IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015 1089

Human–Robot Interaction Control of RehabilitationRobots With Series Elastic Actuators

Haoyong Yu, Member, IEEE, Sunan Huang, Gong Chen, Yongping Pan, Member, IEEE,and Zhao Guo, Member, IEEE

Abstract—Rehabilitation robots, by necessity, have direct phys-ical interaction with humans. Physical interaction affects the con-trolled variables and may even cause system instability. Thus,human–robot interaction control design is critical in rehabilita-tion robotics research. This paper presents an interaction controlstrategy for a gait rehabilitation robot. The robot is driven by anovel compact series elastic actuator, which provides intrinsic com-pliance and backdrivablility for safe human–robot interaction. Thecontrol design is based on the actuator model with consideration ofinteraction dynamics. It consists mainly of human interaction com-pensation, friction compensation, and is enhanced with a distur-bance observer. Such a control scheme enables the robot to achievelow output impedance when operating in human-in-charge modeand achieve accurate force tracking when operating in force con-trol mode. Due to the direct physical interaction with humans, thecontroller design must also meet the stability requirement. A the-oretical proof is provided to show the guaranteed stability of theclosed-loop system under the proposed controller. The proposeddesign is verified with an ankle robot in walking experiments. Theresults can be readily extended to other rehabilitation and assistiverobots driven with compliant actuators without much difficulty.

Index Terms—Force control, observer, physical human–robotinteraction, rehabilitation robotics, series elastic actuator (SEA).

I. INTRODUCTION

IN recent years, due to the rapid population aging in most de-veloped nations, there is an increased need for service robots

and assistive and rehabilitation robots in both domestic [1], [2]and hospital settings [3], [4]. In these applications, the robotsmust have direct physical interaction with humans, and safety isa critical concern. An example of the application scenario is de-picted in Fig. 1, where an exoskeleton robot experiences contactwith the human limb during locomotion. The human body is theplant, which is controlled by the central nervous system. Thisinformation of movements is passed to the muscles by means ofa network of motor neurons, and muscle control performs thelocomotion. When the brain sends a command to the muscle

Manuscript received November 10, 2014; revised June 11, 2015; acceptedJuly 10, 2015. Date of publication August 4, 2015; date of current versionSeptember 30, 2015. This paper was recommended for publication by Asso-ciate Editor N. Simaan and Editor B. J. Nelson upon evaluation of the re-viewers’ comments. This work was supported in part by EDIC Seed Fundof the National University of Singapore under Grant R-261-503-002-133 andAgency for Science, Technology and Research (A∗STAR), Singapore, underGrant 1421480015.

H. Yu, G. Chen, Y. Pan, and Z. Guo are with the Department of Biomedi-cal Engineering, National University of Singapore, 117575 Singapore (e-mail:bieyhy@nus.edu.sg; gong118911@gmail.com; yongppan@gmail.com; biegz@nus.edu.sg).

S. Huang is with Temasek Laboratories, National University of Singapore,117411 Singapore (e-mail: elehsn@gmail.com).

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

Digital Object Identifier 10.1109/TRO.2015.2457314

Fig. 1. Environment of an exoskeleton interacting with a human.

based on information from the environment, the body is actu-ated by the muscle. However, if a human has nervous or muscledisorders, the system cannot work properly. In this case, an as-sistive robot, such as an exoskeleton, can be used to assist thehuman in performing the body movements, as shown in Fig. 1.

Various assistive and rehabilitation robots have been de-veloped [5], [6]. For example, scientists at the University ofTwente, The Netherlands, developed a lower extremity pow-ered exoskeleton for gait rehabilitation for stroke patients [7];a treadmill-based lower limb exoskeleton, Lokomat, has beencommercialized by Hocoma, Switzerland [8]; Kong and Jeondeveloped an assistive device for patients at Sogang Univer-sity, Seoul, Korea (EXPOS) [9]; Sulzer et al. developed a serieselastic remote knee actuator to provide knee flexion torque dur-ing the gait cycle [10]. These devices must handle intentionalphysical interaction as well as unexpected interaction forces.Human–robot interaction control is important for two basic op-eration modes: human-in-charge mode and assistive force con-trol mode. In the human-in-charge mode, the robot should beable to follow the human movement with minimal interactionforce; this is also characterized as low output impedance ortransparency in zero force control. In the assistive force controlmode, the robot should be able to provide accurate force/torqueto human limbs as needed; this is also defined as the force-tracking performance. In both control modes, it is very impor-tant to guarantee the safety of the human–robot interaction; thisis also called the stability of the human–robot interaction.

