Control Strategies for Patient-Assisted Training Using the Ankle Rehabilitation Robot (ARBOT) 2013

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 6, DECEMBER 2013 1799

Control Strategies for Patient-Assisted TrainingUsing the Ankle Rehabilitation Robot (ARBOT)

Jody A. Saglia, Member, IEEE, Nikos G. Tsagarakis, Member, IEEE, Jian S. Dai, Member, IEEE,and Darwin G. Caldwell, Member, IEEE

Abstract—This paper presents the control architecture and ex-perimental results of the high-performance Ankle RehabilitationroBOT, ARBOT. The goal of this study is to design suitable con-trol algorithms for assisted training and rehabilitation of the anklejoint in presence of musculoskeletal injuries. A position controlscheme is used for patient-passive exercises, while an admittancecontrol technique is employed to perform patient-active exerciseswith and without motion assistance. The selection and design ofthe control algorithms are based on the analysis of the rehabilita-tion protocol taking into account the dynamics of the system andthe dynamics of the interaction between the human and the robot.The performance of the proposed control algorithms is analyzedthrough experiments on a group of healthy subjects.

Index Terms—Biomechatronics, parallel robots, rehabilitationrobotics, robot control.

I. INTRODUCTION

OVER the past decades, several studies demonstrated thatrehabilitation robots have a great potential in improving

diagnostics and physiotherapy outcome [1]–[4]. The main ad-vantage of the automated rehabilitation systems is the capabilityto perform a large number of repetitions, which was proved tobe extremely beneficial in the treatment of neuromuscular in-juries [5]. Furthermore, such systems turn out to be extremelyprecise diagnostic tools and can provide quantitative measuresof the patient’s recovery state after an injury [6]. As a result,many systems are being currently developed and tested [7] andrequire the implementation of advanced control strategies forassisted training.

In the aspect of ankle rehabilitation systems, the “Rutgers An-kle” introduced by Girone et al. [8], [9] was the first system tobe based on a parallel mechanism, with a position controller forpassive training to drive the patient’s foot along certain trajec-tories and a force controller for active (only resistive) exercises.

A single degree of freedom (DOF) device proposed by Zhanget al. [10] employed velocity control to mobilize the impaired

Manuscript received July 8, 2011; revised October 27, 2011, February 5,2012, and May 20, 2012; accepted July 25, 2012. Date of publication Septem-ber 6, 2012; date of current version December 11, 2013. Recommended byTechnical Editor A. Menciassi. This work was supported by the Istituto Italianodi Tecnologia in collaboration with King’s College London.

J. A. Saglia, N. G. Tsagarakis, and D. G. Caldwell are with the Isti-tuto Italiano di Tecnologia, 16163 Genoa, Italy (e-mail: [email protected];[email protected]; [email protected]).

J. S. Dai is with King’s College London, London, WC2R 2LS, U.K.,and also with the Istituto Italiano di Tecnologia, 16163 Genoa, Italy (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2012.2214228

foot in a certain range of motion (ROM) and a torque sensor tomonitor the resistive torque provided by the patient’s foot. This1-DOF system could perform only passive exercises.

A wide set of rehabilitation exercises were proposed by Yoonet al. [11], ranging from passive mobilization (ROM recovery)up to proprioceptive training such as balance exercises. Posi-tion and impedance control theories were used to implementthe rehabilitation regimes. Furthermore, a pseudo-assistive con-troller was developed to assist the patient to complete the giventask. The performance was limited by the actuation technologyused (i.e., pneumatic cylinders) and the indirect estimation ofinteraction force/torque (FT).

Torque sensing for assistive–resistive exercises was used byLin et al. [12]. A fuzzy logic controller, which regulated the jointangle and torque of a single DOF device, was implemented toassist or resist the patient when trying to follow a target on ascreen. Constant assistive and resistive torques were used foractive training.

The passive mechatronic device MecDEAR by Bucca et al.[13] used only position control for passive ROM recovery ex-ercises and did not provide any control strategy for active exer-cises.

Although all the works mentioned previously are well justi-fied and show promising results, none of the systems met therequirements considered in this study such as providing controlalgorithms for most of the exercises foreseen by standard reha-bilitation protocols, including passive and active training witheffective assistive and resistive capabilities.

