Gait-Event-Based Synchronization Method for Gait Rehabilitation Robots via a Bio-inspired Adaptive Oscillator

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1 TBME Gait-Evet-Based Sychroizatio Method for Gait Rehabilitatio Robots via a Bio-ispired Adaptive Oscillator Gog Che, Peg Qi, Member, IEEE, Zhao Guo ad Haoyog Yu, Member, IEEE Abstract I the field of gait rehabilitatio robotics, achievig huma robot sychroizatio is very importat. I this paper, a ovel huma robot sychroizatio method usig gait evet iformatio is proposed. This method icludes two steps. Firstly, seve gait evets i oe gait cycle are detected i real time with a hidde Markov model (HMM); secodly, a adaptive oscillator is utilized to estimate the stride percetage of huma gait usig ay oe of the gait evets. Sychroous referece trajectories for the robot are the geerated with the estimated stride percetage. This method is based o a bio-ispired adaptive oscillator, which is a mathematical tool, first proposed to explai the pheomeo of sychroous flashig amog fireflies. The proposed sychroizatio method is implemeted i a portable kee-akle-foot robot ad tested i 5 healthy subjects. This method has the advatages of simple structure, flexible selectio of gait evets ad fast adaptatio. Gait evet is the oly iformatio eeded, ad hece the performace of sychroizatio holds whe a abormal gait patter is ivolved. The results of the experimets reveal that our approach is efficiet i achievig huma robot sychroizatio ad feasible for rehabilitatio robotics applicatio. Idex Terms rehabilitatio robotics, huma robot sychroizatio, gait evet, adaptive oscillator, HMM T I. INTRODUCTION HE icidece of stroke keeps growig rapidly with the icrease of the agig populatio []. Stroke survivors suffer from muscle weakess, paralysis, gait disorder ad pai ad are affected i their ability to perform activities of daily livig [2]. As the mai therapy for stroke patiets, physical exercise aims to evoke brai plasticity to improve locomotive fuctios [3]. I the past few decades, robotic devices have bee developed to assist maual gait rehabilitatio traiig, ad have bee itroduced ito the early phase of stroke patiet recovery [4, 5]. This work was supported i part by the A*star BEP program uder Grat No Correspodig Author is Haoyog Yu. Gog Che, Peg Qi ad Haoyog Yu are with the Departmet of Biomedical Egieerig, Natioal Uiversity of Sigapore, 9 Egieerig Drive, Sigapore ( che.gog@u.us.edu, peg.qi@us.edu.sg, bieyhy@us.edu.sg,). Zhao Guo is with the School of Power ad Mechaical Egieerig, Wuha Uiversity, Chia. (guozhao@whu.edu.c) Copyright (c) 206 IEEE. Persoal use of this material is permitted. However, permissio to use this material for ay other purposes must be obtaied from the IEEE by sedig a to pubs-permissios@ieee.org. I the field of gait rehabilitatio robotics, the sychroizatio betwee the motio of the robots ad the actual huma gait is very importat. For example, i impedace-cotrol-based strategies, the robotic assistace is specified based o the deviatio of the actual positio of the lower-limb joits from the referece trajectories of the robots [6 9]. The commo cocer i these strategies is that if the robot trajectory is ot sychroized with the huma gait, the robot may resist the huma walkig, ad may eve cause ijury [0, ]. Asychroous assistace is particularly dagerous i robotic systems without body weight support, which may lead to fallig [4]. I strategies which are ot based o referece trajectories, sychroizatio is required to esure timig accuracy. For example, i gait traiig aided by fuctioal electrical stimulatio (FES, which is a techology to stimulate muscle cotractio through electric curret applied to the muscles), FES must be triggered at the correct time to accomplish a ormal gait patter ad safe walkig [2]. Motivated by the eed for huma robot sychroizatio, researchers have developed various cotrol strategies. Jezerik et al. developed a adaptatio algorithm o Lokomat that ca sychroize the robot trajectories with the huma joits by miimizig the huma machie iteractio torque [3]. I this method, the iteractio force is resposible for both power trasmissio ad huma itetio estimatio, which may cause resoace betwee huma ad robot, ad limited applicability for more severe patiets [4, 5]. Aoyagi et al. developed a algorithm o POGO ad PAM that ca adjust the replay timig of the referece trajectories accordig to a state, which is a 8-dimesioal vector of positio ad velocity sigals of the robot ad huma joits []. This algorithm is effective i sychroizig the user's gait ad their ow recorded gait trajectories; however, the applicability for sychroizatio betwee ormal gait refereces ad subjects or patiets with abormal gait patters is ot esured [6]. Besides, the positio ad velocity sigals from ie degrees-of-freedom are required, which requires a large amout of sesig ad sigal processig. More recetly, various adaptive oscillators have bee implemeted i rehabilitatio robotics i order to provide sychroous assistace [5 9]. Adaptive oscillators as a type of mathematical tool ca sychroize with a exteral periodic sigal ad extract the frequecy or/ad phase iformatio. Complex sesig or complicated adaptatio rules are ot required to achieve sychroizatio. Rosse et al. implemeted

