Impedance control for a pneumatic robot-based around pole ...

Control Engineering Practice 13 (2005) 291–303

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*Correspondi

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0967-0661/$ - see

doi:10.1016/j.con

Impedance control for a pneumatic robot-based aroundpole-placement, joint space controllers

Robert Richardsona,*, Michael Brownb, Bipin Bhaktac, Martin Levesleyd

a Department of Computer Science, University of Manchester, M13 9PL Manchester, UKb WS Atkins Consultants Ltd., 220 Aztec West, Park Avenue, Almondsbury, Bristol, UK

c Rheumatology and rehabilitation research unit, University of Leeds, UKd School of Mechanical Engineering, University of Leeds, UK

Received 19 December 2002; accepted 19 March 2004

Available online 10 May 2004

Abstract

Traditionally the control of pneumatic actuators has been limited to movement between pre-set stops or switches. Modern

pneumatic systems exhibit great power to weight ratio, are backdrivable and can be precision controlled. As such these actuators

offer great advantages over direct drive electric motors for robotic devices.

Increasingly robots are required to interact directly with humans requiring control of not only the robot position but also taking

into account the applied forces. Robotic physiotherapy is one such application. This paper describes the implementation of a force

and position control strategy, termed impedance control, on a pneumatic robot designed to implement robotic physiotherapy. The

controller is shown to work appropriately over a range of conditions. The performance achieved is limited by the quality of force

measurement in multiple axes.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Pneumatic systems; PID controllers; Position control; Force control; Impedance control; Model-based control

1. Introduction

Many people suffer from debilitating illnesses such asstroke. These patients require physiotherapy to aidtowards full or partial recovery of any effected limbs,however patients often do not receive an optimumamount of exercise due to resource limitations. Robotswould be able to administer physiotherapy for greaterperiods of time more consistently. In this situationrobots are connected directly to humans. This level ofintimacy requires safe interaction where the robot doesnot dominate the partnership. In this robotic phy-siotherapy context the robot guides the patient’s limbthrough a pre-set series of motions, applying forces togently assist the patient’s limb movement, rather thandominate it.

Several force and position control schemes have beendevised for robotic interaction tasks. Chiavervini and

ng author. Tel.: +44-161-275-6169.

ss: [email protected] (R. Richardson).

front matter r 2004 Elsevier Ltd. All rights reserved.

engprac.2004.03.011

Sciavicco (1993) proposed a parallel approach to forceand position control, where position trajectories aresacrificed due to force demands. For physiotherapy,specifying specific position demands would be difficult,as they would be masked by the dominance of the forceloop. Ferretti, Magnani, and Rocco (1997) proposed ahybrid force/position control strategy for robots withmultiple degrees of freedom. Force is controlled inconstrained directions, while position is controlled inunconstrained directions. With the robot operating in aconstrained environment the controller would behavepurely as a force controller. Schutter and Brussel (1987)used a position control strategy combined with anexternal force loop to alter demand position andvelocity. An extension to this was devised by Hogan(1985) who developed a force/position control strategy,termed ‘impedance control’, for which the desired forceand position are connected through mass, spring anddamper characteristics. Several prototype physiotherapyrobots use this technique for robot and human interac-tion. Krebs, Hogan, Aisen, and Volpe (1998) have

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Fig. 1. Physiotherapy robot.

Fig. 2. Robot workspace.

R. Richardson et al. / Control Engineering Practice 13 (2005) 291–303292

implemented force-based impedance control on a lowinertia prototype physiotherapy robot-based uponelectric motors. Noritsugu and Yamanaka (1996) haveused position-based impedance control on a rubberartificial muscle (RAM) for a prototype physiotherapyrobot, incorporating addition pressure controllers toensure pressures within the RAM are accuratelycontrolled.

Recent developments in pneumatic actuators andvalves allow them to be considered for applicationswhich previously only electric motors were suitable.Using pneumatic actuators to implement impedancecontrol has major benefits. Pneumatic system’s inherentlow stiffness and direct drive capabilities enable smoothcompliant motion, which is difficult to obtain fromconventional geared electric motor systems. Moreover,pneumatic actuators can cost up to 10 times less thanelectric motors, while offering a higher power to weightratio.