The “Rutgers Ankle” can be considered the most successfulsystem so far. However, the system did not provide assistance incase of patient’s limited motion capabilities. The rehabilitationsystems introduced in [11] and [12] employed some sort ofassistive control; however, the amount of assistive torque/motionneeds to be set a priori by the physiotherapist and does not adaptto patient’s motion during training.

The goal of this study was to design a control frameworkfor the ankle rehabilitation robot ARBOT [14], which allows usto perform most of the rehabilitation exercises foreseen by thestandard rehabilitation protocols and provide assistance whenthe patient’s ankle mobility is limited.

Based on the rehabilitation robot introduced in [14], see Fig. 1,this paper presents the development of the control architecturefor this ankle rehabilitation system. The control system needsto facilitate a wide range of exercises defined by the rehabili-tation protocol (introduced in [14]) and serve as a tool for thephysiotherapist to treat patients in a faster and more effectivemanner. To achieve this, a set of control algorithms, such as po-sition, admittance, and admittance-based assistive control have

1083-4435 © 2012 IEEE

1800 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 6, DECEMBER 2013

Fig. 1. High-performance ankle rehabilitation robot.

been developed, implemented, and tested on a group of healthysubjects.

In this paper, Section II briefly describes the ankle rehabil-itation robot ARBOT, while Section III reports on the analy-sis of the dynamics of the interaction. Consequently, SectionIV presents the control algorithms and shows how those algo-rithms are suitable for the needs of the various rehabilitationexercises. The stability of the proposed control schemes is stud-ied and presented in Section V. Finally, the experimental resultsare reported in Section VI and discussed in Section VII.

II. ANKLE REHABILITATION ROBOT

Fig. 1 demonstrates the ankle rehabilitation robot used inthis study. The robot is basically a 3UPS/U1 parallel mecha-nism with two rotational DOFs. The mechanical structure iscomposed of a fixed base, a central strut [15], [16], a movingplatform, and three actuated limbs with a UPS kinematic chain.The platform is attached to the central strut through a universaljoint. As depicted in Fig. 1, the patient’s foot is constrained tothe foot plate with Velcro stripes.

The limb prismatic joint is actuated by a custom-designedlinear actuator. This actuator makes use of a brushed DC motorMaxon RE40 and a planetary gearbox with a reduction ratio ρof 12:1. A capstan system of pulleys together with a steel cabletransmission transforms rotary motion of the motor into linearmotion of the piston. Optical encoders of 4095 ppr mounted onthe DC motor shafts provide a position resolution of 1.278 μmat the prismatic joint.

The custom-designed actuator can provide a peak force ofover 1100 N and a maximum speed of 60 cm/s. The resultantmaximum device output torque is 120 N·m and the maximumspeed is 500◦/s. More details on the system can be found in [14].

An ATI six-axis FT sensor mounted between the movingplatform and the footplate senses the human–robot interactionforce and torque. The device is interfaced to a standard PCthrough a CAN BUS interface.

1U, P, and S stand for universal, prismatic, and spherical joint, respectively.An underlined letter represents an actuated joint.

Fig. 2. Equivalent kinematic tree. Note, S, U, P, and G stand for spherical,universal, prismatic joints, and ground.

III. DYNAMICS OF INTERACTION

A. Mechanism Dynamics

The dynamics of the redundantly actuated parallel mecha-nisms can be analyzed by considering the dynamics of an equiv-alent tree system [17]–[22], generated by cut-opening some ofthe passive joints in order to break all the kinematic loops (seeFig. 2). In this case, kinematic loops have been cut at the spheri-cal joints in order to create three identical limb tree systems anda strut/platform tree system. The dynamics of the equivalent treesystem is expressed by

Mt (q) q + Ct (q, q) q + Nt (q) = τ (1)

where Mt ,Ct , and Nt are the inertia, coriolis and centrifugaland eventually gravity matrices of the tree system, respectively,q is the vector of generalized coordinates which contains all ac-tive (actuated) and passive joint variables. The vector τ containsforces and torques of the tree system.

