Mechanism and Machine Theory 103 (2016) 51–64

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Mechanism and Machine Theory

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Mechanical design and evaluation of a compact portableknee–ankle–foot robot for gait rehabilitation

Gong Chen, Peng Qi, Zhao Guo, Haoyong Yu ⁎Department of Biomedical Engineering, 9 Engineering Drive 1, National University of Singapore, Singapore

a r t i c l e i n f o

⁎ Corresponding author at: Department of BiomedicaE-mail address: bieyhy@nus.edu.sg (H. Yu).

http://dx.doi.org/10.1016/j.mechmachtheory.2016.04.010094-114X/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Article history:Received 9 December 2015Received in revised form 22 April 2016Accepted 23 April 2016Available online 29 April 2016

This paper presents the mechanical design and evaluation of a knee–ankle–foot robot, which iscompact, modular and portable for stroke patients to carry out overground gait training atoutpatient and home settings. A novel compact series elastic actuator (SEA) is developed forsafe human–robot interactions. As a solution to the limitation of conventional SEA designs,one low-stiffness translational spring and a high-stiffness torsion spring are placed in seriesfor force transmission. The springs are selected based on gait biomechanics to maintain ahigh intrinsic compliance for most period of a gait cycle, while retaining the capacity to providethe peak force. To achieve portability, the robotic joint mechanism is optimized based on gaitbiomechanics, and the mechanical structure is built with lightweight materials. This robotdemonstrates stable and accurate force control in experiments conducted on healthy subjectswith overground walking. The activation level of the major leg muscles of subjects is reducedas indicated by the EMG signals and the normal gait pattern is maintained during the test,which demonstrates that the robot can provide effective assistive force to the subjects duringoverground walking.

© 2016 Elsevier Ltd. All rights reserved.

Keywords:StrokeRehabilitation roboticsKnee–ankle–foot robotBiomechanicsSeries elastic actuator (SEA)

1. Introduction

Stroke has become one of the leading causes of adult disability with the growing aging population [1]. Impairment to neuro-logical systems due to stroke frequently leads to a range of symptoms, including paralysis, muscle weakness, gait disorder andpain, which affect the patients' ability to perform activities of daily living (ADL) [2]. Physical therapy aiming to evoke brainplasticity to regain the lost functions of the brain proves to the main effective treatment for stroke patients [3]. However, conven-tional manually assisted gait training is labor intensive and physically demanding for therapists [4]. The availability, consistency,duration, and the frequency of training sessions are often limited, leaving many stroke patients with permanent disabilitiesuntreated.

Rehabilitation robots have been introduced into the earlier phases of recovery after stroke to overcome the major limitationsof traditional manual therapy [5]. High-quality rehabilitation therapies can be delivered by robots with good quantitativemeasurements and consistency. Over the years, various gait rehabilitation robotic devices have been developed based on differentconcepts [6,7]. However, most of existing robotic gait training systems, such as Lokomat [4], ReoAmbulator [8], LOPES [9], ALEX[10] and Auckland University's system [11], integrate treadmills and fixed platforms [12]. They are meant for acute patients atbig rehabilitation centers or hospitals; and rehabilitation progress of which is inferior to overground gait training [13,14].

l Engineering, 9 Engineering Drive 1, National University of Singapore, 117575, Singapore.

2

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Therefore, there is a great need for portable wearable robotic systems for chronic stroke patients at community rehabilitationcenters or home settings. Such portable devices should be lightweight, safe, and easy to don and doff.

A number of gait rehabilitation devices targeted at specifically either the ankle joint [15–18] or the knee joint [19–23] havebeen developed. However, the weight remains to be the main challenge to achieve portability. The ankle robot developed atMIT [16] weighs 3.1 kg for just the ankle joint. The commercialized knee assistive device developed by Tibion [20] weighsmore than 4.5 kg for just the knee joint. A quasi-passive compliant stance control orthosis (CSCO) for knee joint assistance recent-ly developed by Shamaei et al. weighs 3 kg [23]. Besides, portable devices aimed at providing active assistive torque to both theknee and ankle joints are very rare due to ineffective and bulky actuation design. The lightweight knee–ankle–foot orthosis(KAFO) is recently attempted at University of Michigan [24], but it is designed with pneumatic actuators tethered to a stationarycompressor and so the system cannot be truly portable and used at home.

