A Methodology to Control Walking Speed of Robotic GaitRehabilitation System using Feasibility-Guaranteed Trajectories

Chan-yul Jung1, Junho Choi2, Shinsuk Park3, and Seung-Jong Kim2

Abstract— This paper presents a novel methodology to con-trol walking speed of an exoskeleton for gait rehabilitationof stroke patients using feasibility-guaranteed trajectories.The controller uses interaction forces to estimate the desiredwalking speed. Instead of allowing each joint to move around anominal trajectory, which could lead to infeasible gait patterns,the control algorithm proposed in this paper chooses jointtrajectories for desired walking speed, which generates feasiblegait patterns. With the interaction forces measured duringwalking, the walking speed intended by the patient is estimated.Then, based on the estimated walking speed, a referencetrajectory stored in a database, which is checked if kinematicconstraints required for walking are met, is chosen. Sincechecking feasibility is performed off-line before the trainingsessions, it is possible to ensure stability of walking withoutcausing any computational time on-line.

I. INTRODUCTION

Gait rehabilitation using robots has been paid much at-tention by researchers since robots are suitable for labor-intensive and repetitive tasks such as rehabilitation. Duringgait rehabilitation using robot systems, it is typical for thepatients to remain passive during entire rehabilitation sessionwhile the robots move the legs [1].

However, it was found that keeping the patients motivatedwas critical for effective rehabilitation using robots [2]. Inorder to keep the patient motivated, controlling the robotsystem according to the intention of the patients has beenwidely studied. Banala et al. showed that the patients areallowed to move their legs near the nominal trajectories in[3]. While walking with the exoskeleton, the patients wereable to move along the pre-defined trajectories within certainboundaries around the trajectories in Cartesian space. In [4]and [5], the patients were allowed to move their legs so thatthe trajectories in the joint space were deviated from thepre-defined nominal trajectory. Increased active participationin gait training using robotic orthosis was reported whenthe patients were allowed to deviate from the pre-definedtrajectory in [6]. EMG signals measured from a patient wereused to reflect the intention of the patient in [7] and [8].

*This research was supported by the Korea Institute of Science andTechnology (KIST) Institutional Program(Project no.2E25503).

1Chan-yul Jung is with the department of mechanical engineering, Koreauniversity, Seoul, Korea and the Center for bionics, Korea Institute ofScience and Technology, Seoul, Korea sambbayi@korea.ac.kr

2Junho Choi and Seung-Jong Kim are now with the Center forBionics, Korea Institute of Science and Technology, Hwarangno 14-gil5, Seongbuk-gu, Seoul 136-791, Republic of Korea {junhochoi,sjongkim}@kist.re.kr

3Shinsuk Park is with the department of mechanical engineering, Koreauniversity, Seoul, Korea drsspark@korea.ac.kr

Changing walking speed according to the intention ofthe patients is one of ways to keep the patient motivatedduring training sessions. In [9], the speed of a treadmillwas controlled using the position of the patient who wassupported by a body weight support system. Since the patientis suspended by a sling from the body weight supportsystem, the patient is able to swing back and forth. For mostof gait rehabilitation systems using exoskeletons, however,the positions of the patients are controlled and not changedeven if the patients desire to. Therefore, controlling thetreadmill speed using changes in position is not appropri-ate for rehabilitation with exoskeletons. To overcome theproblem, interaction force that is applied to an exoskeletonby the patient was measured during swing phase and usedto control the treadmill speed [10]. Then, the force wasclassified into three categories, which indicate three differentwalking speeds. The threshold values for each category weredetermined by a physical therapist. In [11], a methodology tochange treadmill speed with measured external force actingof the body of the patient was proposed. When walking withan exoskeleton on a treadmill, each joint was controlled tocompensate the gravity and friction torque so that the patientwas allow to move their joint without any resistance from therobot. Then sheer force on the surface of the treadmill wasestimated to be used to control the speed of the treadmill.

Although it is desirable to allow the intention of thepatients within the control loop of the robot system in orderto motivate the patients, it is not desirable to let the patientsentirely control the robot with their intention, since it mayproduce infeasible gait patterns, which, in turn, results indamage to the robot or the patient. Therefore, it is importantto keep the system remain stable while the intention of thepatients is allowed to be a part of the control loop of thesystem.