Motivated by these control tasks, scientists have developednew actuators and control strategies for safe and human-friendlyrehabilitation robots. Many innovative compliant actuators havebeen designed for use in assistive robots [7], [11], [12], [38].The most well-known compliant actuator is the series elasticactuator (SEA) [13], [14], [39], [40], where passive elasticity is

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1090 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

introduced in series between the motor and the load. Two typicalSEA designs are linear SEAs [15]–[17], where a linear springis coupled to a ball screw which is connected to a DC motor,and rotary SEAs [18]–[20], where a torsion spring is used totransmit the output force. The detailed review on SEAs can befound in [21] and [22].

Many control approaches [7], [13], [16]–[18], [23]–[27] havebeen proposed for SEAs. The basic requirement in these con-troller designs is that the actuator can generate the force asdesired. For example, in [7], [17], [23], and [24], pure PID con-trol is used to produce a desired output force; in [16], PD plusfeedforward control is used to improve the dynamical perfor-mance for a class of SEAs. Human–robot interaction controlmay be achieved by impedance control, which may be referredto as dynamic stiffness control. Low output impedance reducesinteraction forces due to disturbance forces and unmodeled dy-namics, providing both safety and comfort for the human inter-acting with the robot. In [18] and [25]–[27], a cascaded controlis presented to ensure low impedance in human–robot interac-tion where a PI torque control is used in the outer loop, while aPI velocity control is used in the inner loop. It should be notedin [18] that the impedance control is also implemented by usingcascaded control where the outer loop is an impedance con-trol. In [13], a modified PID with feedforward term and humanjoint compensator is designed to generate desired force and lowimpedance.

Another requirement for human–robot interaction as statedabove is that the control of a robot interacting with human mustbe stable in the presence of unmodeled human dynamics. Con-trol theory has offered several tools to design stable controllerswith the ability to deal with unknown or poorly characterizedinterference [28]. For example, using a disturbance rejectionapproach, some uncertain dynamics in the human–robot inter-action could be included as disturbance forces; in this case, thedisturbance observer can be used to handle the uncertainty. Theauthors in [19] assumed that the disturbance is constant anddesigned a disturbance observer to reject the modeling error. In[29], the authors used a feedback plus feedforward force control,which was enhanced by a disturbance observer to compensatefor plant variations, where feedback and feedforward controlswere optimally designed. By using adaptive control theory, theauthors in [30] proposed an impedance control scheme to adaptthe robotic assistance according to the disability level. How-ever, the stability analysis was not discussed in these papers.In [31], the authors developed a null-space impedance controlwith a disturbance observer, and stability was discussed in thepaper. Unfortunately, the result was based on an n-link robotmanipulator, and a compliant actuator was not involved in theirpaper.

In this paper, we present a human–robot interaction controlapproach for a rehabilitation robot driven by a SEA. The basicdesign and control of the actuator has been introduced in [21]and [22]. The goal of this paper is to propose and validate acontroller to achieve safe and stable human–robot interaction.First, the robot dynamic model with human motion informationis established with consideration of nonlinear friction. Second,a controller based on the friction and human motion compensa-

Fig. 2. Prototype of the knee–ankle–foot robot.

tions, which are enhanced by a disturbance observer, is designed,where the acceleration of the assistive robot is required for feed-back in the controller. Third, since the acceleration is difficultto obtain in a practical system, the proposed controller is fur-ther modified by introducing an auxiliary variable to removethis requirement. A theoretical proof shows that stability of theclosed-loop system is guaranteed. Finally, experimental resultsare provided to verify the effectiveness of the proposed method.

The main contribution of this paper is that the proposed con-trol method has the following improvements over those methodspresented in [19], [29], and [30]: 1) The nonlinear friction inthe actuation system is compensated for. This can help im-prove transparency of the assistive robot which interacts withthe human. 2) The assumption in [19] that the modeling errorand disturbance are constant is removed. This assumption im-poses a strict restriction, limiting the scope of applications. 3)The modified disturbance observer does not use accelerationinformation. As stated in Section III, requiring the accelerationhas some disadvantages. 4) The rigorous mathematical proof isgiven to show the stability of the closed-loop system, while thisissue is not addressed in [19], [29], and [30].

This paper is organized as follows. In Section II, we brieflyintroduce the rehabilitation robot and give the modeling of theactuator. In Section III, we describe the design of the human–robot interaction controller and stability analysis. Section IVgives experimental results. A conclusion is given in Section V.