In this paper, we present a compact and modular knee–ankle–foot robot aiming for sub-acute and chronic stroke patients toconduct gait rehabilitation at outpatient rehabilitation centers or at home. The system can be easily reconfigured into either aknee robot or an ankle robot to suit different symptoms, such as knee hyper-extension and drop foot. In order for the deviceto be able to provide assistance during human gait, the actuator must be lightweight, compact and have a large range of outputforce. Thus we developed a novel compact compliant series elastic actuator (SEA) [25], and corresponding linkage mechanism toachieve portable and modular robot design. Experiments have been conducted on four healthy subjects to verify the mechanicalperformance of the robot.

The rest of this paper is organized as follows. Section 2 characterizes the compact robot, including the biomechanics analysis,robot design, compliant actuator design, mechanical structure optimization and sensing apparatus integration. Section 3 illustratesexperiment evaluation method. Section 4 shows the experimental results. Section 5 includes discussion and conclusion.

2. Mechanical design

2.1. Design specifications

Since the primary goal of the device is to facilitate the subject overground walking and provide assistance, the designspecification of the proposed robot is determined by analyzing the biomechanics of human gait [26,27]. Clinical Gait Analysis(CGA) data are utilized to guide the design of the exoskeleton and actuator, which are collected from the CGA normative gaitdatabase [28]. Fig. 1 illustrates the biomechanics in terms of torque, joint angle and power of the knee flexion/extension andankle dorsiflexion/plantarflexion when a healthy subject (70 kg, 0.9 m leg-length) walking at 1.0 m/s. The biomechanical datais normalized into gait cycle percent (1–100%), which starts from the heel strike of the right leg and ends with the next heel strikeof the right leg.

Normally, the walking knee flexion is limited to about 60°. The peak knee torque reaches 30 N·m during stance phase (18% gaitcycle, red circle in Fig. 1(a)) when knee angle is about 20° (Fig. 1(a)). It is worth noting that knee torque remains under 10 N·m(30% of peak torque) for most of a gait cycle, and goes beyond this value in a small period only (red dashed line in Fig. 1(a)). Corre-spondingly, the walking ankle angle ranges from−10°–15°, and the peak torque is 60 N·m when the angle is close to 15° (42% gaitcycle, blue circle in Fig. 1(a)) during stance phase (Fig. 1(b)). Similarly, ankle torque stays below 20 N·m (30% of peak torque) formore than half of the gait cycle (blue dashed line in Fig. 1(a)). It is worthy to note that this character is a driving factor for our

Fig. 1. Biomechanics of human ankle and knee joints for a 70 kg healthy subject during normal gait cycle with 1.0 m/s speed, including (a) joint torque, (b) jointangle and (c) joint power. Red and blue lines represent knee and ankle joints respectively. Blue and red circle is the gait percentage where joint torque reaches itsmaximum. Dot dash line in both (a) and (b) illustrates the joint angles and torques where joint torque is maximum. Dashed line in (a) is 30% of peak torque thatcovers the most part of a gait cycle.

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novel SEA design to be discussed in Section 2.3. On the other hand, the power requirement of each joint is a driving factor for themotor selection. Thus, an average mechanical power between 100 W and 150 W is required for the knee and ankle joints(Fig. 1(c)). These biomechanical data will also be utilized for the mechanical optimization of the following robot and the compliantSEA design.