In this paper, a methodology to reflect the intention ofthe patients to the speed of walking and to ensure feasibilityand stability of the system at the same time is presented.Interaction force between the patient and the exoskeletonwas measured. Using the admittance model, desired changesin walking speed are calculated. In order to ensure that theresulted trajectories are feasible and safe, trajectories storedin a database, which are checked for feasibility a priori, areused to change the walking speed. Since only feasible tra-jectories are used, which are assumed to be available at anydesired walking speed, the stability of the system is ensured.Section II describes the COWALK system designed for gaitrehabilitation of stroke patients with hemiplegia. Section IIIexplains the control method to change the walking speed.

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Section IV shows the experimental result. Conclusion isgiven in Section V.

II. COWALK

In this section, “COWALK” is introduced. More detailson COWALK are found in [12]. COWALK is a gait trainingsystem for rehabilitation of stroke patients with hemiplegia.It is composed of an exoskeleton, a treadmill, and a bodyweight support system, see Fig. 1.

Fig. 1. COWALK system is composed of (A)Body Weight Support,(B)Gravity Compensator, (C)Exoskeleton, and (D)Treadmill.

TABLE IMOTION PLANES OF COWALK

Joints Plane Motion ActuationFor-/Backward trans. Active

Transverse Medial/Lateral trans. ActivePelvis Rotation Active

Sagittal Upward/Downward trans. PassiveSagittal Flexion/Extension Active

Hip Coronal Adduction/Abduction PassiveKnee Sagittal Flexion/Extension Active

Sagittal Dorsiflexion/Plantar Flexion ActiveAnkle Coronal Inversion/Eversion Passive

The exoskeleton has 14 degrees of freedom. Four ofthem are for pelvic motion. Nine degrees of freedom areactuated using 10 actuators and 5 degrees of freedom remainpassive. Each leg has 5 degrees of freedom, which areextension/flexion and adduction/abduction of the hip, exten-sion/flexion of the knee, and dorsiflexion/plantar flexion andinversion/eversion of the ankle. Actuators are installed at thehip, knee, and ankle for hip extension/flexion, knee exten-sion/flexion, and ankle dorsiflexion/plantar flexion whereassprings are used at the joints for hip adduction/abductionand ankle inversion/eversion, see table I. Due to the passivejoint at the hip and ankle, it is possible for the pelvis tohave motion in lateral direction. For pelvic motion, fourlinear actuators are used to generate translational motions intransverse plane and rotation about the center of the body.Fig. 2 shows the degree of freedom of the COWALK. The

joints with dashed circles are passive joints whereas otherjoints are actuated with linear actuators.

Fig. 2. Schematics of the COWALK system. It has 14 degrees of freedom.Nine degrees of freedom are actuated and five degrees of freedom, whichare indicated by the dashed circles, are passive.

The exoskeleton is attached to the patients at the thighs,calves, and feet using braces. A load cell is attached toeach brace at the thighs and calves in order to measure theinteraction force between the patient and the exoskeleton,see Fig. 3. The actuators at the joints are equipped with

Fig. 3. Locations of the load-cell sensors. The load-cell sensor are attachedbetween the braces and the links to measure the interaction force.

incremental encoders for position measurement of the joint.There is a custom made tachometer to measure the angularvelocity of the treadmill.

The gravity compensator supports the weight of the ex-oskeleton so that the patient on the robot do not have tosupport the additional load due to the exoskeleton. Thegravity compensator is composed of linear springs, cable,and pulleys. The stiffness of the springs as well as otherkinematic parameters such as the length of the springsand the location of the pulleys were chosen so that thegravitational torque due to the mass of the exoskeleton issupported regardless of the configuration of the robot.

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III. CONTROL METHODIn this section, the control methodology is explained.

Throughout the paper, the intention of the patient is assumedto be either acceleration or deceleration of walking speed.Other possible intentions such as increasing the step lengthor flexing the knee are ignored.

The interaction forces are measured by the load-cellsensors attached to the braces to estimate the intention of theuser. The estimated intention of the patient is interpreted asacceleration or deceleration of the walking speed. Interactiontorques at the joints are calculated using the interactionforces measured with the load-cell sensors attached betweenthe robot and the user. Using the interaction torques at thejoints, the intention of the user to change the walking speedis estimated, which results in the desired walking speed.Instead of independently changing a trajectory for each jointaccording to the measured interaction torque at each joint, aset of trajectories for all joints is selected from the databaseof trajectory sets to produce the desired walking speed, seeFig. 4.

Fig. 4. Block diagram of controller of the COWALK

It is possible to alleviate the restriction imposed on theinterpretation of the intention if other set of trajectories areincluded in the database. For example, if the interpretedintention is increasing step length while maintaining walkingspeed and the trajectories that produce increased step lengthwithout changing walking speed are available, the appropri-ate trajectories are used to control the exoskeleton.