Most impedance controllers are designed aroundforce loops, which make use of the ability of an electricmotor to supply torque on demand (Krebs et al., 1998).Pneumatic and hydraulic actuators could also be used.However, due to factors such as fluid compressibility,stiction and viscous friction, accurate positioning ofhydraulic and pneumatic systems is difficult to obtainfrom a force-based control system. Moreover, anaccurate model of the system dynamics is required,which can be difficult to obtain (Heinrichs, Sepehri, &Thorton-Trump, 1997). Indeed, Krebs et al. (1998) useda low inertia manipulator to reduce the influence ofsystem dynamics. Generally, the inertial dynamics of themanipulator are significant. A position based impedancecontroller does not require consideration of the systemdynamics. Heinrichs et al. (1997) proposed a positionbased impedance controller for an existing hydraulicindustrial robot, validating their work experimentally.Gorce and Guihard (1999) propose a multi-link,position based impedance controller for implementationon a legged robot. They use an actuator model to predictthe torque produced from the pneumatic cylinders. Theperformance of the controller is demonstrated throughsimulation.

In this paper an impedance control strategy isimplemented on a pneumatic robot to implementphysiotherapy. The impedance controller is validatedthrough multiple tests of a human applying forces to therobot end-point, while varying the impedance charac-teristics, as would occur in robotic physiotherapy.Section 2 describes the pneumatic robot and its work-space. Section 3 implements PID joint space controldemonstrating a linearising compensation scheme tonegate the effect of the cylinder angle of action. Datafrom the PID control is used to implement pole-placement joint space position control in Section 4. Ademand filter in the pole-placement controller is used to

reduce the controller response to noise. Section 5examines the pole-placement response of the twodegree-of-freedom (d.o.f.) robot to global positiondemands. Section 6 implements the impedance control-ler on the two d.o.f. robot and finally Section 7 drawsconclusions from the work.

2. The physiotherapy robot

A three d.o.f. robot has been developed to administerrobotic physiotherapy (Fig. 1). A custom made threed.o.f. force sensor measures the contact force betweenthe robot and human. The workspace of the robot isshown in Fig. 2 along with typical hand movementenvelope. Each joint is revolute and actuated by apneumatic actuator system consisting of a low frictionpneumatic cylinder and two electro-pneumatic valves.The low friction cylinder minimises stiction effectsenabling accurate control (Richardson, Plummer, &Brown, 2001) and each valve supplies regulated pressureto a single chamber of the pneumatic cylinder. Thisenables the pressure difference across the cylinder to bespecified by software changes alone and also allowsthe individual chamber pressures to be regulated by the

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valves themselves, avoiding the need for additionalpressure control that has been implemented, forexample, in Liu and Bobrow (1988). To achieve accuratecontrol, it is desirable to control both valves from asingle control signal. This has been achieved through theuse of an equilibrium pressure for which one valve haspressure increased and the other valve has pressuredecreased (Richardson et al., 2001). Thus, throughmanipulation of a single control voltage, the outputforce and, hence link position can be altered.

The robot is constructed with counterbalance weightson each joint to reduce the effect of gravity on the robotmovement. The robot configuration makes it impossibleto completely compensate for gravity effects, thereforethe position controllers are required to operate withsome gravity forces present. It is possible to compensatefor gravity effects using only actuator forces at eachjoint. However, this would result in large control signalsapplied to the actuators under stationary conditions andthe possibility of actuator saturation during motion.

-1

1

5.5 6 6.5 7 7.5 8 8.5 9

0.1

0.2

Normal

Normal

Joint 3 actuator linearisation

With linearisation

With linearisation

-0.5

0.5

0

-0.2

-0.1

0

Con

trol

sig

nal (

V)

Join

t 3 p

ositi

on (

rad)

3. PID joint space control

To achieve global position objectives each joint iscontrolled to achieve a specified angle based upon theinverse kinematics of the robot. Fig. 3 demonstrates thephysical system to be controlled for one link of therobot.

The pneumatic cylinder extends linearly with itsapplied force-causing link 3 to rotate. As a result ofthe robot physical configuration the force exerted onlink 3 to rotate it depends not only upon the actuatorforce output but also upon the joint angle. Thisphenomenon results in different angular accelerationof the link depending upon the link position, foridentical force output from the pneumatic cylinder.The non-linearity manifests itself as an apparentincrease in gain for negative angles. A single PIDcontroller controls the individual joint angles. The PIDgains for each joint were optimised using the downhillsimplex method (Richardson, Brown, Bhakta, & Leves-ley, 2003). The integral squared time-weighed error

Fig. 3. Links 2 and 3 of the physiotherapy robot.

