exoskeleton follow-up control based on parameter ...research article exoskeleton follow-up control...

Research ArticleExoskeleton Follow-Up Control Based on ParameterOptimization of Predictive Algorithm

Shijia Zha ,1 Tianyi Li ,1 Lidan Cheng ,1 Jihua Gu,1 Wei Wei ,1 Xichuan Lin,2

and Shaofei Gu 3

1College of Optoelectronics Science and Engineering, Soochow University, Suzhou Jiangsu Province, 215000, China2Micro-Nano Automation Institute, Jiangsu Industrial Technology Research Institute, Suzhou, Jiangsu Province 215131, China3Shanghai Huangpu District Fire Rescue Detachment, Shanghai 200001, China

Correspondence should be addressed to Wei Wei; [email protected]

Received 28 May 2020; Revised 15 October 2020; Accepted 8 January 2021; Published 21 January 2021

Academic Editor: Jose Merodio

Copyright © 2021 Shijia Zha et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The prediction of sensor data can help the exoskeleton control system to get the human motion intention and target position inadvance, so as to reduce the human-machine interaction force. In this paper, an improved method for the prediction algorithmof exoskeleton sensor data is proposed. Through an algorithm simulation test and two-link simulation experiment, thealgorithm improves the prediction accuracy by 14.23± 0.5%, and the sensor data is smooth. Input the predicted signal into thetwo-link model, and use the calculated torque method to verify the prediction accuracy data and smoothness. The simulationresults showed that the algorithm can predict the joint angle of the human body and can be used for the follow-up control ofthe swinging legs of the exoskeleton.

1. Introduction

The exoskeleton is a wearable device that combines humanintelligence and mechanical power, widely appearing in thefields of assistance, rehabilitation training, and disabilityassistance. In recent years, with the continuous developmentof drive technology and sensor technology, more and moreexoskeletons have appeared in the market [1]. Exoskeletonsare often designed to perform specific functions such as walk-ing, weight-bearing, lumbar support, and spinal support. Inorder to assist the specific movements of the human body,a very critical point for the exoskeleton is to realize the recog-nition of the human motion intention.

1.1. Introduction to Exoskeleton Classification. There aremany ways to classify active exoskeletons. One classificationway is based on the methods of the exoskeleton acquiringthe intention of human motion, which can be roughlydivided into four categories: The first is preprogrammed.The gait of the exoskeleton system is designed, so the wearercan only intervene in limited ways with devices such as but-

tons or HMI (Human Machine Interface). However, onlyrelying on some external devices to obtain the motion inten-tion of the human body limits the use scope of the exoskele-ton, which makes this kind of exoskeleton often appear in therehabilitation and correction equipment with fixed gait [2].The second is the use of EEG (electroencephalogram) signalsto identify the intention of human movement. Such systemsare susceptible to interference from the external environmentand are not suitable for the wearer to perform multibraintasks [3]. The third method uses the surface EMG (electro-myography) signals of the human body to capture the move-ment intention of the human body. Obtaining surface EMGsignals is usually done by attaching electrodes on the skinof the human body, which is also vulnerable to the environ-ment. Sweat on the surface of the skin often affects the accu-racy of the signals [4], and long-term wear is easy to cause thesurface electrode to fall off; some teams have developed exo-skeletons (e.g., HAL) that recognize the body’s intentionsbased on electromyographic signals. The fourth way is to col-lect human body motion mechanics information to identifyhuman body motion intentions. Such systems have installed

HindawiApplied Bionics and BiomechanicsVolume 2021, Article ID 8850348, 13 pageshttps://doi.org/10.1155/2021/8850348

https://orcid.org/0000-0003-1356-7295https://orcid.org/0000-0003-4994-1330https://orcid.org/0000-0001-7984-174Xhttps://orcid.org/0000-0002-1365-4869https://orcid.org/0000-0003-0286-3064https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2021/8850348

a large number of kinematics and dynamics sensing deviceson the exoskeleton and human body to obtain the interactioninformation of the human body and the motion intention ofthe human body. Many lower limb exoskeletons, such asWEAR [5], MEBOTX-EXO [6], and HUALEX [7], use kine-matic information to capture the human body’s intentionand kinetic information to control the motion of the exoskel-eton. This type of exoskeleton has the characteristics of easyto put on and take off, and the system sensor signal is stable,which makes it become the main research direction of exo-skeleton. However, the kinematic sensor requires the humanbody to drive the exoskeleton movement, inevitably causingthe delay of motion intention perception and control.