Considering a set of independent generalized variables qin ,in this case the two angular DOFs of the platform, the mappingbetween the independent platform torques and those of the treesystem can be expressed as

τin = JTτ (2)

while the actuator forces can be mapped to the independentplatform torque with the relation

τin = JTr fa . (3)

The matrix J is the nonsquare Jacobian matrix that relatesthe time derivative of the generalized cordinates of the tree sys-tem q with the time derivatives of the platform independentcoordinates qin , while Jr is the nonsquare Jacobian matrix ofthe redundantly actuated parallel mechanism and f a the actu-ator forces. Inserting (1) into (2) and (3) and expressing the

SAGLIA et al.: CONTROL STRATEGIES FOR PATIENT-ASSISTED TRAINING USING THE ANKLE REHABILITATION ROBOT (ARBOT) 1801

generalized coordinates q in terms of independent coordinatesqin , yield the following equation of motion (EoM) of the parallelmechanism:

Mqin + Cqin + N = JTr f a (4)

where

M = JTMtJ

C = JTMt J + JTCtJ

N = JTNt .

Therefore, the inverse dynamics is given by

f a = J+Tr (Mqin + Cqin + N) (5)

with J+Tr being the pseudo-inverse Jacobian matrix of the re-

dundantly actuated parallel mechanism, computed in the formthat minimizes the actuator forces [23]–[26].

B. Dynamics of Human–Robot Interaction

The dynamics of the robotic rehabilitation system is describedby (5). In a scenario where the robot is applied to rehabilitation,the interaction between the robot and the human as definedby the exercise must be included in the dynamic model. Theinteraction FT can be included in (5) as

fa = J+Tr (M qin + Cqin + N + τ patient) (6)

where τ patient is the torque vector applied by the user to thefootplate. Further to this, when the patient needs to perform ac-tive exercises, it may be necessary to replicate certain dynamicsat the end-effector of the system via imposing specific inertia,stiffness, and damping parameters. In this case, the torque felt bythe patient will be equal to those obtained from the replicationof the desired mass–spring–damper system as

τ patient = τ virtual.

Hence, the expression in (6) becomes

fa = J+Tr (Mqin + Cqin + N + τ virtual) (7)

where τ virtual is the vector of torques required to replicate thedesired dynamics of the regime (see Section V).

IV. CONTROL STRATEGIES FOR REHABILITATION EXERCISES

The rehabilitation protocol for ankle injuries can be seen inTable I [14]. To permit effective execution of these regimes, thecontrol architecture employs a specific control scheme appro-priate to satisfy the requirements of particular exercises.

In the early stage of the therapy, the patient can hardly movehis/her foot; therefore, a passive exercise which delicately movesthe patient’s foot is needed.

Such a task can be accomplished by a position control schemewhich drives the injured foot/ankle along a certain trajectory ata moderate speed. Trajectory parameters, such as wave type,speed, amplitudes, and number of repetitions, can be set by thephysiotherapist.

In order to allow the patient to fully regain his/her ROM and toevaluate the patient’s progress of the first stage of rehabilitation,

TABLE ICONTROL ALGORITHMS FOR REHABILITATION EXERCISES

active exercises can be executed by the device using an assistivecontrol scheme based on admittance techniques.

Suppose the patient is capable of providing moderate torquelevels to initiate the motion; however, he/she cannot provideenough torque to complete the exercise trajectory. In this case,the application of the patient torque to the footplate can be moni-tored by the installed FT sensor, therefore providing informationto the assistive controller about the patient intentioned motion.The assistive control (see Section IV-C) supplies the additionaltorque effort required in order to assist the patient to completethe motion.

The position control algorithm is also used for isometricstrengthening exercises. In this case, the ankle rehabilitationrobot is controlled to maintain a fixed position while the pa-tient tries to apply a certain level of torque to the footplate. Theapplied torque is measured by the FT sensor. Strength train-ing includes also isotonic exercises, as in Table I. For this kindof regime, an admittance controller is implemented in order toprovide a certain resistance to the patient’s motion.

In the last stage of the rehabilitation process, the patient has toundergo proprioceptive training. Balance exercises are typicalfor this kind of training and in such a case, the patient has to standon top of the rehabilitation robot and try to keep the balance,as if he/she was using a wobble board. Since position, velocity,and the dynamic behavior can be controlled, more sophisticatedexercises can be performed with this system, than those allowedby traditional tools (foam rollers, wobble boards, etc.). Hybridcontrol (combination of position and force control) is used todesign this type of exercises.

The study presented in this paper focuses on the first two stepsof the rehabilitation protocol while proprioceptive training willbe treated elsewhere.