2 TBME a adaptive oscillator i the upper-limb exoskeleto NEUROExos to provide siusoidal assistace i cyclical elbow flexio/extesio movemets [6]; ad Gams et al. employed a differet adaptive oscillator i a kee robot to provide siusoidal support i squattig motios [7]. I order to geerate o-siusoidal trajectories for gait traiig, several adaptive oscillators eed to be implemeted [5, 8]. The methods have bee used i LOPES for walkig assistace for hip joits [5], ad i ALEX II to provide hip support durig treadmill traiig [9]. To summarize, the existig oscillator-based algorithms are effective i sychroizig the robot with arbitrary periodic iput trajectory (huma gait trajectory); however, these methods are limited i the followig aspects. Firstly, several oscillators are eeded for the geeratio of a o-siusoid gait trajectory, which is relatively computatioally expesive (as reported i [5], six adaptive oscillators are employed to geerate the trajectory for the hip). Secodly, the adaptatio to achieve sychroizatio is relatively slow (for example i [5], it takes aroud te cycles to achieve sychroizatio) ad the overall system may diverge if the gai of the iput trajectory is set to be large to achieve faster adaptatio. Thirdly, the curret methods focus o recostructig the waveform of the iput gait trajectories. However, for the purposes of gait rehabilitatio, it is more importat to provide a ormal referece trajectory that is sychroous with the abormal gait of the patiets. For example, the method i [9] employs the aforemetioed adaptive oscillator to estimate the frequecy of the gait, ad estimates the stride percetage collaboratig with a foot pressure sesor. The a referece torque trajectory for the robot is geerated usig a lookup table (LUT) accordig to the curret stride percetage. The pheomeo of sychroizatio ca be foud i the biological world. For example, a specific species of firefly, Pteroptyx malaccae, ca achieve both frequecy ad phase sychroizatio i flashig, ad their sychroizatio mechaism is modeled by a adaptive oscillator [20]. The oscillator will alter its frequecy based o its phase differece from the stimulus (other firefly s flash) ad evetually achieve sychroizatio. I this paper, we adopt this adaptive oscillator ito gait rehabilitatio robotics to achieve huma robot sychroizatio. The adaptive oscillator represets the estimated gait percetage ad the actual gait evet durig walkig is regarded as the exteral impulsive stimulus. The phase differece of the estimated gait percetage ad the detected gait evet will drive the frequecy adaptatio of the oscillator, ad evetually the gait percetage ca be accurately estimated. I the proposed method, wearable iertia measuremet uit (IMU) sesors are utilized to measure the gait patter ad the seve gait evets are detected i real time with a hidde Markov model (HMM). The adaptive oscillator is employed to extract the percetage of the huma stride based o the gait evets. Ay oe of the seve gait evets is adequate for sychroizatio; ad two or more gait evets i oe gait cycle is beeficial for faster adaptatio. The sychroous referece trajectories of the robot are geerated with a LUT accordig to the estimated gait percetage. The oscillator-based Fig.. Gait evets ad gait phases i oe gait cycle. sychroizatio strategy is implemeted i a portable kee-akle-foot robot ad a assistive walkig protocol is desiged. Experimets o 5 healthy subjects are coducted to evaluate the performace of the proposed method. The rest of this paper is orgaized as follows: Sectio II itroduces the sychroizatio method, icludig gait-evet detectio, developmet of the adaptive oscillator, ad assistive cotroller. Sectio III presets the experimetal protocol. Sectio IV gives the experimetal results i differet coditios. Sectio V is the discussio ad this paper eds with a coclusio i sectio VI. II. METHODOLOGY Gait describes the patter of huma walkig. A gait cycle ca be subdivided ito seve gait phases, icludig loadig respose, mid-stace, termial stace, pre-swig, iitial swig, mid-swig ad termial swig (Fig. ) [2]. The begiig of each gait phase is deoted as a gait evet. Thus, correspodigly, there are seve gait evets: Iitial Cotact, Opposite Toe Off, Heel Rise, Opposite Iitial Cotact, Toe Off, Feet Adjacet ad Tibia Vertical [2]. This classificatio is based o the three fudametal gait tasks, which are weight acceptace, sigle limb support, ad swig limb advacemet [22]. The sequetial occurreces of these gait evets represet the trasitio of the gait phases, which propels the huma body forward. Gait evets follow a specific sequece ad occur at specific periods withi a gait cycle durig ormal overgroud walkig (Fig. ) [2, 22]. The process of the gait-evet-based sychroizatio method is illustrated i Fig. 2. This method aims to geerate a sychroous referece trajectory for the robot by estimatig the stride percetage of the huma gait based o the gait evet iformatio. The method ca be divided ito two steps: gait-evet detectio with a HMM ad stride percetage estimatio with a adaptive oscillator for sychroizatio.