Since the exoskeleton involved in this paper is the fourthmethod to obtain the human movement intention and thesensor data is collected by the sensor network, it takes sometime until the control signal is generated. The actuators (typ-ically motors or hydraulic) cause time delay, too [8]. Mean-while, the motion signal of the human body is behind themotion intention of the human body. Therefore, it is neces-sary to solve the time delay in the fourth exoskeleton system.

1.2. Introduction to Prediction Algorithm. In the exoskeletoncontrol strategies, only relying on the sensor data detected bythe sensors of the system and giving the exoskeleton drivestructure motion instruction will cause the exoskeleton andthe human body a position deviation. The position deviationis the main source of human-machine interaction. An appro-priate prediction algorithm needs to be added to help thecontrol strategies judge the wearer’s motion intention andthe possible motion position at the next moment accordingto the current and historical motion sensing data, so as togive the system appropriate control commands. Due to thesignificant difference in the delay between the exoskeletonand the wearer due to different wearing methods and thetightness of the binding, some prediction methods can onlypredict the one step size, such as Kalman prediction [9], needto continuously iterate the Kalman gain coefficient accordingto the measured value, and cannot deal with the longer stepsize prediction. Similar problems also exist in the predictionmethods based on the ARMAmodel, such as LMS linear pre-diction [10] and RLS linear prediction [11, 12]. When theprediction step size becomes longer, the accuracy of the pre-diction will decrease significantly [13]. Moreover, LMS linearprediction and RLS linear prediction require more historicaldata and a large amount of computation, and the predictioncurve is not smooth, which makes it difficult to implementsuch prediction algorithm in an embedded system.

Yang [13] et al. compared the performance of LMS andTakens prediction algorithms in the prediction of human gaitdata. The results showed that Takens is more stable, accurate,and suitable than LMS, but it did not solve the zero dead timeproblem of the prediction algorithm. So, Duan et al. [14] usethe combination of the Takens prediction algorithm andNewton-based-method to solve the problem of the zero deadtime of the prediction algorithm but did not make progress insolving the parameter tuning process.

In this work, we have made improvements to the predic-tion algorithm for exoskeleton, so that the parameters of the

prediction algorithm can be optimally determined. Applyingit to exoskeleton gait prediction can accurately predict thejoint angle of the exoskeleton, making joints motor reachthe aim position in advance.

The reminder of this paper is organized as follows:In Section 2.1, we introduce the IMU-based pose capture

system. In Section 2.2, we briefly introduce the Takens pre-diction algorithm. In Section 2.3, we introduce the processof the PSO-Takens algorithm. Section 2.4 is mainly aboutthe simulation of the control of the prediction algorithm inthe two-link model.

In Section 3, the experimental results are analyzed. Wemainly discussed the performance of the improved predic-tion algorithm and the original prediction algorithm in exo-skeleton gait data prediction.

In Section 4, we conclude the paper.

2. Materials and Methods

2.1. Motion Capture System. The process of human lowerlimb movement has the characteristics of high autonomy,complex information, diverse movements, and multipledegrees of freedom. Biomechanical simulation and experi-mental studies have shown that the motion consumptionpower in the sagittal plane of the human body is the largestrelative to the frontal plane and horizontal plane [15], sothe three-dimensional walking motion of human hip jointoften can be simplified to a single plane motion in the sagittalplane. The corresponding position sensor used in the exo-skeleton is usually placed in a position parallel to the sagittalplane of the human body, which describes the motion angleof the sagittal plane of the lower limb joints of the humanbody. With the development of inertial measurement units,more and more IMUs (inertial measurement units) wereused as examples of kinematic sensors, beginning to appearin the motion capture system. Compared with the methodof collecting joint angles using an absolute encoder, IMUhas an advantage of flexible installation and cheap price,and its measurement accuracy can reach 0.1°, which can meetthe needs of the human motion capture system.

In order to collect human gait information and verify theaccuracy of the prediction algorithm, we designed a flexiblemotion capture system for human sagittal plane motionbased on IMUs. The system will automatically capture thesagittal plane motion data of the human body at 50Hz sam-pling frequency and transmit the motion data through CAN(Controller Area Network) (Figure 1(a)) to the data collec-tion and processing module. As shown in Figure 1(b), thesystem mainly collected the pitch angle data of the back,thigh, shank, and the pressure sensor data of the heel. Thesystem also includes power module, data collection and pro-cessing module, and data transmission module. Figure 1(c)shows the actual mechanical structure of the exoskeleton sys-tem, a hinged structure is adopted between the thigh andshank, and this structure can support the exoskeleton systemand reduce the load on the body while standing upright, butit also leads to the inability to directly measure the motionangle of the human knee joint through the angle sensor.

2 Applied Bionics and Biomechanics

Therefore, IMUs were placed on the thighs, shanks, and backto calculate the angle of the human joints.