II. ROBOT DESIGN AND ACTUATOR MODELING

This section is to provide a brief background of the rehabili-tation robot and its actuator design used in this study. Fig. 2shows the prototype of the knee–ankle–foot robot, more ofwhich details can be found in [32]. The modular system consistsof an ankle–foot module and a knee module, which can be con-figured to meet different rehabilitation needs. Each module isdriven by the same linear compliant actuator through a four-barmechanism. Joint angle is measured by a rotatory potentiometer

YU et al.: HUMAN–ROBOT INTERACTION CONTROL OF REHABILITATION ROBOTS WITH SERIES ELASTIC ACTUATORS 1091

Fig. 3. Outline of the dynamics of the actuator.

TABLE IPARAMETERS OF THE ACTUATOR

Symbol Quantity value of the hardware parameters

m 1 equivalent mass of motor 127.4 kgks spring constant 24 × 103 N/mp pitch of the ball screw in the actuator 2 mmM total weight of the actuator 0.84 kg

Since the actuator produces linear output force and motion, the rotatory components ofthe actuator are converted into translational elements, and the parameters in the tableare effective parameters in translational direction, which may refer to [22].

embedded in the robot joints. The robot is easy to don and doff,and the mechanical part weighs only 3.5 kg.

The compliant actuator is powered by one brushless DC mo-tor. Two linear compression springs are placed at both sidesof the ball screw nut for force transmission. One linear poten-tiometer is installed to measure the output force generated bythe spring deflection. The detailed design of the novel SEA canbe found in our previous work in [22]. In this paper, we willfocus on the actuator modeling and control, which will be testedon the ankle module. The result can be extended to the kneemodule without much difficulty.

The physical model of the actuator interacting with the humanbody is as shown in Fig. 3. The output carriage of the actua-tor is driven by human body motion (load). Since the actuatoroutputs linear motion, all the components are transformed intotranslational elements. The mathematical equation is given by

m1 x1 = F − ks(x1 − x2) − b1(x1 − x2) − fl (1)

where m1 is the equivalent mass of the motor, x1 is the motordisplacement, F is the force input from the motor, x2 is thehuman joint displacement, ks is the spring constant, and b1 isthe damping in the mechanism. The parameters of the actuatoris listed in Table I. fl is the friction caused by the motor andball screw. In general, the friction force fl is nonlinear and ismodeled in the form

fl = μ1sgn(x1) + fs1e−(x1 /xs )2

sgn(x1) + bx1 (2)

where u1 is the coefficient of the Coulomb friction, fsl is thecoefficient of the Stribeck friction, and b is the coefficient of theviscous damping. xs is characteristic velocity of the Stribeckfriction [33].

The output force in the spring, F1 , as well as the force feed-back, is a function of two variables: the motor displacementx1 and the joint position x2 . By applying Hooke’s law, i.e.,F1 = ks(x1 − x2), we can describe the actuator as a function

of F1

F1 =ks

m1F − ks

m1F1 −

b1 + b

m1F1 − ksx2 −

bks

m1x2

− ks

m1

(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

). (3)

Remark: As indicated in [16] and [29], the friction reductionwill help enhance the performance of the system by reducingthe output impedance. The friction compensation depends on thedynamical model. Existing actuation models use simple frictionforms such as viscous friction [16], [23], [29]. Here, we adopt anonlinear form [33], which includes Coulomb plus viscous fric-tion together with Stribeck friction. Thus, the present actuationmodel can reflect the actual actuation behavior more precisely.In addition, the variable x1 is the rate of change of the positionfound by differentiating the position signal, which is obtainedfrom the encoder and filtered with a first-order low-pass filterwith the cutoff frequency of 50 Hz.

III. HUMAN–ROBOT INTERACTION CONTROL

In this section, a human–robot interaction control is proposedbased on the modeling of the actuator. The control objectivesinclude: 1) force-tracking control, i.e., following the desiredforce trajectory as closely as possible; and 2) ensuring stabilityand safety when the human motion is involved.

In the force equation (3), it should be noted that the humanmotion is reflected in the term ksx2 + bksx2/m1 , while the fric-tion force is involved in the term ks(μ1sgn(x1) + fs1e

−(x1 /xs )2

sgn(x1))/m1 . To design a human–robot interaction control, wehave to handle these terms. The proposed controller should havethe following terms:

F = uh + uf + ud + uf b (4)

where uh is to compensate for the effect of the human motion,uf is to compensate for the effect of the friction force, ud isto remove the disturbance, and uf b is to design the feedbackcontrol. Substituting the controller (4) into (3) yields

F1 =ks

m1(uh + uf + ud + uf b) −

ks

m1F1

− b1 + fm

m1bF1 − ksx2 −

bks

m1x2 −

ks

m1(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

). (5)

A. Compensation of the Human Body Motion

Ideally, in order to minimize the resistance force when thehuman motion is initiated, the control uh should be designedsuch that the closed-loop system of the actuator interacting withthe human has a zero force, i.e.,

ks

m1uh − ksx2 −

bks

m1x2 = 0. (6)

The control uf should be chosen such that the friction forceis compensated completely, reducing the actuator impedance,

1092 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

Fig. 4. Diagram of control system with disturbance observer.

i.e.,

ks

m1uf − ks

m1

(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

)= 0.