3 TBME The, a sychroously assistive walkig cotrol method is implemeted i a rehabilitatio robot. A. Gait evets detectio usig HMM I this sectio, the real-time gait evet detectio method is itroduced. I our previous work, we have developed a HMM-based algorithm to detect the seve gait phases durig overgroud walkig; the gait evets are the detected with the trasitios of the gait phases [23, 24]. IMU sesors, which are electroic devices combiig accelerometer, gyroscope ad magetometer, are employed to collect the kiematics of the gait. Here it is defied as z [,,,,, ] () t R R L L Rkee Rshak where z t is a six-dimesioal vector deotig the observatio features of the HMM at time t ; R, L are the agular rates of both feet ad R, L are their first-order derivatives; ad Rkee ad Rshak are the agles of the right kee ad the right shak, respectively. These selected features are capable of represetig the gait phases. A HMM with seve states correspodig to seve gait phases is built as S { LR, MSt, Tst, PSw, ISw, MSw, TSw} (2) To implemet the HMM for gait-evet detectio, three steps eed to be carried out cosecutively, icludig iitializatio, traiig ad decodig. HMM is defied as a statistical Markov model i which its uobservable state sequece q q... q2 qt ca be estimated through a observatio sequece Z z... z2 z T, where T is the legth of the observatio sequece [25]. A HMM ca be described by a 5-tuple ( S, z,, A, B), where S s s2 s N {,,..., } is a set of the N hidde states; is the prior state probability vector { i i P[ q0 si ], i,..., N} ; A is the state trasitio probability distributio matrix Olie Viterbi : for i,...,7 do 2: i b TABLE I ONLINE STATE DECODING ALGORITHM () i i, z 3: ed for 4: for do 5: for j 7do 6: ( j) max( ( i) aij ) bj, z i 7 7: ed for 8: ed for 9: retur q arg max 300( i) i 7 where i ad j is the gait phase, is a variable deotig likelihood, ad q represets the decoded gait phase. t Fig. 2. Flowchart of the gait-evet-based sychroizatio method usig a adaptive oscillator. The gait evet of Iitial Cotact as a example is utilized for sychroizatio, which is described with a pulse sigal. Both the frequecy ad the phase of the adaptive oscillator sychroize with the huma gait based o the detected gait evet. Sychroous trajectories are the geerated for the robot. A { a a P[ q s q s ], i, j,..., N} ; ad B is the ij ij t i t j observatio probability distributio matrix B { b ( z ) b ( z ) P[ z q s ], i,..., N}. i t i t t t i For HMM iitializatio ad traiig, subjects or patiets are required to coduct walkig trials for the collectio of the observatio feature data. The bechmark seve phases are firstly aotated based o a adaptive threshold method [23]. With the observatio data ad the labeled gait phases, the parameter set of HMM (, AB, ) ca be iitialized. The iitializatio is based o the statistical results of the duratio of each gait phases ad the sequece of their trasitio. The HMM is further traied usig the Baum Welch algorithm for better performace [23]. The iitializatio ad traiig sessios are doe usig MATLAB ad ca be completed i a few miutes. Details about these sessios ca be foud i [23, 25]. With the derived HMM, the most likely gait phase durig overgroud walkig is decoded. The procedure is described with pseudo-code i Table I. I our applicatio, a olie Viterbi algorithm [25] with a movig widow is implemeted. Specifically, a observatio sequece with 300 observatios is employed for decodig, which is a sequece combiig the curret observatio z t ad prior history observatios. The first state of the decoded path is the regarded as the curret gait phase. The occurreces of the gait evets are the detected i the trasitios of the gait phases. The effectiveess of the HMM-based gait phase detectio has bee validated with experimets of healthy subjects ad demetia patiets i our previous work [23]. High accuracy ad small time delay i the detectio have bee achieved for ormal ad pathological gaits. A geeral HMM ca be established for differet subjects; ad HMM ca be tailored for each idividual for better detectio. This algorithm has also bee tested with

4 TBME robot-aided walkig experimets, i which subjects wear a exoskeleto robot o the right leg (the robot will be itroduced i Sectio III) [24]. Experimetal results demostrate that the seve gait phases ca be detected robustly, which is applicable for gait rehabilitatio robotics. B. Adaptive oscillator As adopted from [20], a self-sustaied oscillator is built to estimate the percetage of stride (stride %): d / dt (3) Fig. 3. Phase respose curve (PRC) G(, ), with example of 0.7, mi 0.2, max 2. where is the phase agle of the oscillator ad the set deotes the uit circle, t is time, ad is the time-depedet variable frequecy of the oscillator. The phase agle varies betwee 0 ad 2, ad grows uiformly withi oe cycle (Fig. 2). The stride percetage is the derived as stride % 00 (4) 2 Cosiderig that oe of the seve gait evets is utilized for sychroizatio, the occurrece of the gait evet ca be described with a periodic Dirac delta fuctio ( t / ), where is the period of the gait cycle. I order to achieve sychroizatio, the oscillator will adapt its frequecy based o the icomig gait evet as d / dt ( ) ( t / ) P G(, ) (5) where deotes the adaptatio rate of the oscillator frequecy returig to the huma gait frequecy, is the frequecy of the gait cycle ad 2 /, P is a positive value that is related to the amout of the frequecy chage, is the phase differece betwee the adaptive oscillator ad the actual gait, ( )mod(2 ), where is the predefied phase of the gait evet, ad G(, ) is the phase respose curve employed to vary the frequecy accordig to the detected gait evet, which is specified as G(, ) g ( )( ) g ( )( ) (6) mi max leadig the gait evet, the oscillator frequecy will be decreased. Coversely, whe 2, i.e. the oscillator is laggig behid the gait evet, the frequecy will be icreased. The period of the gait is estimated by usig the duratio betwee two successive gait evets: 2 / tn tn (8) where t N ad tn represet the time of the Nth ad (N )th occurreces of the gait evet. A firefly oly has oe flash i oe cycle, however, i our applicatio there are m ( m,2,...,7 ) gait evets i oe gait cycle which ca be utilized for faster sychroizatio. Hece, we exted the adaptive