The formula for calculating the angle of the hip and kneejoints is as follows:

θhip =π

2 − θh,

θknee = π − θh − θl:ð1Þ

θh, θl represents the pitch angle of thigh and shank, respec-tively; due to the mirror relationship between the left and rightlegs, the calculated angle values are opposite, and there is aphase difference between the hip joints and knee joints.

2.2. Takens Prediction Algorithm. The continuous walking ofthe human body is periodic and nonlinear. The left and rightleg sensor data are only different in phases and directions.Therefore, the algorithms used in the prediction of the jointangle are the same; the prediction algorithms discussed inthis section are nonlinear time series Takens prediction algo-rithm of the lower limb hip and knee joint data.

The Takens algorithm for nonlinear time series forecast-ing is based on the Takens embedding theorem, which is alsocalled the weighted zero-order local prediction method. Thismethod is closely related to Takens’ reconstruction theorem.It is essentially a nonlinear time series analysis method,which requires historical data of the system to obtain the bestperformance. The main idea is to find several historical datavectors that are the most similar to the current reconstruc-tion delay vector by traversing the sensor data for a periodof time, and the historical data vector is normalized andweighted according to the similarity with the current sam-pling data. The prediction data at a specific time is deter-

mined through function fitting or search. The predicteddata of each vector are multiplied by their respective weightsto obtain the final predicted value at the determined moment.The algorithm implementation steps are as follows:

(1) According to the Takens embedding theorem, for agiven time series yðtÞ, select the appropriate samplinginterval Δt and embedding dimension n, and collectand store n data; the adjacent data differ in time Δt;constitute the reconstruction delay vector DðtÞ. Thetime series yðtÞ can be any type of sensor data inthe motion capture system, such as angle, angularvelocity, or heel pressure data. The contents ofDðtÞ is

D tð Þ = y tð Þ, y t − Δtð Þ, y t − 2Δtð Þ, y t − 3Δtð Þ⋯ y t − n − 1ð ÞΔtð Þ½ �ð2Þ

(2) Calculate the similarity between the current recon-struction delay vector DðtÞ obtained by sampling atthe current time and the historical reconstructiondelay vector DiðtÞ obtained from all previous obser-vations; the methods for calculating similarity inreconstruction delay vectors are usually Euclideandistance, Pearson’s correlation coefficient, Manhat-tan distance, and hash distance. The Euclidean dis-tance has the following expression in this algorithm:

δ ið Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi〠n

k=1y t − k − 1ð ÞΔtð Þ − yi t − k − 1ð ÞΔtð Þð Þ2

s 1 ≤ i ≤Nð Þ:

ð3Þ

DataCollection

SystemCAN BUS

Right ShankIMU

Right HeelPressure

MCUMCU

Right ThighIMUMCU MCU

Left Shank IMU

Left HeelPressure

Left Thigh IMU

(a)

Thigh IMU

Calf IMU

Heel pressure

MCU

Back IMU

Data collectionand processing

system

(b)

𝜃knee

Hinged structure

𝜃l

𝜃hip

𝜃h

(c)

Figure 1: Motion capture system and exoskeleton structure. (a) Nets of the motion capture system. (b) Motion capture system. (c)Mechanical structure of the exoskeleton.

3Applied Bionics and Biomechanics

In formula (3), the value of i represents the position of thecurrently traversed vector, N is the reconstruction delay vectorlength. The smaller the Euclidean distance is, the more similarthe two reconstruction delay vectors are, and the more accu-rate when the historical reconstruction delay vector is usedto predict the data of the subsequent period of time. WhilePearson’s correlation coefficient orManhattan distance is usedas a similarity calculation, the expression becomes

δ ið Þ = ∑nk=1 y t − k − 1ð ÞΔt − �yð Þ yi t − k − 1ð ÞΔt − yið Þð Þð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑nk=1 y t− k − 1ðð ÞΔt − �yð Þ2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑nk=1 yi t − k − 1ð ÞΔt − yið Þð Þ2q 1 ≤ i ≤Nð Þ,

δ ið Þ = 〠n

k=1y t − k − 1ð ÞΔtð Þ − yi t − k − 1ð ÞΔtð Þj j 1 ≤ i ≤Nð Þ: ð4Þ

In formula (4), �y is the average value of the reconstructeddelay vector, Pearson’s correlation coefficient and Manhattandistance can also be used as a similarity calculation function,and the difference is only the amount of calculation. Amongthe three calculation methods, Manhattan has the smallestamount of calculation and Pearson’s correlation coefficient isthe largest