A. Patient-Passive Exercises

As mentioned previously, when the patient is passive, therobot is controlled to follow a reference trajectory imposed bythe therapist or to hold a certain position. In order to obtainhigh position tracking accuracy [27], a computed-torque con-troller was implemented. The inverse dynamics introduced in(5) is used to compute the actuation forces required by the re-habilitation robot to follow a certain trajectory. The EoM istherefore used in the control loop to linearize the system anda proportional-integral-derivative controller is used to compen-sate for modeling errors and its contribution is added to thereference acceleration.


Fig. 3. Assistive control model.

B. Patient-Active Exercises: Strengthening

When considering strengthening exercises, two differentcases need to be distinguished. As mentioned previously, iso-metric training requires a fixed position; therefore, a computed-torque control algorithm as the one used for patient-passiveexercises can be implemented.

To perform isotonic exercises or other types of resistive train-ing, an admittance control is chosen. As in (7), a certain dynamicbehavior of the rehabilitation device can be simulated in relationto the patient–robot interaction.

By measuring the interaction torque applied by the user tothe footplate, it is possible to compute the reference position re-quired to render certain mass, stiffness, and damping parameters.Hence, the reference position qinr

is obtained with an admittancefilter as

qinr=

τm

(ms2 + bs + k)(8)

where m, b, and k are the desired mass, damping, and springparameters, and τm is the interaction torque measured with thesix-axis FT sensor.

Using the computed-torque control scheme, the dynamicsexpressed by the denominator of (8) can be realized, since allthe other dynamic components are compensated by the systemlinearization.

C. Patient-Active Exercises: Assistance

Assistive control is required in the early stage of rehabilitationwhen the patient cannot complete the movement alone and needsto reacquire his/her ROM. Assistance can be provided withthe robot, by monitoring the interaction torque between theuser/patient and the robotic device.

To achieve motion assistance, the robot is controlled in ad-mittance with the reference position of the assistive (i.e., admit-tance) filter being “modified” in the direction toward which thepatient is attempting to move. The patient’s intended directionof motion is considered to be the direction of the measured inter-action FT. As in Fig. 3, when the patient applies a torque along acertain direction, the equilibrium point of the assistive networkwill be moved toward the same direction, therefore generatinga “pulling effect.”

This behavior is achieved by measuring the interaction FTwhich is then integrated over time and used to update the robotreference position, in terms of equilibrium point of an assistivespring-damper network.

Fig. 4. Patient–robot dynamic model.

In particular, the reference position is obtained from

qinr=

τm

(bs + k)+ qas (9)

with

qas =∫ t

0kaτm dt (10)

where qas is the assistive component of the position referenceand ka is a weight constant that determines the level of assis-tance. The greater the value of ka , the higher the assistanceprovided. The torque is measured with the six-axis FT sensor.

V. STABILITY OF THE CONTROLLED SYSTEM

The stability of the position control, based on the computationof the actuator torques via computed–torque control, is wellknown and documented in the literature. This is also true for theadmittance controller, where the reference position is computedthrough the measured torque and an admittance filter as in (8).

On the other hand, the stability of the assistive controllerneeds to be proved and details on the stability analysis are givenin this section.

A. Stability Analysis of the Assistive Control Algorithm

Fig. 4 shows the dynamic model of the rehabilitation robotcontrolled in assistive mode, linked with the patient’s leg.

The model represented in Fig. 4 includes the mechanics ofthe human ankle complex and the mechanics of the assistancefilter. The interaction between the patient and the rehabilitationrobot device is measured by the FT sensor mounted betweenthe platform and the footplate. The measured torque τm resultsfrom the difference of the torque applied by the human τpatientand the assistive torque provided by the device τ as

τm = τ patient − τ as . (11)

By introducing the variable s, it is possible to analyze thesystem in the frequency domain. Therefore, the expression ofthe assistive motion component becomes

qas = Gaτm (12)


with

Ga =[

GaP D

Ga IE

]=

1s

[kaP D

ka IE

]

where GaP D and Ga IE represent the transfer functions betweenthe measured torque τm and the equilibrium position qas of theassistive network. The assistive network is expressed as

Gv = bv s + kv (13)

where bv and kv are the damping and stiffness parameters.The spring–damper network in (13) relates the assistive

torque and the difference between the equilibrium position ofthe network and the actual position of the patient–device systemas

τ as = Gv (qas − qpatient). (14)

The dynamics of the human can be expressed as the differenceof the assistive torque and the dynamics of the foot, resulting in

τ patient = Ghqpatient − τ as (15)

with Gh = [GhP D

Gh IE

], where GhP D and Gh IE are the equiva-

lent impedance of the human ankle for foot plantar–dorsiflexionand inversion–eversion, respectively (where for simplicity thecoupling effects have been neglected).