A. Gait Hypotheses

The gait hypotheses(GH) made in this paper are:GH1) Each leg undergoes alternating swing phase and

stance phase, where the swing phase is when the legis moving forward and the stance phase is when the legis supporting the body;

GH2) Gait consists of alternating single support phase anddouble support phase, where the double support phaseis when both of the legs are in the stance phase and thesingle support phase is when one of the leg is in stancephase and the other leg is in the swing phase;

GH3) During the swing phase, the swing foot is alwaysabove the ground;

GH4) At any time of walking, all the joints of the exoskele-ton remain in the range of motion of the corresponding

joints of the patient so no injuries to the patient iscaused;

GH5) Feasible joint trajectories are available at any walkingspeed.

Under the hypotheses, the phases of walking are shownin Fig. 5. The time at the beginning of the k-th swing phaseis denoted by tSW

k and tDSk is the time of the beginning of

the k-th double support phase.

Fig. 5. Phases of walking

Using the trajectories stored in a database, customized tra-jectories for a patient are synthesized. The trajectories usedto control the exoskeleton are synthesized using trajectoriesgathered from 113 healthy subjects [13]. The synthesizedtrajectories are used only if the hypotheses are met. Sincethe trajectories satisfy the gait hypotheses, the selected jointtrajectory is safe to be used. Note that since trajectorysynthesis is conducted before training session, it is notnecessary to evaluate the feasibility of the trajectory duringthe session, which is computationally expensive.

B. Desired walking speed

During walking, the interaction forces between the patientand the exoskeleton are measured with the load-cell sensorsimplemented at the braces of the femur and the tibia. Inthis research, the interaction forces during swing phases areused to estimate the intention of the users. It is assumedthat if the users are willing to walk faster than the currentwalking speed, the users apply forces to push forward theexoskeleton with the swing leg and if the users are tryingto slow down the walking speed, the interaction forces areapplied in the backward direction with the swing leg. Then,using the measured interaction force, the walking speed ofthe exoskeleton is controlled to reflect the intention of thepatient.

Let F i1 be the interaction force at the femur. Let F i

2 bethe interaction force at the tibia. The length of the femuris L1 and the length of the tibia is L2. The location ofthe sensors at the femur and tibia are denoted by l1 andl2, respectively. Fig. 6 shows the schematics of each legwith parameter conventions. Then, joint torques due to theinteraction force are given as follows.[

τ1τ2

]=

[l1F

i1 + (l2 + L1 cos q2)F

i2

l2Fi2

], (1)

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Fig. 6. Schematics of each leg with parameter conventions

where τ1 and τ2 are the joint torques at the hip and kneejoints, respectively. Let J be the Jacobian of the robot. Then,the equivalent external force applied at the foot is estimatedas [

F ex

F ey

]= (J>)−1

[τ1τ2

], (2)

where the Jacobian is given as

J =

[−L1 sin(q1)− L2 sin(q1 + q2) −L2 sin(q1 + q2)L1 cos(q1) + L2 cos(q1 + q2) L2 cos(q1 + q2)

].

(3)Since the determinant of the Jacobian is

|J | = L1L2 sin q2, (4)

the Jacobian is invertible if sin q2 6= 0, which is when theswing leg is fully extended. In order to avoid singularity,the range of motion of the swing knee is controlled suchthat the knee is not fully extended. This does not limit thegait pattern since the knee is flexed during swing phase forground clearance. In order to calculate the desired walkingspeed, only F e

x in (2), which is a projection to the horizontalplane, is used.

During the double support phase, the robot needs tosatisfy an additional constraint, which is both of the legsbeing on the ground. Therefore, changing trajectory is notallowed during the double support phase since trajectoriesfor different speed results in different step length. Thedesired walking speed is allowed to be changed at thebeginning of each swing phase and kept constant during theswing phase and the following double support phase. Then,the desired velocity for k + 1-th swing phase is calculatedas follows.

vdk+1 = atvdk +

1

bt(tDSk − tSW

k )

∫ tDSk

tSWk

F ex dt, (5)

where at and bt are constants. Note that the equation (5) isa difference equation whose stability is determined by at.It converges to 0 if |at| < 1, remains constant if |at| =1, and diverges if |at| > 1 when the applied interactionforce is 0. If 0 ≤ at < 1, it is necessary for the patient tokeep applying the interaction force to maintain the walkingspeed since the walking speed converges to 0 without the

interaction forces. Then, the patient need to be more engagedin the gait training. If at = 1, since the desired speed remainunchanged as long as the interaction force remain zero, thepatient becomes passive once the desired walking speed isreached. Note that by adjusting at, it is possible to changethe level of engagement of the patient in controlling thewalking speed.