(ISTE) of the demand position and actual position,produced a cost for each response that the controlleroptimised. The optimised PID controller achievedadequate performance (Fig. 4). However, the non-linearity caused by changes in angle C3 (Fig. 3) degradesthe controller performance and renders the systemunsuitable to implement linear model-based controlsuch as pole-placement. As the angle C3 can becalculated it is possible to include a trigonometriclinearising function that can be considered to be partof the plant, causing the input voltage and output torqueto behave in a more linear manner (Fig. 5). Where Udes

is the control output from the PID controller, Uact is thecontrol input to the pneumatic system, y3d is the desiredangle and y3 is the actual joint angle. Including thelinearising element amplifies the system gain, requiringthe PID gains to be optimised again. The resultant linkstep response is shown in Fig. 4 for optimised PID withand without linearising element.

The linearised controller demonstrates improvedlinearity with the overshoot and oscillation almostidentical for the positive and negative steps. It is

5.5 6 6.5 7 7.5 8 8.5 9

Time, t(s)

Fig. 4. Optimised joint 3 response with and without linearising

element.

PID3sin

1

C PLANT

+

-

Udes Uact θ3d θ3

Fig. 5. Improving system linearity.

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interesting to note that the overall performance of thecontroller has improved due to the increased linearityenabling the optimisation strategy to tune the gains withgreater accuracy.

4. Pole-placement joint space control

Using the input/output data of the optimised PIDwith linear element, a plant model was calculated usingleast-squares parameter estimation:

y3 ¼BðzÞAðzÞ

udes ¼0:0845z�2

1 � 1:76z�1 þ 0:76z�2udes; ð1Þ

where y3 is the joint angle (rad) and udes is the controlsignal (V). Note it has been demonstrated that thismodel order is appropriate for this pneumatic valve andcylinder (Richardson et al., 2001) due the valvesapproximating to a zero-order response. Using thisplant model the coefficients F ðz�1Þ and Gðz�1Þ werecalculated for specific closed loop poles by solving thediophantine equation (Astrom & Wittenmark, 1997).

Due to the susceptibility of the potentiometers tonoise, the closed loop poles for conventional pole-placement control are required to be slow to provideadequate robustness, severely limiting the performanceof the controller. However, it is possible to augment astandard pole-placement controller with a demand filter(H) to attenuate the controller’s response to noise(Fig. 6). Where y3d is the demand input, et is themeasurement noise and y3 is the actual position.

Obtaining a transfer function of the controllerin Fig. 6, demonstrates the H filter only appears in thepart of the transfer function that connects errorsin measurement and output response (Vaughan &Plummer, 1990)

yt ¼Bðz�1Þ

Amðz�1Þrt þ

F ðz�1ÞAðz�1ÞAmðz�1ÞHðz�1Þ

et: ð2Þ

Selection of closed-loop poles for pole-placement isalways a trade off between speed of response androbustness to measurement noise. Section of closed looppoles at 0:370:05i; to obtain a fast response, result inthe standard pole-placement controller (without H

-

+ 1/F(z)

G(z)

H B ( z )A ( z

θ3d

Fig. 6. Pole-placem

filter) being very sensitive to measurement noise.Specifying the H filter as a first-order low pass filterwith a cut off frequency at 6 Hz significantly reduces thecontroller response to measurement noise. Experimentalresults of the robot joint 3 response (the angle betweenlink 2 and link 3) with and without the demand filtershow the response time and overshoot to beconsistent, however the steady-state response to noiseis almost completely removed when the H filter present(Fig. 7). This lack of response to measurementnoise is best illustrated by examining the control signalhigh frequency oscillation for the standard pole-placement controller (Fig. 7). A similar linearisationprocess can be performed on the second joint (the anglebetween link 2 and link 1) of the pneumatic robot(Richardson, 2001).

5. Two d.o.f. pole-placement position response

The two joint space controllers, acting on joints 2 and3 can be combined using inverse kinematics to controlthe global position of the robot end-point in two d.o.f.(x; y). To test the performance of the robot it wasprogrammed with a trajectory that causes it to extendhorizontally in the y direction and then retract to itsoriginal position, while only moving slightly in the x

direction (Fig. 8).The global desired and experimental x and y position

and velocities are shown in Fig. 9. The velocity isobtained by differentiation of the angular positionreading from the potentiometers, and as such issusceptible to measurement noise. The position trackingof the robot is not exact with the worst trackingresulting in approximately 5 mm error. This level oferror is acceptable in the final device as the accuracy ofhuman motion is low. The quality of response could beimproved by increasing the speed of the system poles inthe pole-placement joint space controllers, however thiswould result in controller output saturation, potentiallycausing controller instability. A saturation compensatedpole-placement controller could allow the pole-place-ment controller to operate within this saturation region(Ling & Plummer, 1999).