2.2. Mechanical structure design of the robot

Fig. 2 shows the overall design of the knee–ankle–foot robot. Ball bearings are employed as the knee and ankle joint of therobot, which align with the knee and ankle joint of human (Fig. 2(a)). Rotatory potentiometers are installed inside the bearingto determine the joint angles (Fig. 2(c)). The modular design of a knee module and an ankle module (Fig. 2(b)) satisfies therequirements of patients under different conditions, which can also be implemented separately. When using both modulestogether as a whole for the current prototype, a connecting linkage is employed to adjust the length of shank from 40 cm to47 cm adapting to a range of different user heights. The actuation mechanism for both the knee and ankle joints in this designis particular, which is a novel compact linear SEA through a four-bar linkage (Fig. 2(d)). More details of the actuator and actuationmechanism will be discussed in Section 2.3 and Section 2.4. Fig. 2(e) shows a prototype of the robot. The anthropomorphic struc-ture is built with lightweight carbon fiber reinforced plastic (CFRP) composite material. The robot is easy to don and doff. Thetotal mechanical weight of the prototype weighs about 3.5 kg, which makes it portable.

Fig. 2. (a) CAD model of the knee–ankle–foot robot; (b) CAD models of the knee module and ankle–foot module; (c) explosive views of the robotic joint;(d) slider–crank linkage as the actuation mechanism; (e) a prototype of the robotic system.

Fig. 3. (a) Force and torque loaded on robot joint with bilateral and unilateral structures. Green arrow indicates the force in desired direction; red arrow shows thetorque in undesired direction. Fact is the actuation force and Fleg is the interaction force from human leg. (b) Fact, F1, F2 are the forces loaded on the actuator. (c) Theassembly of the robotic joint.

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Furthermore, it is noted that most powered lower-limb exoskeleton robots adopt a unilateral structure to implement amechanical joint [7], such as ReWalk [29] and HAL [30]. However, this approach generates torques in undesired directions andbrings damage to the mechanical structure of the robot (Fig. 3(a)). Besides, very tight straps have to be used in unilateral designsto prevent the slippage between human limbs and robot, which leads to pain, discomfort, and even skin injuries. To overcomethese limitations, bilateral structure is adopted in our design to improve ergonomics of the robot. The force diagram on a bilateraljoint is illustrated in Fig. 3(a). The excess torques in undesired directions can be eliminated, which can improve the safety andcomfort of the device.

As shown in Fig. 3(b), the actuator on the robotic joint is assembled in a symmetric way, which protects the actuator frombeing damaged by the unbalanced load. The output pin of the actuator is placed in the middle of the actuator body instead ofthe extreme end, thus the length of the actuator is reduced and achieves compactness and steady force transmission. The actuatorcan also be fitted into the space between the output frames when the robotic joint bends (Fig. 3(c)). The compactness of the jointdesign and the portability of the robot are thus achieved.

2.3. Compliant actuator design

Current rehabilitation robotics is often limited by an efficient actuator design. Specifically, a small-sized but capable actuator isthe key to achieve a compact robot design. Since rehabilitation robots are intrinsically interactive robots with human, it is impor-tant to control the assistive force based on the needs of an individual patient [25]. A safe human–machine interaction requiresthe compliant actuators to deliver a controlled force with back-drivability and low output impedance [31]. The most commoncompliant actuator design is the SEA designs [17–18]. The SEAs also have been developed for assistive and rehabilitation robots[15,19,20,32–34]. In human friendly robotics applications, SEA offers several advantages over stiff actuators (such as [35]), includ-ing high force controllability and fidelity, low output impedance, back-drivability, and tolerance to shock and impacts.

The performance of the SEAs largely depends on the spring constant [36]. The selection of spring stiffness in SEAs has to com-promise between compliance and force transmission. A low-stiffness spring produces high fidelity of force control and low outputimpedance, but it also limits the output force range and control bandwidth due to the limitation of the deflection length. A highstiffness spring increases the large force bandwidth, but reduces the force control fidelity. Most current SEAs adopted high stiff-ness springs in order to derive the high force transmission, which leads to the compromised force control performance, intrinsiccompliance and back-drivability.

The previous study on gait biomechanics (as shown in Fig. 1) indicates that the average joint torque in human lower-limbjoints during normal gait is much lower than the peak value (as described in Section 2.1). It implies that the actuator for gaitassistive robots only needs to provide a relatively small torque for most periods of a gait cycle, and this can be handled by asoft spring. As for the higher peak torque, a stiffer spring is then required. On the basis of the above analysis, we develop anovel SEA design which overcomes the limitations of the conventional SEA designs and makes it more suitable for the gaitrehabilitation robot application.