oscillator as d / dt m d / dt ( ) ( t / ) P G(, ) where ( / ) is the periodic Dirac delta fuctio deotig t the th (,2,..., m) gait-evet occurrece, ad is the phase differece betwee the adaptive oscillator ad the th gait evet, ( )mod(2 ), where is the predefied phase of the th gait evet. With the modified adaptive oscillator, more gait evets i oe gait cycle ca be used to detect the phase differece betwee the oscillator ad the actual gait, ad thus sychroizatio ca be achieved faster. The period of the gait is estimated by usig the duratio betwee two successive gait evets: (9) where mi, max are the allowed miimum ad maximum frequecies, ad g ( ) ad g ( ) are defied as g ( ) max( si( ),0) 2 g ( ) mi( si( ),0) 2 The phase respose curve G(, ) is illustrated with Fig. 3. I the above model, whe 0, i.e. the oscillator is (7) where t N ad 2 / ( ) m m t t N (0) N t N represet the time of the Nth ad (N )th occurreces of the th gait evet. The stability of the adaptive oscillator ad the covergece of the phase error have bee rigorously proved i [20], which shows that the adaptive oscillator sychroizes to the frequecy ad with a phase error of O ( ). I this method, the value of P is related to the velocity of the frequecy adaptatio. A large P leads to a faster covergece of

5 TBME phase error betwee the oscillator ad actual gait ad vice versa. However, with a large P, the oscillator is more sesitive to the phase differece. The value of determies how fast the frequecy of the oscillator returs to that of the huma gait. With a large, the oscillator ca fiish adaptatio i a short period of time, leadig to a sharp chage of the estimated phase, ad vice versa. These two parameters collectively determie the performace of the sychroizatio method. Fie-tuig of ad P is required i actual applicatio. The referece trajectories for the robot are geerated usig the estimated stride percetage based o a LUT. A example is illustrated i Fig. 4, where a 2D-LUT is show, correspodig to the robotic kee ad akle joits. The referece trajectories are recorded from a healthy subject durig free walkig, ad are ormalized based o the stride percetage [8]. The phase of each gait evet is also collected ad averaged as the referece phase durig sychroizatio. I our paper, we use 0%, 2 7%, 3 48%, 4 50%, 5 60%, 6 77%, 7 86%. It is worth metioig that the trajectories for differet robot joits ca be easily geerated from the same oscillator without implemetig other oscillators. Fig. 5. Cotrol diagram of the kee-akle-foot robot, where represet,, the kiematics of the kee ad akle joits; is the referece trajectory from 0 the adaptive oscillator; is the output of the impedace cotroller; I is the d desired assistive torque; the blue dashed box represets the series elastic actuator (SEA), i which is the feedback torque, x, x2 are the motor positio ad robot positio; ad k is the sprig stiffess i the actuator. S τ θ θ () I KV ( 0 ) where θ [,, ] is the agles of joits, θ 0 is the joit agle referece, K V diag( kv,, kv ) is a virtual stiffess matrix, where kvi is the virtual stiffess of the cotroller for the ith joit, ad I τ is the desired assistive torque from the cotroller. To avoid a sudde chage of assistive torque, the assistive torque is smoothed usig a expoetial fuctio [25]: τ Ατ ( Ι Α) τ (2) dt It d( t ) Fig. 4. The referece trajectory for the robot is geerated with a LUT based o the estimated stride percetage from the adaptive oscillator. Referece trajectories for multiple robotic joits ca be geerated from the same stride percetage. C. Implemetatio o rehabilitatio robots Based o the referece trajectory that is sychroous to the huma gait, a assistive walkig method is implemeted o a rehabilitatio robot with joits to provide assistace durig overgroud walkig (Fig. 5). The gait-evet iformatio is trasmitted to the adaptive oscillator (Fig. 5, gree arrow) to achieve sychroizatio betwee the robot ad the huma walkig. The robot starts i zero-assistive cotrol mode ad switches to impedace cotrol mode after five steps (Fig. 5, red arrow). The umber of steps is couted with the gait evet of Iitial Cotact. Furthermore, with regard to potetial safety issues, if huma robot sychroizatio is ot guarateed, i.e. the phase differece betwee the trajectory ad the actual huma gait is large, the robot switches to the zero-assistive mode, so that o assistace is give. The impedace cotroller is implemeted i the robot to determie the assistive torque based o the referece trajectory, which is described as where τ It is the desired torque I τ dt is the smoothed desired torque d i τ at time poit t, τ at time t, ad Α diag(,, ) is a smoothig factor matrix, where 0 is the smoothig factor for the ith joit (show i Fig. 5 as the block labeled smooth ). Proportioal-derivative (PD) cotrollers plus feedforward term as the ier cotrol loop to cotrol the output force of the actuator, which are give as where u K ( τ τ) K ( τ τ) τ (3) τ ad d d P d D d d τ are the desired force ad its first-order derivative, τ ad τ are the force feedback ad its derivative, u is the cotrol output, ad K diag( k,, k ) ad P p p D d d K diag( k,, k ) are the matrices represetig the proportioal ad derivative cotrol gais. I our robotic system, the robot is drive by a series elastic actuator (SEA, Fig. 5, blue dashed box). The force feedback of each actuator is estimated by the deflectio of the sprig based