PLANT

et

+ +

)

θ3

ent control.

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1

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Con

trol s

igna

l (V

)

Without filterWith filterDemand

Without filterWith filter

Fig. 7. Pole-placement joint space response with and without demand filter.

xy

Initial position (retracted) Extended position, at mid-point of motion (15s)

Y=0.62m Y=0.62m Y=0.7m

End position

Joint 3

Joint 2

Fig. 8. Robot configuration in retracted and extended.

R. Richardson et al. / Control Engineering Practice 13 (2005) 291–303 295

6. Impedance control

Position control is not appropriate for physiotherapy,where the relationship between external forces andposition (the ‘feel’ of the robot to the patient) is requiredto be directly specified. Impedance control has beendeveloped over the last decade to enable robots tosmoothly move between contact and non-contact phasesof motion. Examining how humans interact with theirenvironment was an integral part of this development.Impedance control fixes the relationship between themanipulator end-point and external forces as mass,spring and damper system. This transfer function forposition-based impedance control (sometimes termedadmittance control) can be specified in the s-domain as:

xi

Fx

¼1

Ms2 þ Cs þ K; ð3Þ

where xi is the change in position due to external force(Fx), M is the inertial component, C is the dampingcomponent and K is the stiffness component.

Rearranging Eq. (3) so that position becomes theinput (known as force-based impedance control) gives:

Fx

xi

¼ Ms2 þ Cs þ K : ð4Þ

Eqs. (3) and (4) are known as the duality ofimpedance control. These two subtly different ap-proaches require different controller structures. A moredetailed discussion of these differences can be found inRichardson (2001), but a summary of the advantagesand disadvantages of each type of impedance controlleris given in Table 1. As highlighted by Heinrichs et al.(1997), position-based impedance control (admittancecontrol) is more appropriate for pneumatic systems. Toimplement position-based impedance control, Eq. (3) isimplemented. A multiple d.o.f. force sensor measurescontact forces which are then fed into the impedancefilter. The output of the filter is the required change inglobal position due to the external force.

As mentioned in Table 1 to implement position-basedimpedance control requires a position controller that isrobust to external force disturbances. The backdrivablenature of pneumatic cylinders results in the positioncontrollers having little robustness to externally appliedforces. Indeed, significant position control errors occurfor varying externally applied force. Often, theseexternally applied forces are unknown, and as suchcannot be directly compensated for. In this situation theforce sensor measures the externally applied forces,

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Fig. 9. Two d.o.f. pole-placement position response.


allowing the addition of a feed-forward force element toimprove the performance (Richardson, Brown, &Plummer, 2000). Measured forces are converted intovoltage control signals, which are directed straight to thepneumatic system. The valves are pressure proportionalso this open-loop voltage produces a force to balancethe externally applied force.

The effect of the feed-forward force element is toreduce the backdrivable properties of the robot. How-

ever, it should be remembered that although the directeffect of the external force is negated, the measuredforce results in the position control-loop implementing anew position, specified by the impedance filter char-acteristics. Therefore the desired impedance character-istics are achieved.

A flow chart of the multiple d.o.f. controller is shownin Fig. 10. The desired end point trajectory is specifiedbefore implementing the controller, in the form of global

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Matrix of impedance filters

xp, yp

xi ,yi

xd, yd

KCsMs ++2

1

Inverse kinematics

Pole-placement joint position controllers

Joint space open-loop force controllers

Resolve external forces to joints

Pneumatic robot

Actual joint angles 2, 3

θ θ2d, 3d

Forward kinematics Actual global positions x,y

Actual global forces, Fx,Fy

Joint angle sensors

ex2, ττ ex3

Control signals u2,u3

+ +

+

+

θ θ2, 3

Desired global positions

Force sensor

Human arm applying unpredictable forces to the

robot end-point

θ θ

Fig. 10. Implementing impedance control in multiple d.o.f.