Considering a rehabilitation exercise where only plantar–dorsiflexion are involved, with GhP D = IhP D s2 + bhP D s +khP D , and by substituting (11) into (12), then combining with(14) and (15) yield

τasP D

τpatientP D

=GvGaP D GhP D − Gv

GvGaP D GhP D + GhP D + Gv(16)

which represents the assistance ratio.By substituting (14) and (15) into (11) and rearranging yields

qpatientP D

qasP D

=1 + 2GaP D Gv

GaP D GhP D + 2GaP D Gv(17)

which represents the transfer function between the equilibriumposition of the assistive spring–damper network as input and thehuman–robot measured position. Expanding the transfer func-tion results in

qpatientP D

qasP D

=((1/kaP D ) + 2bv ) s + 2kv

IhP D s2 + (bhP D + 2bv ) s + (2kv + khP D ).

(18)It is possible to notice that the transfer function of the human–

device system, controlled in assistive mode, results in a second-order system with certain inertia, damping, and stiffness param-eters.

The characteristic equation of the transfer functions in (18) is

IhP D s2 + (bhP D + 2bv ) s + (2kv + khP D ).

This characteristic equation is subject to change as a result ofthe variation in the mass and damping coefficients of the humanankle/foot. Note that if (bhP D + 2bv ) > 0 and 2kv + khP D > 0,then the characteristic equation is Hurwitz. This may also be

Fig. 5. Bode diagram of the transfer function that relates the displacement ofthe foot with the equilibrium position of the virtual admittance filter.

rewritten as

2kv + khP D

IhP D

= ω2n

ζ =bhP D

+ 2bv

2IhP Dωn

=bhP D

+ 2bv

2√

IhP D(2kv + khP D

)(19)

where ωn is the natural frequency for a stable, second-order,closed-loop system and ζ is the damping ratio. Through the con-trol parameters of the assistive spring–damper network (kv , bv ),independent regulation of the natural frequency and damping ra-tio can be obtained.

Considering the scenario in which the dynamics of the humanankle is precisely known, the stiffness and damping values of theassistive network could be selected in order to obtain a desiredsystem response. Since this is not true in the real case, certainassumptions need to be made in order to guarantee the stabilityof the system.

According to [28], the impedance of a youngster’s an-kle is characterized by a mean damping value of bhP D =2 N·m·s·rad−1 , an inertia value of the foot of IhP D = 0.22 kg·m2 .

Given the dynamic characteristics of the human ankle, it ispossible to calculate the parameters of the spring–damper sys-tem such as the complete human–device system features a cer-tain bandwidth and is stable. Therefore, to obtain device systembandwidth of 30 Hz, the stiffness parameter kv and the dampingparameter bv were chosen as

kv = 10N · m · rad−1

bv = 20N · m · s · rad−1

and the value of kaP D , which determines the level of assistance,was set to kaP D = 1.

Using these parameters, together with those relative to thehuman foot dynamics aforementioned, it is possible to draw aBode diagram of the transfer function in (18). Fig. 5 shows the


Fig. 6. (a) Equilibrium position of the admittance filter and the real positionof the patient. (b) Human and the assistive torques versus time.

one input–one output Bode plot relative to a plantar–dorsiflexionmotion.

From the Bode diagram shown in Fig. 5, it is possible tonotice that the frequency response of the human–robot system,under assistive control, is that of a single-order system with acutoff frequency of about 30 Hz.

B. Simulation of Assistive Control

A simulation was performed by giving as input a pulse of1 N·m for a period of 0.5 s to the human torque and evaluatingthe human–robot displacement together with the equilibriumpoint of the admittance filter. Fig. 6(a) reports the trajectory ofthe equilibrium point of the admittance filter compared with realposition of the patient’s ankle.

It is clear that the equilibrium point moves faster than thehuman–robot system and, as a result, the patient is pulled bythe rehabilitation robot toward the direction of attempted mo-tion. Fig. 6(b) shows the torque applied by the patient and thatprovided by the assistance. The simulation results had beenobtained with an assistance level kaP D = 1. The amount of as-sistive torque can be increased by setting kaP D to a higher value.