6 TBME Fig. 6. (a) Prototype of a kee-akle-foot exoskeletal robot; (b) motio capture system with IMU sesors. o Hooke s law as ks ( x x2), where k S is the stiffess of the sprig i the actuator, ad x, x 2 are the motor positio ad robot joit positio. More details about the actuator cotroller ca be foud i our previous work [26]. To be oted, this cotrol strategy is ot costraied o the robots drive by SEA, but ca implemeted ito ay other robotic systems. improve the gait patter. B. Experimetal protocol The experimet is tested o 5 healthy subjects (25.5±5.3 years old, 74.9±6. cm i height, 70.2±0.7 kg i weight) to evaluate the effectiveess of the gait-evet-based sychroizatio method. The subjects were iformed of the protocol of the experimet ad siged a coset form, which was approved by the Istitutioal Review Board of the Natioal Uiversity of Sigapore. The subjects were required to wear the exoskeleto o their right leg, except i the Free walkig coditio, which is explaied below. The subjects were also asked to wear the IMU sesors o both legs i all coditios. Several trials served as practice before the collectio of data to make the subjects familiar with the exoskeleto ad the test sceario. At the begiig of each test, the subjects were asked to stad upright. After the experimeter started the robot, the participats could start walkig at ay time. The subjects were the asked to perform overgroud walkig i a straight lie at a preferred speed for about 30 m ad stop i stadig-up posture. There are five types of sceario, which are as follows. III. EXPERIMENTAL PROTOCOL Experimets are coducted to evaluate the effectiveess of the sychroizatio method, ad the feasibility of applicatio i rehabilitatio robots. Differet gait evets are used for sychroizatio to prove the flexibility of the proposed method. The domiatig parameters of the adaptive oscillator are also discussed with the results of trials with differet cofiguratios. A. Experimetal setup The proposed cotrol strategy was tested with a portable, modular, compact kee-akle-foot robot for gait rehabilitatio (Fig. 6(a)) [27]. The robot is optimized based o the biomechaics of the huma gait to provide capable ad safe assistace durig overgroud walkig. Rotatory potetiometers are employed to measure robot joit agles. A wearable sesig system with seve IMU comprisig commercial sesor chips (ADIS6405, Aalog Devices, Ic.), which combies accelerometer, gyroscope ad magetometer, is placed o the waist ad two legs, icludig thighs, shaks ad feet, to measure gait kiematics (Fig. 6(b)) [23]. The cotrollers are implemeted i the NI (Natioal Istrumet) CompactRIO 9074 embedded system with iterface modules for data acquisitio ad cotrol output. The samplig frequecy for the robotic system is 2 khz. I our experimet, a abormal gait patter is simulated to resemble commo pathological coditios of stroke patiets, such as the stiff-kee gait [28, 29]. A elastic badage is wrapped aroud the kee ad akle joits of the exoskeleto to iduce resistive torque. Flexio motio of the kee joit, ad both dorsiflexio ad platar flexio of the akle joit, are hidered. The experimet aims to ivestigate the robustess of the sychroizatio method whe a abormal gait patter is ivolved. It also aims to test the feasibility of the robotic gait traiig applicatio, i.e. the robot provides assistace to ) Free walkig (FW): subjects perform walkig with the IMU sesors but without the robot. The average trajectories of the kee ad akle joits are recorded as the robot referece for each subject, ad will be used i other coditios. 2) Zero-assistive walkig (ZA): subjects wear the robot o their right leg. The robot fuctios i zero-assistive mode ad tries to be trasparet to the subjects. 3) Simulated abormal walkig (SAW): the subjects wear the robot o the right leg, which fuctios i zero-assistive mode. Elastic badages are ivolved to provide resistive torque o the joits. 4) Walkig with low assistace (ASL): the subjects wear the robot o the right leg, with elastic badages o the joits. The impedace cotroller is implemeted i both kee ad akle joits to provide assistace. The gait evets of Opposite Iitial Cotact ad Tibia Vertical are used for sychroizatio. A set of parameters were selected for the adaptive oscillator: mi 0.2, max 2, 0.02, P. The impedace cotroller as described i () with k 0.2 Nm/deg. was implemeted i the kee ad akle v joits to provide assistace. The smoothig factor i (2) was chose to be ) Walkig with high assistace (ASH): this sceario is similar to the ASL sceario, except with kv 0.4 Nm/deg. for the impedace cotroller to provide higher assistive torque durig walkig. C. Data aalysis The kiematics of the kee ad akle joits ad the results of gait-phase detectio were recorded. Each walkig trial was segmeted ito gait cycles with the gait evets of iitial cotact. Kee ad akle joit agles of te gait cycles were take ad averaged i each coditio. The correspodig assistive torque

7 TBME Fig. 7. Experimet results of FW usig Iitial Cotact for sychroizatio, icludig the actual kee (a) ad akle (b) joit agles, ad their correspodig oscillatig referece trajectory; (c) phase differece betwee the adaptive oscillator ad the actual gait; (d) frequecy of the adaptive oscillator ad the estimated frequecy of the actual gait; (e) phase agle of the adaptive oscillator. was also collected ad segmeted. The statistical sigificace of the chages i differet coditios was evaluated with repeated measures ANOVA. Whe a sigificat effect was foud, Tukey s post hoc test was performed to cotrast differeces amog the experimetal coditios, with a p factor of To eable better uderstadig, the phase error is ormalized from [0, 2 ) to [, ). Hece, a egative phase error represets a delay of the referece trajectory, ad vice versa. I order to quatitatively evaluate how fast the adaptio is, we defie a value of ±0.5 rad. Whe a step is reached after which the phase errors i the followig five cycles are below this value, the umber of this step is recorded. This umber ca be further compared amog differet experimetal coditios to evaluate the robustess of the proposed method. IV. EXPERIMENTAL RESULTS A. Evaluatio of sychroizatio I this sub-sectio, experimetal results of a represetative subject are give to show the details of the sychroizatio Fig. 8. Experimetal results of ZA usig Opposite Iitial Cotact ad Tibia Vertical for sychroizatio, icludig the actual kee (a) ad akle (b) joit agles, ad their correspodig oscillatig referece trajectory; (c) phase differece betwee the adaptive oscillator ad the actual gait; (d) frequecy of the adaptive oscillator ad estimated frequecy of the actual gait. process, icludig the referece ad actual gait trajectories, the adaptatio of the frequecy ad the estimated phase error. The efficiecy ad flexibility of the proposed method is ivestigated with differet cofiguratios ad sychroizatio usig differet gait evets. The reliability ad feasibility of rehabilitatio robot applicatio is also evaluated with various experimetal coditios. ) FW test. Fig. 7 shows the experimetal results of the FW test, i which the gait evet of Iitial Cotact ( 0% ) is used for sychroizatio. The results iclude kee ad akle joit agles (Fig. 7(a) ad (b)), the phase differece betwee the adaptive oscillator ad the actual gait (Fig. 7(c)), the frequecy of the adaptive oscillator ad the estimated frequecy of the actual gait (Fig. 7(d)), ad the phase agle of the adaptive oscillator (Fig. 7(e)). It should be oted that i this cofiguratio, where Iitial Cotact is used for sychroizatio, the phase agle of the adaptive oscillator equals the phase differece betwee the adaptive oscillator ad the actual gait whe Iitial Cotact is detected (Fig. 7(c) ad (e)). The figure shows that the test bega with the subjects stadig still. The subjects started walkig at a radom time poit. The gait frequecy is aroud 0.7 Hz (Fig. 7(d)). The gait evet of Iitial Cotact was detected i real time (orage circle i Fig. 7(b)), ad the phase error betwee the