Table 1

Comparison of admittance control and impedance control

Admittance control Impedance control

Advantages Most appropriate for environments consisting of

stiffness and damping elements.

Most appropriate for environments consisting of inertial

element.

Only requires addition of a force sensor on

conventional robotic devices based around

measurement of link position.

Easy to implement on direct-drive electric motor systems due

to the ease at which torque can be controlled during motion.

Disadvantages Requires a high gain position controller robust to

external force disturbances

Difficult to implement on actuator systems where force

output is effected by robot movement.

Requires robot inertial model, which can be difficult to

obtain.


position co-ordinates (xp; yp). These co-ordinates, whenadded to the desired change in position due to externalforces (as a result of the impedance filter) (xi; yi;), formthe desired robot position at any instant. The desiredglobal positions are converted into joint space demands(y2d ; y3d ), using the robot inverse kinematics. Two

independent controllers implement the desired jointspace positions.

External forces are resolved through the robot toobtain their influence on each joint (tex2; tex3). An equal,but opposite force is generated by the joint space open-loop force controllers, to reduce the effects of theseexternal forces on link position.

The forward kinematics of the joint positions revealthe robot end position in task space co-ordinates (x; y).External forces are measured at the robot end-pointusing a multiple axis force sensor (Richardson et al.,2003). Separate impedance filters convert the globalexternal forces Fx and Fy into changes of the x and y

desired task space co-ordinates, respectively. Note thatit is possible to implement different impedance filters fordifferent d.o.f. enabling one d.o.f. to be stiff whileanother is compliant. The mass element is used in hapticinterfaces where the robot is required to mimic thephysical characteristics of objects.

In the physiotherapy context only stiffness anddamping is required to move the arm to the correcttrajectory. When subjects experience difficulty followinga predefined trajectory, a force will exist between thehuman limb and robot. Due to the impedance controlstrategy this force is dependent on the stiffness anddamping parameters specified. To assess the controllerperformance, five alternative stiffness and dampingparameters were assessed. Due to the inertia of therobot links and delays in the robot response it is notpossible to implement zero damping and stiffness (thiswould result in zero force for any movement of therobot end-point). A stiffness value of 50 N/m anddamping of 50 N/ms represents the approximate mini-mum values (test 1). Test 2 increases the stiffness to170 N/m while maintaining damping at 50 N/ms. Thisassesses the performance of increased stiffness thatwould be used in a physiotherapy context, to increasethe force towards the desired trajectory if the patientwas experiencing difficulty. Test 3 implements a stiffnessof 50 N/m with damping of 170 N/ms. The increaseddamping here could be used to reduce tremor that maybe present in a patients motion. Test 4 increases thestiffness to 250 N/m and damping to 250 N/ms. This is

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x po

sitio

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) x

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forc

e (N

) y

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y v

eloc

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forc

e (N

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Fig. 11. Pole-placement impedance controller (K ¼ 50; C ¼ 50).


designed to be an extreme test of controller performancewith large forces resulting in little displacement. Theseare likely to be the largest values use due to the strengthand weight of the human arm combined with the motionof the robot. Finally test 5 implements a stiffness of130 N/m and a damping of 130 N/ms to test thecontroller performance at around the middle of theavailable stiffness and damping parameters. For all ofthese experiments a circular force crossing the x� and y-axis was applied by a human subject, resulting insinusoidal forces in the x and y direction.

Note there are now three graphs to demonstrate theperformance. The desired trajectory of the robot end-point if no force is applied to the robot.

The robot desired position altered due to the externalforce depending upon the specified damping and

stiffness parameters and finally the actual robot posi-tion. Note if the robot tracking was perfect the robotend position would be identical to the desired positionincorporating the external force. Below is a summary ofthe performance of each test.

Test 1. K=50, C=50 (Fig. 11): Sinusoidal forces of78 N are applied in x and y to the robot end-point whileit extends and retracts in the y-plane. A small delay ispresent in the x position response, however the magnitudeof the response is correct. The velocity of the x plane isalso accurately tracked. A similar performance is found inthe y response with the robot extending and retractingwhile accurately behaving with the correct stiffness anddamping due to the external forces.

Test 2. K=170, C=50 (Fig. 12): Sinusoidal forces of78 N are applied in x and y to the robot end-point while

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it extends and retracts in the y-plane. The x positiontracking has the correct shape however the magnitude ofthe motion is less than the desired. This is likely to bedue to errors in force measurement as the multiple axisforce sensor has been shown to be susceptible to inputtorque. The y response is again accurate with theposition response slightly delayed.

