proportional valves connected directly to the actuator. The control circuitry

of the valves was used to directly control the pressure in the chambers,

assuming their slow dynamic is still responsive enough for slow actuation of the

system. Assuming this is not a problem, the equation of motion of the system

should be described by equation (23),

, (23)

where represents environment force on the end-effector. Parameters marked

with a (~) indicate those identified in the system identification and their counter-

parts sans (~ are the true values of the parameters.

5.4. Results

Step inputs, a ramp input and several needle insertion simulations were

performed using different natural impedance and desired impedance settings

were tested. The default control desired impedance settings for the system were

4000 , , and . The default was 8 Bar. An image of the

simulink model used to control the system is in the appendix.

49

Figure 47 – 1mm Step Response at default settings.

The system exhibits slow rise time with minimal overshoot for small steps.

For large step inputs, the system exhibits short rise time with significant

overshoot oscillations as in figure 48. Careful attention care must be taken to

avoid sudden movements when the pneumatic system is used in teleoperation as

it can be very unstable. Figures 49 & 50 show the tracking and error of a slow

ramp triangle input respectively. The pneumatic system has trouble adjusting to

change in direction but can track the input with sub-millimeter accuracy

approximately 2 seconds after.

Teleoperated needle insertion simulations were performed with 1:1 force

feedback ratio, just as the hydraulic system was, under default settings. Figures

50-52 show the results.

0 1 2 3 4 5 6 7 8 9 1010

10.2

10.4

10.6

10.8

11

11.21mm Step Response

Time (s)

Pos

ition

(m

m)

Input

Output

50

Figure 48 – 20 mm step response at default settings.

Figure 49 – Slow ramp triangle wave input tracking.

0 1 2 3 4 5 6 7 8 9 1010

15

20

25

30

35

40

45

50

5520mm Step Response

Time (s)

Pos

ition

(m

m)

Input

Output

0 1 2 3 4 5 6 7 8 9 105

10

15

20

25

30

35Triangle Wave Response

Time (s)

Pos

ition

(m

m)

Input

Output

51

Figure 50 – Slow ramp triangle wave input tracking error.

Figure 51 – Teleoperated needle insertion position tracking.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

4Triangle Wave Tracking Error

Time (s)

Pos

ition

Err

or (

mm

)

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35Teleoperated Needle Insertion

Time (s)

Pos

ition

(m

m)

Input

Output

52

Figure 52 - Teleoperated needle insertion force feedback.

Figure 53 – Teleoperated needle insertion tracking error.

The experiment resulted in an over shoot less than 0.5 mm after rupture.

The error before rupture was approximately 1.5 mm behind desired position. This

is because the the compliance of the end-effector. Upon rupture, the stored

0 1 2 3 4 5 6 7 8 9 10-6

-5

-4

-3

-2

-1

0

1Teleoperated Needle Insertion Force

Time (s)

For

ce (

N)

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

1.5

2

2.5

3Teleoperated Needle Insertion Tracking Error

Time (s)

Pos

ition

Err

or

53

energy is released while the human operator’s hand jolts forward as well. To

exclude the influence of the human operator, ramp commands were used to

perform the simulation again. Figures 53-55 show the results of this trial,

performed with default settings.

Figure 54 – Ramp needle insertion, default settings.

Figure 55 – Ramp needle insertion force, default setting.

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40Ramp Needle Insertion, Default

Time (s)

Pos

ition

(m

m)

Input

Output

0 1 2 3 4 5 6 7 8 9 10-6

-4

-2

0

2Ramp Needle Insertion Force, Default

Time (s)

For

ce (

N)

54

Figure 56 – Ramp needle insertion tracking error, default settings.

The resulting error of the automated needle insertion does not differ much

from that performed by a human operator. The compliance of the actuator

causes nearly the same pre and post puncture errors. To test the effects of

changing the natural compliance of the same experiment was conducted with

set to 4 Bar.

Figure 57 - Ramp needle insertion, bar.

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

3

4Ramp Needle Insertion Tracking Error, Default

Time (s)

Pos

ition

Err

or (

mm

)

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40Ramp Needle Insertion, Psum=4bar

Time (s)

Pos

ition

(m

m)

Input

Output

55

Figure 58 – Ramp needle insertion force, bar.

Figure 59 – Ramp needle insertion tracking error, bar.

As a result of lowering the natural impedance, post-puncture overshoot

has increased to 1 mm. This may be a result of reduced ability of the increased

natural compliance to cancel the inertia of the end-effector. This may also

indicate the hypothesized shortcoming of the impedance controller to regulated

impedance for sudden events.