2.3.1. Working principleThe novelty of this actuator design is the utilization of two springs in series with vastly different stiffness values to handle

different force ranges. A soft translational spring handles low-force range, which enables the actuator to achieve the high force

Fig. 4. (a) CAD model and (b) the prototype of the compliant force controllable SEA and (c) exploded views of the actuator and directions of motion transmission.

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fidelity, low output impedance and high intrinsic compliance. A torsion spring with high effective stiffness, handles high-forceoperation when the soft spring is fully compressed. The torsion spring extends the output force into a larger range and improvesthe control bandwidth of the actuation system.

Fig. 4(a) illustrates the composition of the proposed compliant actuator. The actuator consists of an electrical motor that drivesa ball screw through two sets of spring assemblies. Two unidirectional torsion springs are fitted into a custom-made coupler,which becomes a bidirectional torsion spring. Two rotary encoders are located at both sides of the motor and the difference ofthe two encoders' readings will be used to determine the deflection of the torsion spring. A pair of spur gears with 1:1 transmis-sion ratio transfers the force to another parallel shaft of the ball screw, which helps reduce the total length of the actuator.Then, two linear springs are placed within an output carriage and pushed by the ball screw nut. Besides, a linear potentiometeris installed to measure the deflection of the linear spring, thus deriving the output force of the actuator based on Hook's law.

Table 1Parameters of the actuator prototype.

Geometry size 230 mm × 78 mm × 43 mmMotor power 120 WOutput force ±1128 NLow-force range ±240 NLinear spring stiffness 24 × 103N/mTorsion spring stiffness 0.29 N·m/radEquivalent torsion spring stiffness 2.8622 × 106 N/mPitch of the ball screw 2 mmStroke 60 mmForce resolution in low-force range 0.146 NForce resolution in high-force range 5.6 NTotal weight 0.85 kg

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Fig. 4(c) further illustrates the design of the actuator in an exploded view. And the directions of the motion transmission areindicated as well.

In the current prototype of the actuator, please refer to Fig. 4(b), a Maxon DC brushless motor (EC-4pole 120 W, 36 V) isadopted as the power source. A linear potentiometer from ETI is applied as the linear spring deflection sensor. Two incrementalencoders with 1024 tics/rev are used to measure the deflection of the torsion spring. The ball screw is chosen to be 140 mm inlength with 2 mm/rev. The stroke of the actuator is 60 mm. The total weight of the SEA prototype is 0.85 kg.

2.3.2. The selection of spring stiffnessThe selection of the two spring stiffness values is based on the biomechanical analysis of gait, which aims to achieve biome-

chanical efficiency. The soft linear spring is implemented to increase the intrinsic compliance of the actuator, and keeps theactuator working within the low-force range for most of a gait cycle. The torsion spring is used to extend the range of the outputforce, and thus should be rigid enough to cover the peak force.

The required output force of the actuator depends on the optimization of the actuation mechanism, which will be given in thefollowing section. According to the optimized results, the required peak force of the actuator along a gait cycle is around 800 N.Based on the gait biomechanics in Section 2.1, the required force is lower than 30% of peak force for most periods of a gait cycle;hence, the low-force range (the output force range of the soft spring) is chosen to be 240 N. Two linear springs with workingstroke of 10 mm and the stiffness of 24 N/mm are placed at both sides of the ball screw nut to achieve the bidirectional force.

The torsion spring integrates the high effective stiffness to achieve the large output force range. However, large stiffness bringsbad force resolution due to the limitation of encoders. We chose 0.29 N·m/rad torsion springs with 72° deflection range of thecoupler. The resultant output force range is 1128 N, with a force resolution of 5.6 N. The relevant modeling and preliminaryexperimental results were presented in [25]. The section of key parameters of this actuator is summarized in Table 1.

2.4. Mechanism design and optimization

The robotic knee and ankle joints are rotated by the SEA through a four-bar linkage, i.e. a slider–crank linkage. The schematicdiagram of the mechanism is shown in Fig. 5. This mechanism is optimized to minimize the required force for the compact SEAdesign. The geometrical constraints with the physical structure are proposed to provide the adequate and safe range of motion(ROM). The optimization procedure is identical for knee and ankle joints, which follows two steps as shown in Fig. 5 with theknee joint as an example.