8 TBME oscillator ad the actual gait was detected (Fig. 7(c)). The frequecy of the adaptive oscillator was adapted accordig to (5) (Fig. 7(d)) ad the phase agle grows accordig to the frequecy (Fig. 7(e)). The phase error betwee the adaptive oscillator ad the actual gait was reduced gradually (Fig. 7(c)). I the last six steps i this figure, the averaged phase error is rad, which shows a good performace. It was foud that the referece trajectory was sychroized with huma motio ( 0.5 rad; shaded bar i Fig. 7(c)) at the fourth step ad owards. 2) ZA test. This part describes the results of ZA mode to show the performace of the proposed algorithm with differet gait evets ad experimetal coditios. Without loss of geerality, two gait evets, Opposite Iitial Cotact ( 50% ) ad Tibia Vertical ( 2 87% ), are used for sychroizatio. The results of the ZA test are show i Fig. 8. It is observed that the joit agles of the kee ad akle were slightly altered compared to those i the FW test (Fig. 7(a) ad (b)). The first peak i the kee joit agle was suppressed ad the platar flexio of the akle joit was slightly reduced. However, the gait evets were accurately detected i this coditio (red circle ad blue cross i Fig. 8(c)) ad sychroizatio was achieved with the proposed method. I additio, it ca be see that with the same parameters, whe compared to the FW test, the phase error adaptatio was faster with more gait evets detected (Fig. 7(c)). The sychroizatio was achieved after the third step, which was faster tha the test where oly oe gait evet was used for sychroizatio. The average phase error i the last six steps is rad. 3) SAW test. Aother SAW test was coducted to evaluate the reliability of the proposed strategy. Aother two differet gait evets, Heel Rise ( 48% ) ad Feet Adjacet ( 2 77% ), were used for sychroizatio. Uder this coditio, the gait patters of the kee ad akle joits were seriously altered (Fig. 9(a) ad (b)). The first peak of the kee joit agles was suppressed ad the rage of kee motio was sigificatly reduced; the platar flexio of the akle durig push-off was also limited. However, the gait evets could still be detected reliably, as show i Fig. 9(c) (gree circle ad orage triagle). Sychroizatio was achieved at the third step (Fig. 9(c) gray shaded bar). The average phase error i the last six steps i this figure is aroud rad. This result idicates the robustess of the proposed sychroizatio method, sice the gait evets are the oly iformatio used for sychroizatio which miimizes the ifluece of the abormality i the gait patter. The trajectory thus could be employed i the robot for referece. B. Efficiecy of the adaptive oscillator Statistical results of experimets ivolvig 5 subjects are preseted i this sectio. Fig. 0 ad Table II show the mea ad stadard deviatio of the steps eeded to achieve huma robot sychroizatio ( 0.5 rad) amog all Fig. 9. Experimetal results of SAW usig Heel Rise ad Feet Adjacet for sychroizatio, icludig the actual kee (a) ad akle (b) joit agles, ad their correspodig oscillatig referece trajectory; (c) phase differece betwee the adaptive oscillator ad the actual gait; (d) frequecy of the adaptive oscillator ad estimated frequecy of the actual gait. experimet coditios. From these results, it ca be see that the sychroizatio was achieved i less tha four steps i all experimet coditios. The adaptatio process was ot elogated whe a abormal gait patter was ivolved ad repeated measures ANOVA failed to reach sigificace Fig. 0. Statistical results of all subjects regardig the umber of steps eeded to reduce the phase error to below 0.5 rad i differet experimetal coditios. ( F(4,56) 0.078, P 0.99 ). This was because the gait evet was the oly iformatio eeded to achieve sychroizatio ad it miimized the ifluece of the abormality o the gait patter. This result demostrated that the proposed cotrol strategy was efficiet ad robust i achievig huma robot sychroizatio.

9 TBME TABLE II RELEVANT VARIABLES WITH DIFFERENT CONDITIONS Variable FW ZA SAW ASL ASH Akle movemet rage (deg.) Kee movemet rage (deg.) Fig. 2. Statistical results of all subjects regardig the joit agles of (a) kee ad (b) akle i differet experimet coditios. The gray shadig is the stadard deviatio of the joit agles i the FW coditio. Fig. 3. Statistical results of all subjects regardig the assistive torque of kee ad akle i ASL ad ASH coditios. The gray shadig is the stadard deviatio of the torque i the ASH coditio. Fig.. Experimetal results of ASH, icludig the actual kee (a) ad akle (c) joit agles, ad their correspodig oscillatig referece trajectory; robotic assistive torque profiles o the (b) kee ad (d) akle joits. C. Evidece of assistace I this subsectio, experimetal results of the robot-assisted walkig are show. We first provide results of a represetative subject to illustrate the robot performace; the provide statistical results across all subjects. The results of the ASH test o oe represetative subject are show i Fig. as a example. Accordig to the protocol, the robot worked i zero-assistive mode i the first six steps i order to achieve huma-robot sychroizatio. I these steps, the gait patters of the kee ad akle joits were seriously altered as i the SAW coditio (Fig. (a) ad (c)). The desired assistive torque was zero ad the robot tried to miimize the iteractio torque (Fig. (b) ad (c)). Startig from the seveth step, the robot provided assistive torque durig walkig. The figure shows that the