0 1 2 3 4 5 6 7 8 9 10-6

-4

-2

0

2Ramp Needle Insertion Force, Psum=4bar

Time (s)

For

ce (

N)

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

3Ramp Needle Insertion Tracking Error, Psum=4bar

Time (s)

Pos

ition

Err

or (

mm

)

56

To observe of the effect of the impedance controller on the system, the same

experiment was performed again with 8 bar (default) and with the desired

spring coefficient set to 1000 , a fourth of the default value. Figures 59-61

show the results of a trial using these settings.

Figure 60 - Ramp needle insertion, .

Figure 61 – Ramp needle insertion force, .

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40Ramp Needle Insertion, k=1000N/m

Time (s)

Pos

ition

(m

m)

Input

Output

0 1 2 3 4 5 6 7 8 9 10-6

-4

-2

0

2Ramp Needle Insertion Force, k=1000N/m

Time (s)

For

ce (

N)

57

Figure 62 – Ramp needle insertion tracking error, .

The lowered stiffness of the desired impedance results in poor tracking but

also no overshoot. It is interesting to note that the sudden change in position

after puncture in this experiment is approximately 3mm while it is approximately

2.5 mm in the earlier experiments.

0 1 2 3 4 5 6 7 8 9 10-4

-2

0

2

4

6Ramp Needle Insertion Tracking Error, k=1000N/m

Time (s)

Pos

ition

Err

or (

mm

)

58

6. Discussion

After experimenting with both systems, the hydraulic system was found to

be more stable and capable of greater precision tracking error. Though both

systems were capable of sub-millimeter tracking, the hydraulic system has

smaller tracking error compared to the pneumatic system when changing

direction. The pneumatic system probably had trouble tracking when changing

direction because of the slow response of the proportional valves. It is the

author’s opinion that the hydraulic system is better suited for needle insertion as

the compliance of the pneumatic actuator can lead to unpredictable positioning

behavior in the presence of environment forces. This and a failure of the control

system or either of the valves could lead to sudden and repeated insertion of the

needle into a patient very easily. Methods of preventing this could include

increasing piston-cylinder friction or using pneumatic actuators to move

mechanisms which indirectly move components like the pneumatic actuators in

the PneuStep device [10].

Hydraulic actuation does have notable drawbacks. Sterility of the water in

the system should be maintained by regularly changing it and perhaps adding

some sterilizing chemical agent. After several weeks of having the same water in

the system during the experiments, the water has developed a foul odor. Though

the hydraulic actuators in the experiment experienced no leakage, leakage may

be an issue with polymer actuators.

The natural compliance of pneumatic actuators should prove ideal in

creation of a phantom intended to simulate the breathing motion of the human

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chest. Implementation of pneumatic actuators in this aspect can be done so

safely with some appropriate mechanical design.

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7. Conclusions

7.1 Summary

A comparative study on a pneumatic and hydraulic system was performed

to evaluate their potential in imaging device compatible actuation. Needle

insertion simulations were used as a case study to examine their position

tracking behavior both with and without the presence of external forces and

within haptic force feedback teleoperation. The hydraulic system was found to

track more closely and with greater stability than the pneumatic system, making it

a better candidate for needle insertion. The compliant behavior of pneumatic

actuators was verified and found more suitable for other tasks such as phantom

actuation.

7.2 Future work

For the hydraulic system, modeling friction accurately was difficulty

because of its complexity. Further research into the behavior of ball-screw

bearing friction could be done to more effectively compensate it. Position control

of the motor angle using a method different than current control may also present

an interesting solution and eliminate the need for further research into friction

compensation. Machining metal parts to replace the certain plastic parts

discussed in the results section of the hydraulic system could improve position

tracking as well.

For the pneumatic system, pressure control within the chambers can be

greatly improved. This could be done with controlled designed using the models

of the valves and pipes that were identified in this report. An example could be to

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create a LQG-controller to send pressure commands to each valves control

circuit. Purchasing proportional valves that allows one to directly control orifice

area may also enable creation of more responsive chamber pressure control

systems.

In addition to improvements to the systems, a more in depth study of the

performance of both systems in teleoperation should be performed. As only

experimental results show the effectiveness of the systems, an analytical

assessment of the systems should be done to calculate transparency of the

haptic feedback. Doing so would provide insight into which parameters of the

systems have greatest impact on performance.

62

8. References

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9. Appendix

Figure A

1 – Sim

ulink model of B

all-Screw

Motor S

ystem used in identification.

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Figure A

2 – Sim

ulink model of H

ydraulic Control S

ystem.

68

Figure A

3 – Sim

ulink model of P

neumatic C

ontrol System

.

FLUID ACTUATION FOR IMAGING COMPATIBLE DEVICES

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