Step 1: selecting the initial crank angle θ when the joint angle φk is zero. It satisfies θ + φTmax = 90°, where φTmax is the kneejoint angle corresponding to the maximum joint torque in a gait cycle (as shown in Fig. 1). This ensures the crank is vertical tothe connection rod when the required torque reaches its peak so that it maximizes the length of the lever-arm to apply the forceF (please refer to Fig. 5). The actual crank angle θ for each joint is illustrated in Table 2.

Fig. 5. Schematic diagram and optimization procedure of the slider–crank mechanism for the robot. φk and φa denote the knee joint angle and ankle joint angle,respectively. Step 1: selecting the angle θ, where θ is the crank angle when joint angle is zero; step 2: geometrical parameters optimization, where l1, l2 are thelengths of the frame and crank, d is the length of the connection rod, φ1, φ2 are the relative angles of each bar, F is the output force of the actuator in the directionof the connection rod, M is the output torque of the robotic joint torque during human gait cycle.

Table 2Optimized parameters of the robotic joints.

Knee Ankle

Initial angle θ (°) 70 75Required range (°)φmin req.–φmax req.

0–70 −10–20

limiting range (°)φminlim–φmaxlim

0–120 −30–40

l1 (mm) 168 136l2 (mm) 45 70ROM (°) 0–90.5 −20.8–38Peak force (N) 687 830

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Step 2: optimizing the geometrical parameters of the four-bar linkage to minimize the required peak force of the actuatorwithin a gait cycle. The trajectories of knee joint angle φk and joint torque M are derived from CGA data as described in Fig. 1.Geometric constraints are also considered to ensure the ROM in the normal gait to protect the patient.

Referring to Fig. 5, the kinematics of the four-bar mechanism can be described as

and φ

Fig. 6. (the optcycle w

d cosφ1 ¼ l1 þ l2 cos φ2ð Þd sinφ1 ¼ l2 sin φ2ð Þ

�ð1Þ

and from which, the crank joint φ2 can be derived as:

φ2 ¼ a cos d2min−l21

� �= 2l1l2ð Þ

� �ð2Þ

2 also meets

φ2 ¼ φk þ θ: ð3Þ

The robotic joint torque generated by the actuator is given by

M ¼ F � l2 sin φ2−φ1ð Þ: ð4Þ

The objective function, i.e. the required peak force in a gait cycle, is thus defined as the infinite norm of the actuator force

f Xð Þ ¼ Fk k∞ ¼ Ml2 sin φ2−φ1ð Þ

��������∞: ð5Þ

a) The results of the required peak force on both knee joint and ankle joint with different configurations of l1 and l2, respectively. The green dot representsimum point, where the required peak force is minimum. (b) The output force trajectories of actuators on knee (red) and ankle (blue) joints during a gaitith the optimized configuration.

Fig. 7. (EMG ele

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The lengths of the frame l1 and crank l2 are the parameters to be optimized. The search space is then defined as

l ¼ l1 l2½ �T : ð6Þ

The geometrical constraints are given by

dmaxbl1 þ l2 ð7Þ

l1−l2bdmin ð8Þ

l2bl1 ð9Þ

φmaxreq:ba cos d2min−l21

� �= 2l1l2ð Þ

� �−θbφmax lim ð10Þ

φmin lim ≤a cos d2max−l21

� �= 2l1l2ð Þ

� �−θ≤φminreq: ð11Þ

where dmin, dmax are the limiting output displacements of the actuator, of which the range is 125–185 mm. φmin req., φmax req. rep-resent the required range of joint angles for free human gait. φminlim, φmaxlim are the limiting joint angles for a safe motion range.