(7)From the above analysis, the control uh should be designed

as

uh =m1

ks

(ksx2 +

bks

m1x2

). (8)

Unfortunately, the term x2 is obtained from the differentiationof the human joint displacement x2 , which may be very noisy.Following the design of [19], a filter is added into the control.The filter is described in frequency domain as

Uh(s) =1

(TN s + 1)2

m1

ks

(kss

2X2(s) +bks

m1sX2(s)

)(9)

where s is a complex variable, Uh (s) and X2(s) are the Laplacetransformations of uh and x2 , respectively, and TN is a suffi-ciently small time constant (see [19] for the selection of TN ).

B. Compensation of the Friction Force

The friction force increases the impedance of the actuator.Ideally, the designed control should reduce the friction force sothat low output impedance is achieved. The compensation termis chosen as

uf =ks

m1

(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

). (10)

Considering that x1 may contain some noise, the gain shouldbe selected to be small in application.

C. Disturbance Observer

Since the compensation of the human motion and frictionis not perfect, the system has an error which is regarded as adisturbance after the compensation, i.e.,

F1 =ks

m1(ud + uf b) −

ks

m1F1 −

b1 + b

m1F1 + d (11)

where d is the system disturbance. To reduce the sensitivity ofthe control performance to disturbance, a disturbance observer isdesigned. Fig. 4 shows the block diagram of the control systemthat employs an estimate of the actual disturbance, deducedfrom a disturbance observer, to handle the disturbance, whered represents the estimated disturbance, P is the actual systemmodel, and Pn is the nominal model without the disturbance.

From (11), it follows that

Pn =ks

m 1

s2 + b1 +bm 1

s + ks

m 1

(12)

where we use the frequency domain to represent the system.The disturbance observer incorporates the inverse of the sys-tem model, and thus, a low-pass filter is necessary to make theobserver practically realizable. A filter can take the followingform:

filter =α2

s2 + α1s + α2(13)

where the parameters α1 and α2 have to be tuned so that thedisturbance suppression characteristics are satisfied. Thus, thedisturbance observer is given by

ud = − α2

s2 + α1s + α2d. (14)

D. Force Feedback Control

For the force feedback control, we have to ensure that the con-troller can generate accurate output force following the desiredforce profile.

Define the force error e = Fd − F1 . The force equation (11)is rewritten as

e = Fd +ks

m1Fd +

b1 + b

m1Fd − ks

m1uf b

− ks

m1e − b1 + b

m1e − ks

m1ud − d. (15)

Let e := [e, e]T . The above equation can be written as acompact form

e = Ae + B

(uf b − Fd − b1 + b

ksFd − m1

ksFd + d

)(16)

A =

⎡⎣

0 1

− ks

m1−b1 + b

m1

⎤⎦ , B =

⎡⎣

0

− ks

m1

⎤⎦ (17)

where d = ud + m 1ks

d. The following feedback control is given:

uf b = Fd +b1 + b

ksFd +

m1

ksFd + Ke (18)

where K is the feedback gain.

E. Modified Nonlinear Observer Interaction Control

A disadvantage of the disturbance observer proposed aboveis that the acceleration must be measured or obtained by differ-entiating the position measurements. In a practical situation, anaccurate accelerometer is not available in many robotic applica-tions. Using a second derivative of the position measurementsmay bring a large noise into the system. To solve this problem,we define the auxiliary variable [34]

z = d − w (19)

YU et al.: HUMAN–ROBOT INTERACTION CONTROL OF REHABILITATION ROBOTS WITH SERIES ELASTIC ACTUATORS 1093

where the variable w is determined by

d

dtw = LF (20)

where L is the observer gain. Based on the auxiliary variable,we propose the following nonlinear controller:

F = uh + uf + Fd +b1 + b

ksFd +

m1

ksFd + Ke − m1

ksd

(21)where the terms uh and uf are the same as in Sections III-Aand III-B.