huma-robot sychroizatio has bee achieved ad the assistive torque was provided based o the deviatio of the actual gait ad the referece trajectories. The robotic assistive torque improved the gait patter ad pushed the actual gait patter closer to the referece. The averaged agles of the kee ad akle joits of all subjects i differet experimetal coditios are show i Fig. 2. The movemet rages of the akle ad kee joits are show i Table II. It ca be see that the kiematics of both akle ad kee were similar i FW (blue curve) ad ZA (gree curve). The rage of motio for both kee ad akle joits were reduced i the SAW coditio. The gait patter of the kee ad akle was improved with the assistace of the exoskeletal robot. The akle agles i ASL ad ASH were closer to that i FW, which was the referece trajectory of the robot. The motio rage of the kee was exteded compared to the SAW sceario. The peak kee agle was about 45 i ASL ad 52 i ASH, which were sigificatly larger tha that i the SAW coditio. Repeated measures ANOVA reached sigificace, with a post hoc test establishig a sigificat differece amog the two assisted coditios ad the abormal coditio ( F(4,56) 8.0, P ). The averaged assistive torque profile across all subjects o the kee ad akle provided by the robot i ASL ad ASH is show i Fig. 3. The stadard deviatio of the torque profile i ASH is also show i the figure (gray-shaded bar). It ca be

10 TBME see that assistive torque was provided by the robot, which was based o the deviatio of the actual kee ad akle positios from the referece trajectory. The assistive torque i ASH was relatively larger i amplitude tha that i ASL, which resulted i a more improved gait patter. This result idicated that the robot, by employig the proposed cotrol strategy, was able to sychroize with the huma gait ad provide assistive torque to improve the gait patter durig overgroud walkig. V. DISCUSSION Our study provides a ew solutio for achievig huma robot sychroizatio i gait rehabilitatio robotics. The priciple of the proposed method is to achieve sychroizatio by estimatig the stride percetage based o the gait-evet iformatio. The sychroizatio method ca be applied to a wide rage of cotrol strategies, such as idetifyig the stace ad swig phase [30 32], or applyig FES sychroously [2]. With the estimated stride percetage, referece trajectories ca be easily geerated for the robots with a LUT. I actual rehabilitatio applicatios for patiets with abormal gait patters, the LUT ca be built with the trajectories recorded from healthy subjects [8], or cliical gait aalysis (CGA) data [33] ad ca either be positio trajectory or torque trajectory [9]. I the area of gait rehabilitatio, huma volutary participatio should be maximally evoked, which ca lead to better rehabilitatio progress. Hece, it is importat to allow the patiets to iitiate their walkig ad sychroize the referece trajectory with the actual huma gait. There is a geeral agreemet that a domiat portio of stroke survivors ca walk idepedetly but their gait patters are usually abormal [34], hece the proposed method has a wide applicatio of these patiets. However, the proposed method may be limited i the applicatio of sever patiets who caot iitiate their gait. Passive traiig usig robotic device with body weight support may be more suitable for their early-phase recovery. Our method is very fast to achieve sychroizatio durig walkig. Compared with [5] with about 0 cycles for sychroizatio, our method takes less tha 4 steps i all coditios. Besides, the referece trajectory for differet joits ca be geerated with the same adaptive oscillator, istead of employig multiple oscillators as [5]. The adaptive oscillators i [5-9] are capable of recostructig a arbitrary iput trajectory, hece ca be applied ito a wide rage of robotics applicatios [8, 35]. Differetly, our method tries to sychroize a predefied ormal trajectory with a abormal gait of patiet, which is more suitable for the applicatio of robotic gait rehabilitatio. Aother oscillator-based method is proposed to estimate the stride percetage [36], which is based o the adaptive oscillators i [5]. This method firstly recostructs the iput gait trajectory with a pool of adaptive oscillator as [5]; the extract the stride percetage usig the fudametal phase of the first adaptive oscillator [36]. Compared with this method, our method directly estimates the stride percetage, which is faster to achieve sychroizatio ad is less complicated i the algorithm structure. The performace of the proposed adaptive oscillator is determied by the parameters ad P: decides how fast the frequecy of the oscillator returs to the gait frequecy, ad ad P collectively determie how quickly huma robot sychroizatio ca be achieved. Geerally, a relatively small should be employed to have getle adaptatio, which leads to a smooth referece trajectory. However, if is too small, the frequecy of the oscillator caot retur to the gait frequecy. I this coditio, the frequecy of the oscillator caot coverge ad the adaptive oscillator caot fuctio stably. Istead, a relatively large P should be selected for the applicatio so that the phase error ca be decreased rapidly. A proper P that makes the system coverge withi four steps is suggested for applicatio. Fig. 4 shows aother experimetal result i the FW test. The same gait evet (Iitial Cotact) was employed for sychroizatio. The parameters of the oscillator were selected to be 0.02 ad P 5. Compared to the FW result i Fig. 7, a small P was selected i this test. It is observed that sychroizatio ca be achieved with this cofiguratio. However, phase error is reduced less i oe gait cycle, ad it Fig. 4. Experimet results of huma robot sychroizatio usig Iitial Cotact, icludig (a) the phase error betwee the estimated phase ad actual phase of the gait; ad (b) the frequecy of the adaptive oscillator ad the estimated frequecy of the actual gait. The parameters of the oscillator were selected to be 0.02, P 5. Fig. 5. Experimetal results of huma robot sychroizatio usig Iitial Cotact, icludig (a) phase error betwee the estimated phase ad the actual phase of the gait; ad (b) the frequecy of the adaptive oscillator ad the estimated frequecy of the actual gait. The parameters of the oscillator were selected to be 0.06, P.