Eqs. (7)–(9) ensure the existence of the slider–crank mechanism. Eqs. (10)–(11) specify the range of joint motion with theterminal displacements of the actuator. The target ROM of the robotic joint should cover the required range (φmin req., φmax req.)to allow a normal gait; and is within the limiting joint angles (φminlim, φmaxlim) to prevent the robot from moving into excessivemotion. The values of φmin req., φmax req. and φminlim, φmaxlim are listed in Table 2. With these constraints, the ROM of the roboticknee joint is bounded by physical structure and the knee joint movements can be restricted in an adequate and safe range.These equations are subjected to the MATLAB fmincon optimization function to minimize the peak force in the feasible workspace.

The required peak force on the actuator with different configurations of l1, l2 is drawn on Fig 6(a). It is marked as zero if theparticular combination does not meet the constraint. In Fig. 6(a), the green dot denotes the minimum peak force for the actuator,which is taken as optimum. The minimum peak force guiding for spring selection is 687 N and 830 N on knee and ankle joints,respectively. Fig. 6(b) presents the trajectories of required actuator output force for both joints during a gait cycle with the opti-mized configuration. The resulting ROM meets the demands of human walking and is mechanically restricted in the safe range toprotect human lower-limb joints. The optimized configurations and resultant ROM of the robotic joints and required peak force ofthe actuators are shown in Table 2.

a) experimental setup of the overground walking test, including the exoskeleton robot, IMU sensors (red circle) and EMG electrodes; (b) the location of thectrodes on the right leg major muscles.

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2.5. Robot sensing system

This robot implemented a suit of sensors to monitor human kinematics, muscle activity and interaction force. Encoders andpotentiometers are installed on the actuator as described in section 2.3. These sensors can be used as the feedback informationfor the force control of the actuator [25]. Rotatory potentiometers are installed on the robotic joint to determine the angles(Fig. 2(c)). Joint angles can be used as a control input of the conventional impedance-based control strategy to determine the as-sistance, such as [6]. It is also an important evidence to evaluate the progress of the gait rehabilitation. EMG (electromyography)amplifiers are integrated to record muscle activation patterns (Fig. 7). EMG signals can be used to estimate human intention [10]or to evaluate human effort during rehabilitation training. We have also developed an inertia measurement unit (IMU) sensingsystem to measure kinematics of both legs and human trunk [37]. The IMU sensors are located at the back of the waist, thighthighs, shanks and feet (Fig. 7).

3. Experimental evaluation

A preliminary experiment is conducted to evaluate the effectiveness of this rehabilitation robot in terms of force trackingperformance and physiological activation of lower-limb muscles. Four healthy subjects participated in the experiment. Theiraverage height was 172.5 ± 7.6 cm (mean ± standard deviation), and weight was 66.3 ± 8.1 kg.

3.1. Experimental protocol

The experiment consists of walking along a corridor at 0.5 Hz gait with different levels of robotic assistance. Subjects arerequired to conduct 20 m uninterrupted gaits in straight line under different conditions. Several trials serve as practice for thesubjects to get familiar with the exoskeleton and experiment protocol. In the training sessions, subjects are required to performthe gait as naturally as possible. The experimenter will start collecting data after confirm with the subjects that they can walkcomfortably with the robotic assistance. Fig. 7 shows the experimental setup with the robot on the subject's right leg. The exper-imental conditions are listed as:

Without robot: subjects walk without wearing the robot in order to measure the baseline kinematics and muscle activations.Zero assistive torque: subjects are equipped with the robot on the right leg. Subjects walk in zero-torque mode, in which the

desired force is set to be zero. It is intended to be transparent to its user and minimize the interaction between the robot and thewearer.

Force assistance: A certain percentage of the force trajectories is provided by the robot, i.e. low assistive torque (knee 10% andankle 5%) and high assistive torque (knee 25% and ankle 10%). The force trajectories are adopted from the CGA data in Section 2.1,but normalized based on the weight of each subject.

In the tests, EMG activities and joint angles are measured from the assisted right leg. Surface EMG from four major muscles ofthe leg (Rectus Femoris, RF; Semitendinosus, SM; Tibialis Anterior, TA; Gastrocnemius Lateralis, GL) are collected from four bipolarelectrodes using ASA-Lab (Advanced Neuro Technology, The Netherlands). The sampling rate is set at 2 kHz. The foot pressuresensor is positioned under the right heel and served to detect heel strike event, which indicated the beginning of a gait cycle.The subject's joint angular positions are recorded for the right knee (flexion/extension) and ankle (plantar flexion/dorsiflexion)by the potentiometer assembled in the robotic joint.