By introducing the force error e and variable vector e as inSection III-D, (3) can be written as

e = Ae + B

(F + Fd +

b1 + b

ksFd +

m1

ksFd

)+ d + ksx2

+bks

m1x2 +

ks

m1

(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

)

(22)

where A and B are the same as in (17). Substituting the con-troller (21) into the above system yields

e = Ae + B

(Ke − m1

ksd +

m1

ksd

)(23)

where the feedback control gain K is chosen as

K = −γ−1BT P (24)

where γ is a constant, and the matrix P is given by the followingequation:

AT P + PA − γ−1PBBT P + Q = 0 (25)

where Q should be a positive-definite matrix, which is selectedby users. The criterion of the selection is that the larger Q isselected, the smaller the tracking error can be achieved.

The auxiliary variable z is obtained from

z = −Lz + L

(− ks

m1u0 +

ks

m1F1 +

b1 + b

m1F1 − w

)

+m1

kseT PB (26)

where u0 = Fd + b1 +bks

Fd + m 1ks

Fd + Ke − m 1ks

d.

F. Stability Analysis

Consider the Lyapunov function

V = eT Pe + d2 (27)

where d = d − d. Its time derivative is given by

V = eT(AT P + PA − 2γ−1PBBT P

)e

+ 2m1

kseT PBd + 2d

(d − ˙

d)

= − eT(Q + γ−1PBBT P

)e

− 2m1

kseT PBd + 2d

(d − ˙

d)

. (28)

The derivative of the estimated disturbance d is given by

˙d = z + w

= −Lz + L

(− ks

m1u0 +

ks

m1F1 +

b1 + b

m1F1 − w

)

+m1

kseT PB + LF

= −Lz − Lw + Ld +m1

kseT PB

= −Ld + Ld +m1

kseT PB = Ld +

m1

kseT PB. (29)

Substituting the above equation into (28) produces

V = − eT(Q + γ−1PBBT P

)e

+ 2m1

kseT PBd + 2d

(d − Ld − m1

kseT PB

)

= − eT(Q + γ−1PBBT P

)e + 2d

(d − Ld

). (30)

The disturbance is assumed to be slowly varying, i.e.,∣∣∣d

∣∣∣ ≤ o

with o being a constant. Thus, it follows that

V ≤ − eT (Q + γ−1PBBT P )e + 2|d|o − 2Ld2

≤ − eT (Q + γ−1PBBT P )e + Ld2 + L−1 o2 − 2Ld2

= − eT (Q + γ−1PBBT P )e − Ld2 + L−1 o2

≤ − λmin(Q + γ−1PBBT P )||e||2 − Ld2 + L−1 o2 (31)

where we have used the fact that 2|d|o ≤ Ld2 + L−1ε2 .Equation (31) follows V ≤ −λmin (Q + γ−1PBBT P )||e

||2 + L−1 o2 . Then, V < 0 as long as

‖e‖ >

√L−1 o2

λmin (Q + γ−1PBBT P ). (32)

We can also infer from (31) that V ≤ −Ld2 + L−1 o2 , whichgives

∣∣∣d∣∣∣ >

oL

. (33)

Therefore, this demonstrates that the state e and d are ulti-mately uniformly bounded [35], which means the state e and dwill converge to a predetermined set whose size can be chosento be small by selecting appropriate parameters Q and L.

Remark 3.1: If the disturbance d is constant, i.e., d = 0, itis well known from the above analysis that V < 0. This im-plies that ||e|| → 0. This also implies that the tracking error ecan converge to zero and the controller can reject the constantdisturbance.

Remark 3.2: The state e can be made small by selectinga large value of L or control gain K, while the disturbanceestimation error d can be made small by selecting a large valueof L. By combining the control designs uh and uf , the proposedhuman–robot interaction control can implement the followingfunctions:

1094 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

Fig. 5. Experimental setup.

ks

m1uh − ksx3 −

bks

m1x3 ≈ 0 (34)

ks

m1uf − ks

m1

(μ1sgn(x1) + fs1e

−(x1 /xs )2sgn(x1)

)≈ 0 (35)

which implies that the output impedance of the actuator is verylow. In addition, d ≈ 0 implies that the proposed controller iscapable of cancelling the disturbance, and e ≈ 0 implies thatthe proposed controller can generate the desired output force.