Test 3. K=50, C=170 (Fig. 13): Sinusoidal forces of78 N are applied in x and y to the robot end-point whileit extends and retracts in the y-plane. Due to theincreased damping the number of force cycles thesubject has applied to the robot end-position has

decreased. The increased damping results in less delaybetween the desired and actual position response. Againthe x position response has the correct shape but errorsin the magnitude due to input torque effecting forcemeasurement.

Test 4. K=250, C=250 (Fig. 14): Increasing thestiffness and damping results in the subject experiencingdifficulty applying external forces to the robot end-pointwhich are large enough to assess the controllerperformance. Due to this approximate sinusoidalforces of 715 N were applied in the x and y plane.This represents the most extreme test of controller

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performance with the controller required to accuratelycontrol the position while balancing these externalforces. Both the x and y responses are accuratelytracked with the magnitude of the x position responsenow greater than required.

Task 5. K=130, C=130 (Fig. 15): Sinusoidal forces of712 N are applied in x and y to the robotend-point. The reduction in the stiffness anddamping parameters from task 4 enables animprovement in the sinusoidal input force. Theposition tracking is worse than that of task 1 due tothe increased input forces. However both the x and y

responses have approximately the correct magnitudeand shape.

The results show the robot capable of implementingan impedance control strategy with varying stiffness anddamping parameters. These experiments have high-lighted the requirement for accurate force measurementwhich is not susceptible to input torque’s. Moreover anynoise from the force sensor is fed directly to thepneumatic cylinder due to the force balancing strategyand also into the demand position. This can result invibration at the robot end-point. This is particularlyapparent when large input forces are applied. Theseresults also highlight the need to assess any impedancecontrol strategy across a range of impedance’s as it ishighly likely that performance will be impedanceparameter specific.

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7. Conclusions

An impedance controller for a pneumatic robot ispresented here based around joint-space pole-placementposition controllers. The impedance control strategy hasbeen successfully implemented on the robot.

Due to the robot configuration a linearising strategyhas been implemented to improve the performance ofthe joint space controllers. The increased linearisationhas enabled an optimisation strategy to improve thePID joint space response. Moreover the increasedlinearity has enabled pole-placement (a model-basedlinear controller) to be implemented on the individualjoints, improving the step response by decreasing the risetime and reducing the overshoot. It may have beenpossible to implement a pole-placement controller on

the original system without linearisation however thiswould severely effect the controller robustness tomeasurement errors. Control signal saturation alsoeffected the performance of the joint space controllers,requiring the speed of the closed-loop poles to berestricted. Faster poles result in larger control signals,which would breach the saturation limit and result inpoor controller performance or instability. Actuatinglink 2 with two pneumatic actuators, rather than one,would increase the force output enabling higher forceoutputs before controller saturation.

Combination of the two joint space controllers usinginverse kinematics enabled x and y position tracking ofthe robot end-point. The robot tracked the desiredposition with a small error. The error is a result of thefore-mentioned control signal saturation problem.

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rce

(N)



The impedance controller was implemented success-fully and enabled the robot to respond differently tosimilar levels of input force. The large values of stiffnessand damping produced the poorest response due toincreased errors in force measurement and as largerforces are a more extreme measure of controllerperformance. Increasing the stiffness of the impedancecharacteristics results in the robot applying larger forcesto achieve the desired trajectory. Increasing thedamping restricts large velocities even if the robot isnot in the correct position. In a physiotherapycontext stiffness will be used to assist the patienttoward the required position. Patients with low abilitywill perform the exercises with high stiffness. Thestiffness will be decreased with the patients increasingability. The damping will be set depending upon the

level of tremors the patient experiences during motion.Both the stiffness and damping will be specified by atrained physiotherapist to ensure the correct therapy isimplemented.

The force sensor is the crux of the entire controlstrategy with errors in measurement resulting in anincorrect impedance response being implemented butalso providing an incorrect signal for the open-loopforce controllers. The force sensor used in theseexperiments is custom made and susceptible to error inforce measurement when torque is applied. Overall thecontrol strategy performed well enabling safe robot/human interaction. Future work will improve themultiple degree of freedom force sensor, improve theresponse of the joint space controllers and test the roboton a few sample patients.

ARTICLE IN PRESSR. Richardson et al. / Control Engineering Practice 13 (2005) 291–303 303

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