Fig. 8. Close-loop force control diagram, where m1 is the equivalent mass of the motor plus the torsion spring coupler and the encoder, m2 is the equivalent massof the ball screw and the gears, k1 and k2 are the stiffness of the torsion spring and linear spring respectively, and b1, b2 and bm are the viscous damping for themotor and ball screw respectively. Fd is the input desired force. F1 and F2 are the output force reading as well as force feedbacks on the torsion spring and linearspring respectively. e is the force tracking error.

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3.2. Force control strategy

A force control strategy is developed to exert user-defined assistive force. More details can be found in our previous work in[38]. To investigate the force tracking performance of the robot, all rotatory elements are transformed and modeled as translation-al elements. Fig. 8 shows the force control diagram, which involves two sets of PD plus feed-forward controllers corresponding tolow- and high-force ranges. The force controller in low-force range is specified as:

Fig. 9. Athe nomrepresen

F ¼ Kp Fd−F2ð Þ þ Kd_Fd− _F2

� �þ Fd ð12Þ

where Fd and _Fd is the desired force and its derivative, F2 and _F2 is the force feedback and its derivative, F is the control output ofthe motor, Kp and Kd is the proportional and derivative control gain. The force controller in high-force range shares the samestructure with F1 as the feedback force. In our experiment, Fd is the assistive torque trajectory as mentioned in the previous sub-section; and _Fd is its derivative.

The interaction force between the subject and the robot, i.e. the feedback force, is calculated based on the Hooke's law, whichis given by

F2 ¼ k2 x2−x3ð Þ: ð13Þ

When the linear spring is fully compressed, the actuator works in high force range and the controller switches. The force feed-back is calculated by

F1 ¼ k1 x1−x2ð Þ: ð14Þ

3.3. Data analysis

Raw EMG data derived from the experiment are processed by a band-passed filter (2nd order Butterworth filter, cutofffrequency of 10–550 Hz) and a band-stopped filter (2nd order Butterworth filter, cutoff frequency of 49–51 Hz). The linear enve-lope of the processed EMG signals is obtained by applying root mean square (RMS) and filtered by a 4th order Butterworth low

n example of force and angle profiles in both knee and ankle joints within two complete gait cycles. The desired force trajectory (black profile) is 10% ofinal torque on ankle joint, and 25% of that on knee joint. Blue and red profiles represent the results of ankle and knee joints respectively. Green dashed linets the switch point between low- and high-force ranges.

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pass filter of 5 Hz to achieve a better representation of the EMG signals. To remove the variability among individuals, the EMGsignal is normalized with the maximal voluntary isometric contraction (MVIC) method [39]. Thus, the EMG profiles can be rep-resented as a percentage of the MVIC value. The EMG profiles can be compared across the subjects and statistical analysis canbe conducted.

All gait data and processed EMG signals obtained from each muscle are segmented and normalized to the percentage of a gaitcycle. A total sample of 10 strides is taken for each condition and is interpolated in the same length to compute an average EMGsignal and joint angles.

4. Results

4.1. Kinematic and force tracking

Fig. 9 shows experimental results in the gait assistive tests to illustrate the performance of the robot. Force tracking perfor-mance of the robot in knee (red curves) and ankle joints (blue curves) and the joint angles are recorded. Here we only presentthe results with larger assistance to evaluate our robotic actuation design concept, and the results of two complete cycles aregiven in this figure. It is noticeable that part of the force trajectory on the knee enters into the high-force range of the actuator(Fig. 9 middle row, green dashed line). The high-force range performance and the switch between two force ranges are involvedin this test.

As shown in Fig. 9, the subject walked with a ROM of 5°–60° on the knee joint and −15°–15° on the ankle joint. The error offorce control on the ankle joint is less than 4 N, which is about 4% of the peak force, and on the knee joint is less than 16.3 N,about 5% of the peak force. The maximum force error in low-force range is 15.1 N, which is about 4% of the peak force. It alsoillustrates that the force transition between low- and high-force ranges is stable and fast.