IV. EXPERIMENTAL RESULTS

In this section, the proposed control is applied to the an-kle module of the exoskeleton as shown in Fig. 5. The systemconsists of the linear compliant actuator, ankle joint, a motordriver, and a PC with the controller. Limit of motor velocity ispreset in the motor driver to prevent the robot from overspeedand ensure safety. The angle of the ankle joint is measured bya rotary potentiometer. The controller is the NI CompactRIO9074 programmable automation controller that is an advancedembedded control and data acquisition system designed for ap-plications that require high performance and reliability. In thecontroller, we use NI 9215 (Analog Input module), NI 9263(Analog Output module), and NI 9516 (Encoder module) for thedata acquisition. The entire control algorithm is written into twomodules: monitoring (signal generator and program monitoring)and field-programmable gate array (FPGA) (control algorithm).The sampling period chosen for our test is 0.5 ms.

For the control application, it is necessary to identify themodel of the compliant actuator. From the analysis of SectionIII, it is known that the model structure is a linear second-ordermodel. Thus, a system identification tool is used to identifyparameters of the models [36]. The input signal for the testis a square wave with a frequency of 1 Hz, which is aroundthe working frequency. The Coulomb friction can be estimatedby checking whether the force commences for a given a smallamount of input signal; if it does not have, i.e., it is still zero,we have to increase the input signal until the force occurs. It isobserved that the output force commences when the input signalis 850. Thus, the coefficient of the Coulomb friction is 850. TheStribeck speed xs depends on lubrication and material propertiesand is usually determined empirically. Usually, it ranges from0.00001 to 0.1 m/s. In our motor, it is 0.1 m/s. The nonlinear

Fig. 6. Model validation: solid line represents actual signal; dash-dot linerepresents model output.

model obtained is given by

F1 = − 207.21F1 − 10.80F1 + 195.69u − 850sgn(x1)

− 680sgn(x1)e−( x 1 / 2 0 0 0 00 . 1 )2 − 1.5x3 − x3 (36)

where the parameters of the frictional model are obtained byusing a similar method as shown in [37].

The comparison of the simulated output and the actual mea-sured output is shown in Fig. 6. One complete sinusoid cycle isincluded in the result. As observed, the model output is closeto the measured actual output force, and the estimated model isacceptable. It should be noted that the output signals obtainedin the figure are based on 32-bit FPGA and have no units. Toillustrate their corresponding actual meanings, the second labelsof the Y-axis are given in the figure.

For designing the controller (21), the feedback control isdetermined by computing the (25) where Q = diag{1500, 15}and γ = 1. The solution of P is

[151.9311 0.1926

0.1926 0.0198

].

The feedback control gain is K = [37.6854 3.8751]. In theauxiliary variable z, the parameter L is taken as 3000.

A. Interaction Torque and Stability Test

For the interaction torque and stability test scenario, the jointmotion is excited by hand. This is to move the joint close to a sinewave and measure the interaction forces at different frequencies.Concerning human gait, the testing frequency is less than 2 Hz.Figs. 7–9 show the interaction torques and joint motions fromslow speed to fast speed. The measured output torques in Figs.7–9 show good performance of the proposed controller. At alow frequency, the interaction torque is near zero with minorpeaks of about 0.12 N·m. As the frequency of the excitationis increased, the interaction torque is still oscillating with theheight of the peaks below 0.6 N·m. It is observed that at allfrequencies, the human–robot control system is stable.

If we use the same PD controller without the compensationand disturbance observer, the result is shown in Figs. 10 and 11.It is observed that at very low frequency, the system is stable,and the interaction torque is near zero. However, when in-creasing the frequency, the phenomenon of unstable oscillation

YU et al.: HUMAN–ROBOT INTERACTION CONTROL OF REHABILITATION ROBOTS WITH SERIES ELASTIC ACTUATORS 1095

Fig. 7. Stability tests using the proposed controller (frequency is about 0.7 Hz).(a) Torque (N·m). (b) Joint motion (degrees).

Fig. 8. Stability tests using the proposed controller (frequency is about 1.2 Hz).(a)Torque (N·m). (b) Joint motion (degrees).

is observed from the second cycle as shown in Fig. 11. Thisdemonstrates that the stability issue may arise when applyinga traditional PD control to the human–robot interactionenvironment.

The result with no control, i.e., with motor power OFF, isshown in Figs. 12 and 13. It demonstrates that the robot is back-drivable even with no power; however, the resistive interactiontorque is large compared with the results with control. At lowfrequency, the measured interaction torque is about 3 N·m, andat higher frequency, the interaction torque is as larger as 7 N·m.It can be seen that the interaction torque with the proposedcontroller is less than 1/30 of that with no control. The resultsindicate that the proposed controller is stable and effective in

Fig. 9. Stability tests using the proposed controller (frequency is about 1.6 Hz).(a) Torque (N·m). (b) Joint motion (degrees).