TABLE IIADMITTANCE CONTROL PARAMETERS

Fig. 7. Experimental evaluation of stiffness.

Increasing the assistance level implies an increase of theamount of assistive torque provided by the device.

On the other hand, reducing the level of assistance (e.g.,kaP D < 1), it reduces the amount of help provided to the pa-tient’s intentioned motion. In such a case, the patient initiallyperceives a certain resistance given by the admittance filter. Atthe same time, the equilibrium point starts to be upgraded ac-cording to the torque measured. Once the difference betweenthe equilibrium point and the patient position becomes positive,the rehabilitation robot will start assisting the motion.

Furthermore, increasing damping and stiffness values ofthe assistive network improves the position tracking perfor-mance when considering the equilibrium point as the referenceposition.

VI. EXPERIMENTAL RESULTS

A. Torque-Sensing-Based Admittance Control

Using the computed-torque control scheme and the expres-sion in (8), experiments were performed in order to evaluate theability of the system to reproduce certain stiffness and dampinglevels.

The parameters of the admittance filters are given in Table II.Note that the mass m has been set to zero and, in the case of purestiffness simulation, a small damping of bv = 1 N·m·s·rad−1 wasnecessary to guaranty system stability. The experiments havebeen performed at low speeds (when reproducing pure stiffness)in order to avoid the effect of inertial torques and forces. Thetrials have been performed with a young volunteer, sitting on achair with his right foot constrained to the robotic device. Thesubject was instructed to perform voluntary plantar–dorsiflexionmovements at self-selected low speed (maximum angular speedreached was 0.06 rad/s) for the stiffness and high speed (as in


Fig. 8. Experimental evaluation of damping.

TABLE IIIADMITTANCE CONTROL RESULTS—STIFFNESS

TABLE IVADMITTANCE CONTROL RESULTS—DAMPING

Fig. 8 the speed ranged between 0.5 and 2 rad/s) for dampingexperiments. The results are shown in Figs. 7 and 8 and reportedin Tables III and IV. The graphs present the measured torqueapplied by the user to the footplate versus the platform positionand velocity computed through the forward kinematics from themeasured limb lengths. It is possible to see that the stiffnessfelt by the user in Fig. 7 and Table III matches the referencestiffness value. Table III reports the slopes of the curves shownin the graph.

Looking at the last column of Table III, it is evident that therobot performance decreases with the increase of desired stiff-ness. The reason is that for high desired output stiffness, theeffect of the actuator passive compliance (due to the elasticityof the transmission cable) on the overall stiffness increases. Thiscan be improved by either adding pretension in the redundantparallel mechanism using the actuation force null space or con-trolling the actual position of the piston rather than the positionof the motor (see [25]).

Fig. 8 shows the results for the rendering of damping. Thenoise that can be observed in the curves is due to the numericalderivation of the angular position. It can be seen in Table IV thatthe efficacy of the robot in rendering damping is high for all thereference damping values.

Fig. 9. Subject’s leg with two pairs of electrodes for EMG signals collection.

B. Torque-Sensing-Based Assistive Control

A first experiment was conducted in order to evaluate theproposed assistive control algorithm. A young male subject wasasked to perform the experiment. The subject right foot wasconstrained to the footplate and two pairs of electrodes wereapplied to his leg to measure the muscle activity during motionaccording to [29], see Fig. 9.

During the experiment, the electromiographic (EMG) signalswere recorded in order to evaluate the amount of subject’s mus-cular effort. The signals were collected via surface electrodesplaced on leg flexor (tibialis anterior) and extensor (gastrocne-mius) muscles. The EMG signals collected by a portable deviceat the frequency of 128 Hz had to be filtered to remove artifactsand interference [30]. In particular, a preliminary high-pass fil-tering at 20 Hz was employed to remove artifacts and trendcomponents. Subsequently, the signal was rectified and finallylow-pass filtered at 5 Hz to obtain an envelope.