Fig. 10 shows the averaged results of the knee and ankle angles of the four subjects in different experimental conditions.Standard deviation in the high assistive torque condition is also presented with errorbar. In Fig. 10, it can be seen that the patternof both the knee and ankle joint angles are similar in different conditions, which indicates that a natural gait has been achievedwhen robotic assistance was provided.

The experiment result demonstrates that excellent force tracking performance is obtained during the gait cycles. The force isaccurately controlled before and after the controller is switched and no disturbance is observed at the transition between the twoforce ranges. We can infer that the assistive force from the robot is effectively delivered to lower-limbs. More importantly,

Fig. 10. Averaged results of the knee and ankle joint angles of four subjects in different conditions: free walk (black curves), zero torque (blue curves), low assistivetorque (green curves) and high assistive torque (red curves). The errorbar represents the standard deviation of the angles in the high assistive condition.

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subjects managed to maintain a natural gait pattern with the aid of the robotic device, making it possible for the limb musclephysiological study which is described in the next section.

4.2. Muscle activation analysis

Fig. 11 illustrates experimental results of EMG profiles of four lower-limb muscles in different experimental conditions. TheEMG profiles were normalized to the MVIC and averaged in four healthy subjects. The EMG profiles show overall decreasing ofmuscle activation of the four muscles with the increasing assistive support during the gait cycle. The decreasing is even significantwith the high force support. Both assistance modes demonstrate a lower RMS value and peak value for the four muscles. In TAand RF, EMG activations in zero torque and low assistive torque support are larger than that of free modes. This is probablycaused by the weight of the robot. Looking at the SM EMG profile, for both force assistance modes, there is approximately agradual decrease in the peak value.

In conclusion, a significant overall reduction in muscle activity is found in the experiment, which demonstrates that the robotis able to provide effective assistive forces to the subjects during the walking action.

5. Discussion and conclusion

In this paper, we present the mechanical design and experimental evaluation of a compact, portable knee–ankle–foot robotaimed for stroke patients to carry out overground gait training at outpatient and home settings. A novel compliant SEA utilizestwo springs in series with different stiffness values to achieve back-drivability, large force range and low output impedance forsafe human robot interaction. The mechanism for the joint motion was designed and optimized based on gait biomechanics.Overground walking trials on healthy subjects demonstrated accurate force tracking performance of the novel actuator both onknee and ankle joints. Muscle activation represented by EMG signal was reduced gradually with increased levels of assistance,demonstrating that the robot can provide stable and effective assistive forces during gait cycles.

As part of our continuing work, we are working on advanced sensing and control methodologies for the robot to be used forclinical trials on stroke patients. For example, we are developing advanced control strategies based on gait phase, which is detect-ed with hidden Markov model (HMM) [40]. The idea is to detect the gait deficiency and the abnormal gait phases of the individ-ual patient and apply the appropriate assistive force at the corresponding phases of the gait. We are also developing a newprototype that integrates the power source and controller in a backpack, which makes the overall robot system self-containedand portable. The functionality of the robot in terms of the effectiveness of the robotic assistance or its ability to restore thegait function will be further investigated [41]. Clinical study will also be conducted to further evaluate the effectiveness of therobotic system.

Fig. 11. Averaged surface EMG profiles of four subjects for each of the four muscles in walking under four different conditions: free walk (black curves), zerotorque (blue curves), low assistive torque (green curves) and high assistive torque (red curves). The errorbar represents the standard deviation of the EMG profilesin the high assistive condition.

63G. Chen et al. / Mechanism and Machine Theory 103 (2016) 51–64

Conflict of interests

There are no conflicts of interest.

Acknowledgment

The authors thank Aaron Wong Wei Shen for his contributions to the experiments. This work was funded by the FRC Start-upGrant under WBS No. R-397-000-114-133 and EDIC Seed Fund under WBS No. R-261-503-002-133, Faculty of Engineering,National University of Singapore. Ethical approval was from NUS IRB, Ref No. 13-444. All subjects gave informed consent to thework.

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