Fig. 10. Tests using pure PD control (frequency is about 0.8 Hz). (a) Torque(N·m). (b) Joint motion (degrees).

reducing the output impedance and improving the transparencyof the robot.

Moreover, it is interesting to observe the effect of the fric-tion compensation. In this scenario, only friction compensationis implemented without feedback control. The results can becompared with that when the motor is turned OFF (results inFig. 12 and 13). Fig. 14 shows the result of the simple frictioncompensation (without Stribeck friction), while Fig. 15 showsthe performance of the proposed friction compensation. Withthe simple friction compensation, the peak interaction torquewas about 5 N·m, while with Stribeck friction model, the peakinteraction torque was reduced and was less than 2.5 N·m.It is observed that the friction compensation can improve the

1096 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

Fig. 11. Tests using pure PD control (frequency is about 1.6 Hz). (a) Torque(N·m). (b) Joint motion (degrees).

Fig. 12. Tests with motor turned OFF (frequency is about 0.7 Hz). (a) Torque(N·m). (b) Joint motion (degrees).

performance of the designed exoskeleton, especially in use ofour proposed friction compensation with the Stribeck model.

B. Human Walking Test

To verify the performance of the proposed controller, the an-kle robot was attached to ankle joint of human subjects. Duringthe testing, the movements of the ankle joint may be differ-ent in order to demonstrate the effectiveness of the proposedhuman–robot control.

1) Human-in-Charge Control: To test this control mode,healthy subjects wore the exoskeleton and walked in overgroundgait to measure the zero force control. It is desired that the

Fig. 13. Tests with motor turned off (frequency is about 1.2 Hz). (a) Torque(N·m). (b) Joint motion (degrees).

Fig. 14. Tests with simple friction compensation. (a) Torque (N·m). (b) Jointmotion (degrees).

subject does not feel any resistance from the robot, which meansthe robot is transparent to the human subject. Walking motionsare divided into two basic motions: stance and swing.

This control scheme is tested in three subjects (personaldata are shown in Table II). Figs. 16–18 show the control re-sults of the human-in-charge mode. The red circle representsthe starting point of a gait cycle with the gait event of heelstrike. The interaction torques are less than 0.5 N·m duringthe whole walking motion, which is small that it could not befelt by the subject. The interaction torque peaks at the stancephase. This may be caused by the impact when foot contactsthe ground at heel strike, introducing sharp signals during theinteraction control. However, it is also observed from the figure

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Fig. 15. Tests with the proposed friction compensation. (a) Torque (N·m).(b) Joint motion (degrees).

TABLE IIPERSONAL DATA

Parameters Subject 1 Subject 2 Subject 3

Age 26 19 40Height 167 cm 176 cm 182 cmweight 65 kg 73 kg 90 kg

Fig. 16. Human-in-charge control (subject 1). (a) Output torque (N·m). (b)Joint motion (degrees).

Fig. 17. Human-in-charge control (subject 2). (a) Output torque (N·m). (b)Joint motion (degrees).

that even in this situation, the controlled human–robot systemis still stable and the gait pattern is normal. This further verifiesour theoretical analysis.

2) Assistive Force Control: In this test scenario, the human–robot interaction enters assistive force control mode, and therobot provides torque tracking control to the human motions.In the actual rehabilitation, the desired force profile has to bedetermined by analyzing different walking phases. In this paper,sinusoidal force signals are used as desired torque trajectoriesfor testing purpose.

a) Case 1: In this case, the subject was asked to followthe torque generated by the ankle robot to do motions natu-rally. Using the proposed control law (21), we tested the systemperformance at a frequency of 1 Hz. Fig. 19 shows the controlresults, where the top figure is the output torque response, themiddle figure is the torque tracking error, and the bottom oneis the joint motions. It is observed that the maximum trackingerror is ±0.3 N·m.

b) Case 2: In this case, the subject was asked to stand thereand resist the output torque. The control results are shown inFig. 20, where the top figure is the output torque, the middlefigure is the torque tracking error, and the bottom one is thejoint angle motions. The maximum tracking error is less than ±0.2 N·m.

We use two cases to show the performance of the assistiveforce control: In one, the subject follows the robot motions,and in the other, the subject stands there and blocks the robotmotions. The torque tracking performance in the second caseis better than that of the first case. The reason is that in the

1098 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

Fig. 18. Human-in-charge control (subject 3). (a) Output torque (N·m). (b)Joint motion (degrees).

Fig. 19. Assistive control (Case 1). (a) Output torque (N·m). (b) Torque track-ing error (N·m). (c) Joint motion (degrees).