Two trials were conducted and consisted in extending andcontracting the foot to reach about 15◦ of maximum extensionand return back to the start position in presence and absence ofmotion assistance. During the first extension/flexion trial, thesubject experienced a zero counteracting torque with the reha-bilitation device being controlled for zero torque. In the secondtrial, the admittance parameters are set to kv = 80 N·m/rad andbv = 8 N·m·s/rad, resulting in an overall system bandwidth ofabout 10 Hz. These spring–damper network parameters kv andbv were used with the addition of the assistive control com-ponent described in Sections IV-C and V. The results of thisexperiment can be seen in Fig. 10.

Fig. 10(a) reports the amount of EMG signals required toperform the motion, while Fig. 10(b) depicts the angular dis-placement of the foot/platform. Dashed lines represent motionwithout assistance (first trial), while continuous lines show mo-tion with assistance (second trial).

It is possible to notice that, during the first trial, the subjecthas to provide a certain effort in terms of muscle activity [seeFig. 10(a)]. Differently, in the second trial, the application ofthe assistive control keeps the peak force applied by the subjectat lower level during the initiation of the movement.


Fig. 10. Comparison of human–robot interaction with and without assistivecontrol.

Once the subject applies a torque to initiate the motion, theassistive control becomes active, by updating the equilibriumposition qas [shown in (9)] of the assistive spring–damper net-work. This results in the device starting to pull the subject’s foottoward the direction he previously begun the movement. Notethat the maximum speeds of the two trials [when the foot movesfrom the starting position to the target position of about 15◦,Fig. 10(a)] are comparable and reach about 40◦/s. As for thereturn phase, the foot motion is helped by muscle relaxation.

In order to further evaluate the effectiveness of the proposedassistive controller, more experiments have been performed witha group of five healthy subjects. The experimental group wasa sample of male subjects, aged between 30 and 35, with anaverage height of 1.73 ± 0.15 m and a mean weight of 75.4± 3.8 kg. Each subject was in a sitting position with the rightfoot constrained to the ankle rehabilitation robot, as in Fig. 9.The robot was equipped with a screen displaying the angularposition of the subject’s foot (which corresponded to the robotplatform as well). The subject was instructed to plantarflex hisfoot from the initial position of 0◦ to the target position whichwas represented by the area between 15◦ and 20◦. Fig. 11 showsthe experimental results.

The curves reported in Fig. 11(a)–(c) represent the averageand standard deviation of the results obtained from the fivesubjects. Fig. 11(a) shows the equilibrium position of the assis-tive admittance filter qasP D generated by (10) and the effectiveposition of the robot and the subject’s foot qpatientP D

. It is pos-sible to notice that the equilibrium position is moved towardthe target position and the subject’s position follows due to thepulling assistive torque τasP D , as shown in Fig. 11(b). More-over, Fig. 11(b) depicts the subject’s torque τpatientP D

whichhas been computed using (11) (where τas is the assistive torqueproduced by the robotic device estimated through motor currentmeasurement). It is noticeable that the magnitude of the assistivetorque is comparable with and greater than the subject’s torque.Fig. 11(c) shows the instantaneous work done by the interactionbetween the subject and the robotic device which was obtainedconsidering the interaction torque τmP D and the instantaneousfoot-robot displacement ∂qpatientP D

. In other words, it is the

Fig. 11 Experimental results of assisted motion.

work that the patient does on to the device. As reported in thegraph, the work becomes negative during the motion meaningthat the device is pulling the subject in the direction of motion.

These results demonstrate the effectiveness of the proposedassistive controller and confirm the results reported in Fig. 10. Itshould be noted that by varying the assistance constant in (12),it is possible to regulate the level of assistive torque.

VII. CONCLUSION

This paper presented the control schemes of a high-performance parallel robot used for robot-aided ankle exercises.


The rehabilitation protocol has been considered as the basis fordesign of the control strategies. Both patient-passive and activeexercise modes have been addressed using position and admit-tance control schemes and the stability of the assistive controllerwas addressed. The experimental trials of the stiffness/dampingtracking demonstrated the high performance of the rehabilita-tion robot and the experimental results obtained on a groupof healthy subjects showed the effectiveness of the proposedadmittance-based assistive controller.

The control algorithms presented in this study will serve asframework for the design and development of patient-orientedrehabilitation exercises.

Future work will look at the development of rehabilitationexercises in collaboration with a team of clinicians and theintegration of a virtual environment to stimulate the patientduring training. Further studies will also focus on the integrationof the EMG information in the control algorithms.