11 TBME takes more cycles (seve steps) to achieve sychroizatio. Fig. 5 shows the result of the third trial with the same gait evet of Iitial Cotact used for sychroizatio. The parameters of the oscillator were selected to be 0.06 ad P. Compared to the FW result i Fig. 7, a large was employed i this test. From the result, it ca be see that the frequecy of the oscillator retured to the estimated gait frequecy faster, ad the adaptatio of the oscillator fiished i a short period of time (Fig. 5(b)), which could result i a sharp chage i the referece trajectory. The focus of this paper is o the gait-evet-based sychroizatio method. I order to evaluate the feasibility of the robotic applicatio, we implemeted the method i a rehabilitatio exoskeletal robot. To further ivestigate the reliability of the sychroizatio method whe iteractio torque betwee the robot ad the huma is ivolved, we desiged the impedace-based assistive cotrol strategy for the robot. However, we foud that there was very little robotic assistace durig the assistive walkig tests if the elastic bad was ot wrapped aroud the joits. That is because the experimet was coducted o healthy subjects whose gait trajectories were close to the sychroous referece, thus resultig i a small robotic assistive torque. This was cofirmed by the kiematics result (Fig. 8, ZA coditio). Hece, we desiged the SAW coditio so the gait patter was seriously altered ad greater assistive torque could be iduced. I the proposed method, the frequecy of the gait is estimated usig the duratio betwee successive gait evets. If the detectio of a gait evet is delayed or lost, the frequecy estimatio will be less accurate, which deteriorates the performace of the sychroizatio. Hece a reliable gait evet system is required. I our method, we employed a HMM-based algorithm to detect seve gait evets. I practical applicatio, other sesors ca be implemeted to detect the gait evets. I additio, the reliability of the adaptive oscillator ca also be improved with a more robust estimator of the gait frequecy, such as the aforemetioed adaptive oscillator, which ca extract the frequecy iformatio through gait kiematics [9]. I the experimet, we set up a abormal walkig coditio i healthy subjects to simulate the abormal gait patter of stroke patiets. Sigificat decrease i the rage of motio of both the kee ad akle joits was observed ad huma robot sychroizatio was still achieved. However, the pathological coditios i cliical practice ca be more complicated. The feasibility ad robustess of the proposed sychroizatio method should be further ivestigated with cliical experimets. The potetial solutio is to fid the available gait evets i several pre-traiig trials ad employ oe or more gait evets for sychroizatio. VI. CONCLUSION I this paper, a ovel adaptive-oscillator-based method to achieve huma robot sychroizatio usig gait evets iformatio has bee proposed for robot-aided gait traiig. The gait evets are detected i real time durig overgroud walkig based o HMM. A adaptive oscillator has bee developed to estimate the stride percetage of the huma gait based o the gait evets. Referece trajectories sychroous to the huma gait are the geerated accordig to the estimated phase. As a proof of cocept, the proposed cotrol strategy has bee implemeted o a portable kee-akle-foot robot with a impedace-based assistive cotrol strategy to provide gait traiig. Experimets have bee coducted, which show that ) the adaptive oscillator has a simple structure ad is easy to implemet; 2) the proposed algorithm is effective at achievig sychroizatio with the gait-evet iformatio; 3) our method is efficiet i adaptatio (i less tha four steps); 4) this method is robust i sychroizatio with abormal gait patters so it is applicable to cliical applicatio; ad 5) the implemetatio ito rehabilitatio robots is feasible ad robotic assistace ca be effectively delivered to the subjects based o the sychroous referece trajectories. We will develop advaced cotrol strategies for robot-aided gait traiig based o the sychroous trajectory i our future work. This robotic system also provides a good platform to ivestigate the biomechaical effects of huma motor adaptatio i the robot-aided walkig. This will be further evaluated with cliical trials. REFERENCES [] A. S. 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Gog Che received his B.E. from Shaghai Jiao Tog Uiversity, Shaghai, Chia i 20. His backgroud is i Mechaical Egieerig & Automatio, with a mior i Computer Sciece. He is curretly workig towards the Ph.D. degree i Biomedical Egieerig, Natioal Uiversity of Sigapore with his supervisor Dr. Yu Haoyog. He is curretly a research fellow at the Natioal Uiversity of Sigapore. His curret research iterests iclude rehabilitatio robots system, compliat actuator ad cotrol theory. Zhao Guo (M 3) received his Ph.D. degree i Mechatroics Egieerig from Istitute of Robotics, Shaghai Jiao Tog Uiversity, Chia, i 202. From 202 to 205, He was a Research Fellow with the Departmet of Biomedical Egieerig, Natioal Uiversity of Sigapore (NUS), Sigapore. He is curretly a lecturer with School of Power ad Mechaical Egieerig, Wuha Uiversity, Chia. His research iterests iclude compliat actuator, exoskeleto desig, modelig ad cotrol, ad physical huma robot iteractio. He maily focuses o the area of rehabilitatio robotics. Peg Qi (S') received the B.Eg. degree i automatio from Beijig Jiaotog Uiversity, Beijig, Chia, i 200 ad the M.S. degree i electrical egieerig from KTH Royal Istitute of Techology, Stockholm, Swede, i 202. He obtaied the Ph.D. degree i Robotics from Kig's College Lodo, Uited Kigdom, i Feb Dr. Qi is a Research Fellow at the Natioal Uiversity of Sigapore sice Sep His research is cetered o desig, modelig ad cotrol of cotiuum/soft maipulators as surgical assistats. IEEE Studet Member, from 20; IEEE Member from 206; Haoyog Yu received his B.S ad M.S degrees i Mechaical Egieerig from Shaghai Jiao Tog Uiversity i 988 ad 99 respectively, ad his Ph.D. i Mechaical Egieerig from Massachusetts Istitute of Techology (MIT) i He worked i DSO Natioal Laboratories of Sigapore as a Pricipal Member of Techical Staff before he joied the faculty at the Departmet of Biomedical Egieerig, Natioal Uiversity of Sigapore i September 200. His research areas i DSO icluded exoskeleto ad humaoid robots as well as itelliget groud ad aerial robots. His curret research focus at NUS is o robotics for eurorehabilitatio, especially o usig exoskeleto systems ad smart mobility aids for patiets with stroke ad Parkiso's Diseases.