Fig. 20. Assistive force control (Case 2). (a) Output torque (N·m). (b) Torquetracking error (N·m). (c) Joint motion (degrees).

second case, the subject interacts less with the robot, therebyintroducing less disturbance to the robot control. Both trialsdemonstrate that our robot is capable of providing an accurateassistive torque to human joint.

V. CONCLUSION

We have presented a new controller for human–robot interac-tion control for a rehabilitation robot with a SEA. By combin-ing joint motion compensation, friction compensation, a distur-bance observer, and feedback control, our control can implementhuman–robot interaction control ranging from human-in-chargemode to assistive force control mode. Theoretical analysis forthe proposed controller has proven that it can guarantee the sta-bility of the human–robot interaction. Experimental results haveconfirmed that the proposed controller can achieve stable forcecontrol with good performance in different modes for the re-habilitation ankle robot. Without much difficulty, the proposedcontroller can also be used in the knee module and any otherrehabilitation robot with SEAs. In the next stage, we will im-plement the controller in the complete robot for gait training forstroke patients.

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Haoyong Yu (M’12) received the B.S. and M.S. de-grees in mechanical engineering from Shanghai JiaoTong University, Shanghai, China, in 1988 and 1991,respectively, and the Ph.D. degree in mechanical en-gineering from Massachusetts Institute of Technol-ogy, Cambridge, MA, USA, in 2002.

He was with DSO National Laboratories of Singa-pore as a Principal Member of Technical Staff beforehe joined the faculty of the Department of Biomed-ical Engineering, National University of Singapore(NUS), Singapore, in September 2010. His research

interests include DSO-included exoskeleton and humanoid robots as well asintelligent ground and aerial robots. His current research at NUS is focused onrobotics for neurorehabilitation, especially on using exoskeleton systems andsmart mobility aids for patients with stroke and Parkinson’s disease.

1100 IEEE TRANSACTIONS ON ROBOTICS, VOL. 31, NO. 5, OCTOBER 2015

Sunan Huang received the Ph.D. degree from Shang-hai Jiao Tong University, Shanghai, China.

He is currently a Senior Research Scientist withTemasek Laboratories, National University of Singa-pore, Singapore. He was formerly an Executive En-gineer with National University Health System. Hisresearch interests include neural network control andlearning, modeling, and control of robotics. His cur-rent research is focused on rehabilitation exoskeletonrobot modeling and control.

Gong Chen received the B.E. degree from Shang-hai Jiao Tong University, Shanghai, China, in 2011.His background is in mechanical engineering andautomation, with a minor in computer science. He iscurrently working toward the Ph.D. degree in biomed-ical engineering with National University of Singa-pore, Singapore.

His research interests include rehabilitation robotssystem, compliant actuator, and control theory.

Yongping Pan (M’14) received the B.Eng. degree inautomation and the M.Eng. degree in control theoryand control engineering from Guangdong Universityof Technology, Guangzhou, China, in 2004 and 2007,respectively, and the Ph.D. degree in control theoryand control engineering from the South China Uni-versity of Technology, Guangzhou, in 2011.

He was a Control Engineer with Santak ElectronicCompany, Ltd., Eaton Group, Shenzhen, China, andthe Light Engineering Company, Ltd., Guangzhou,from 2007 to 2008. From 2011 to 2013, he was a

Research Fellow with the School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore. He is currently a ResearchFellow with the Department of Biomedical Engineering, National Univer-sity of Singapore, Singapore. He has authored or coauthored more than 50peer-reviewed research papers in journals and conferences. His research in-terests include automatic control, computational intelligence, and robotics andautomation.

Dr. Pan is an Associate Editor of International Journal of Fuzzy Systemsand is a Reviewer for a number of flagship journals. He was a recipient of theRockwell Automation Master Scholarship and the GDUT Postgraduate Aca-demic Award in 2006, and the SCUT Innovation Fund of Excellent DoctoralDissertations and the SCUT Excellent Graduate Student Award in 2010.

Zhao Guo (M’13) received the B.S. and M.S. degreesin mechanical engineering from Jiangsu University,Zhenjiang, China, in 2004 and 2007, respectively, andthe Ph.D. degree in mechatronics engineering fromInstitute of Robotics, Shanghai Jiao Tong University,Shanghai, China, in 2012.

He is a Research Fellow with the Departmentof Biomedical Engineering, National University ofSingapore, Singapore. His research interests includecompliant actuator design, neuromuscular modelingand robot control, and physical human–robot interac-

tion. He mainly focuses on the area of rehabilitation robotics.