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Jody A. Saglia (M’09) received the B.Eng. degreein automation engineering and the M.Sc. degree inmechatronics engineering from the Polytechnic ofTurin, Turin, Italy, in 2004 and 2007, respectively,and the Ph.D. degree from King’s College London,London, U.K., in 2010.

He was a researcher at King’s College Londonin 2006. Since 2007, he has been a Research Fellowat the Istituto Italiano di Tecnologia, Genoa, Italy,where is currently a Postdoctoral Researcher in theDepartment of Advanced Robotics. His research in-

terests include mechanisms design, rehabilitation robotics, mechatronic design,actuation systems, and human–robot interaction.

Dr. Saglia received the Professional Engineering Publishing Award from theJournal of Systems and Control Engineering in 2009.


Nikos G. Tsagarakis (M’00) received the B.Eng. de-gree in electrical and computer science engineeringfrom the Polytechnic School of Aristotle Universityof Thessaloniki, Thessaloniki, Greece, in 1995, andthe M.Sc. degree in control engineering and the Ph.D.degree in robotics from the University of Salford, Sal-ford, U.K., in 1997 and 2000, respectively.

He is currently a Senior Researcher at the IstitutoItaliano di Tecnologia, Genoa, Italy, where he is re-sponsible for humanoid design and human-centeredmechatronics. He is the author or coauthor of more

than 150 papers in research journals and international conference proceedings,and is the holder of six patents.

Dr. Tsagarakis received the Professional Engineering Publishing Award fromthe Journal of Systems and Control Engineering in 2009 and the Best PaperAward at the International Conference on Advanced Robotics in 2003. He wasalso a finalist for the Best Entertainment Robots and Systems—20th Anniver-sary Award at the International Conference on Intelligent Robots and Systems(IROS) in 2007 and for the Best Manipulation Paper at the International Confer-ence on Robotics and Automation (ICRA) in 2012. He has been on the programcommittees of more than 40 international conferences including ICRA, IROS,Robotics Science and Systems, and Humanoids.

Jian S. Dai (M’95) received the B.Sc. and M.Sc. de-grees from Shanghai Jiao Tong University, Shanghai,China, and the Ph.D. degree from the University ofSalford, Salford, U.K.

He became a Lecturer at Shanghai Jiao Tong Uni-versity in 1985. In late 1980s, he joined the Univer-sity of Salford as a Research Scholar. In 1997, hewas a Senior Lecturer in mechanisms and roboticsat the University of Sunderland. In 1999, he joinedKing’s College London, University of London, Lon-don, U.K., as a Lecturer, where he later became a

Reader in mechanisms and robotics and the Chair of mechanisms and robotics.He is also with the Istituto Italiano di Tecnologia, Genova, Italy. He has authoredor coauthored more than 400 papers. His research interests include screw the-ory, mechanisms development, reconfigurable mechanisms and robotics, mul-tifingered robot hands, grasping and manipulation, rehabilitation robotics, andmechanisms and robotics in assembly and packaging.

Dr. Dai is the recipient of a number of best journal papers and conferencepapers awards, and many IEEE and American Society of Mechanical Engineers(ASME) service awards. He is the Chair of Mechanisms and Robotics, and aFellow of ASME and the Institution of Mechanical Engineers.

Darwin G. Caldwell (M’92) received the B.Sc. andPh.D. degrees in robotics from the University ofHull, Kingston upon Hull, U.K., in 1986 and 1990,respectively.

He is currently a Director at the Italian Institute ofTechnology, Genoa, Italy. He is a Visiting/HonoraryProfessor at The University of Sheffield, The Uni-versity of Manchester, The University of Bangor,King’s College London, all in the U.K., and Tian-jin University, China. He is the author or coauthor ofmore than 350 academic papers, and holds 15 patents.

His research interests include innovative actuators, humanoid and quadrupedalrobotics and locomotion (iCub, HyQ, and COMAN), haptics, exoskeletons,dexterous manipulators, and rehabilitation and surgical robotics.

Dr. Caldwell is the recipient of several awards from international journalsand conferences. He is an Associate Editor for the IEEE/ASME TRANSACTIONS

ON MECHATRONICS and a member of the Editorial Board of the InternationalJournal of Social Robotics and Industrial Robot.

Control Strategies for Patient-Assisted Training Using the Ankle Rehabilitation Robot (ARBOT) 2013

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