Note that the walking speed of the k + 1th step iscalculated using the equivalent force at the ankle during thekth step. In results in one-step delayed change of walkingspeed. For stroke patients with hemiplegia, since they havedifficulties in applying interaction forces with their pareticleg as intended, the estimation of the intended walking speedusing the interaction force on the paretic leg has errors. Inorder to avoid the errors, the interaction force is measuredduring the swing phase of healthy leg. Then, the walkingspeed is changed at the beginning of the swing phase of theparetic leg, which results in changing walking speed everyother steps.

IV. EXPERIMENTS

In this section, the results of a preliminary experiment arepresented.

A. Method

A healthy male subject in the COWALK system walkedat a given speed at first and was instructed to apply forceto change the walking speed according to the a sequence ofcommands. The commands were:1) Maintain the walking speed;2) Accelerate;3) Maintain the walking speed;4) Decelerate;5) Maintain the walking speed;6) Accelerate;7) Decelerate;8) Maintain the walking speed.The subject was instructed to accelerate the walking speedutile the speed reached the maximal speed during acceler-ation and decelerate the speed until the speed became theminimal speed. The subject was commanded to maintainthe walking speed otherwise. Each command was given insequence every 10 seconds.

Interaction force is measured using a load-cell sensorattached between each brace and link of the robot. Thebraces are located at the femurs and tibiae of the robot, seeFig. 3.

B. Results

Fig. 7 shows the desired walking speed and measuredspeed of the treadmill along with the commands given. Thesolid line is actual speed of the treadmill and the dottedline is the desired walking speed. For safety reason, walkingspeed of the system has limitation at 2.5km/h. at is set tobe 1, which means that the walking speed remains constantunless the subject applies interaction forces.

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Fig. 7. The desired walking speed and actual speed of the treadmill

Fig. 8 shows the desired walking speeds with different at.The solid line is the actual speed of the treadmill, the dashedline is the desired speed of the system, and dotted line iscorresponding values of at. The desired speed converges to0 with at less than 1. The convergence rate of the desiredspeed is determined by at. As at becomes smaller, the rateof convergence becomes faster. Therefore, in order for thedesired walking speed to be remain constant, interactionforce needs to be applied to compensate the deviation fromthe desired speed.

Fig. 8. Walking speed with different at. For at > 1, acceleration occurswhereas the walking speed decreases for at < 1.

Fig. 9 compares the interaction forces of the swing legunder different at. The subject was asked to keep thewalking speed as constant as possible by applying necessaryinteraction forces if the walking speed becomes differentfrom the desired value. The solid lines represent the walkingspeed in the upper graph and the corresponding interactionforce in the lower graph when at = 0.95. The dashedlines represent the data gathered when at = 0.99. Whenat = 0.95, the mean value of the interaction force of the

Fig. 9. The interaction forces measured at the swing leg with differentat. The user was asked to maintain the desired walking speed by applyinginteraction force if necessary

swing femur was −20.71N whereas the mean value ofthe interaction force of the swing femur is −1.32N whenat = 0.99. These graphs show that the interaction forcerequired to maintain a certain desired value becomes largerwhen at is smaller. Therefore, by adjusting the value of at, itis possible to change the level of participation of the patientduring gait training.

V. CONCLUSIONSIn this paper, a methodology to control walking speed

of a gait rehabilitation system using feasibility-guaranteedtrajectories was introduced and implemented in the COW-ALK system. The intention of the patient, which was in-terpreted into acceleration or deceleration of the walkingspeed, was estimated with the interaction force measuredwith the load-cell sensors between the patient and the robot.The interaction force was used to calculate the equivalentforce at the swing foot. Using the equivalent force, thedesired walking speed for the next step was obtained. Sincethe desired walking speed was in the form of a differenceequation, the desired walking speed for the next step wasmodeled with a difference equation. It was found that thelevel of involvement of the patient was able to be varied.Since trajectories suitable for the desired walking speed,which had been checked for feasibility before the trainingsessions, were used, the stability of walking was ensured.Experimental result showed that the actual walking speedwas varied with different interaction forces.

The experiment showed the feasibility of changing walk-ing speed using interaction force. However, the experimentwas carried out with only one healthy subjects and furtherinvestigation is necessary. It is necessary to conduct experi-ments with stroke patients with hemiplegia.

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