(3) From the observed historical reconstruction delayvector DiðtÞ, the best matching M sets of reconstruc-tion delay vectors fD1ðtÞ,⋯,DMðtÞg are selectedaccording to the similarity with the reconstructiondelay vector DðtÞ at the current moment. The corre-sponding Euclidean distances are fδð1Þ,⋯, δðMÞg.The predicted value fy1ðt + bΔtÞ,⋯, yMðt + bΔtÞg ofeach group of reconstruction delay vectors is deter-mined by searching, T = bΔt is the predicted dura-tion. The weighting factor formula of each bestmatching amount in the final prediction amount cal-culation formula is as follows:

wi =1

∑Mj=1δi

1δi 1 ≤ j ≤Mð Þ ð5Þ

(4) According to the predicted values and weight factorsof each historical reconstruction delay vector group,the estimated predicted values at time bΔt after thecurrent moment yðtÞ are calculated as follows:

ŷ t + bΔtð Þ = 〠M

i=1wiyi t + bΔtð Þ ð6Þ

The flow chart of the algorithm is shown in Figure 2.The Takens algorithm is to make predictions on the sen-

sor data for a period of time by searching historical sensordata, which means that the prediction algorithm is to findthe most similar data out of the current motion situationfrom the historical vectors. The sensor data of the humanwalking motion detected on the sagittal plane has obviousperiodicity, so the Takens algorithm has a well performancein predicting such signals. Among multiple optimal recon-struction delay vectors, the algorithm can dynamically adjustthe weight factor through the Euclidean distance, which canadjust the proportion of the optimal reconstruction delayvector in the final prediction data.

2.3. PSO-Takens Prediction Algorithm Design. Although theTakens algorithm cannot predict that all motion sensor dataare completely correct, some papers also give an optimizationmethod based on this algorithm [14], which makes theTakens algorithm used in embedded systems become possi-ble. Whitney’s topological embedding theorem shows thatthe phase space of the original system can be reconstructedby any value of the delay time of the single variable timeseries in the case of noiseless and infinitely long time series.In fact, the measured time series is of limited length and isinevitably polluted by noise. Therefore, arbitrary delay timecannot reconstruct the phase space of the system; the key toreconstruct the phase space using the measured time seriesis how to select these reconstruction parameters. However,the Takens embedding theorem does not indicate how toselect these parameters. This problem has become an impor-tant issue in nonlinear time series analysis.

Duan et al. have found that inappropriate historical vec-tor dimension and embedding dimension will cause irrele-vant data to enter the reconstruction delay vector, resultingin lower prediction accuracy [14]. While inappropriate pre-diction duration and optimal matching number will causedata jitter and affect the smoothness of the predicted data.Fortunately, the predicted duration, which is also called delaytime, is a constant we want to compensate. It is mainly causedby inertial sensors and inherent defects of the system, and theduration can be measured by wearing exoskeletons. Thedelay time is expressed as the angle difference between thehuman body and the exoskeleton.

In order to evaluate the algorithm performance andadjust the parameters of the algorithm, the following two for-mulas were introduced which are aimed at judging the prosand cons of the prediction effect:

Current reconstructiondelay vector D(t)

EXO sensor datay(t)

Historical reconstructionDelay vector Di(t)

Euclidean distance𝛿(i) = ||D(t) − Di(t)||

Prediction data ofreconstruction delay vector

yb(t + b𝛥t)

Best match reconstructiondelay vectors Db(t)

Weight factor assignment

Predicted value of sensor data

= 1Mj=1

1wi 𝛿i 𝛿i∑

M

i=1∑y(t + b𝛥t) = wi yi(t + b𝛥t)ˆ

Figure 2: Flow chart of the Takens algorithm.


2.3.1. Prediction Accuracy Rate (PR).

ek tð Þ = y tð Þ − ŷ t ∣ t − bΔtð Þ,

RMS ekð Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n〠n

t=2ek tð Þ2

s:

ð7Þ

ekðtÞ records the error between the predicted value andthe actual value at each sampling point, and RMSðekÞ (RootMean Square error) characterizes the degree of deviation ofthe overall predicted value from the actual value. The greaterthe RMSðekÞ is, the greater the deviation of the predicted datafrom sensor data and the worse the predicted performance.By normalizing the RMSðekÞ, the prediction accuracy rate(PR) is defined as

PR y tð Þ, ek tð Þð Þ = 1 −RMS ek tð Þð ÞRMS y tð Þð Þ × 100%: ð8Þ

2.3.2. Smooth Factor (SF).

SF ŷ tð Þð Þ = 1tend max ŷ tð Þð Þ −min ŷ tð Þð Þð Þ

ðtend0

f tð Þ − ŷ tð Þj j:

ð9Þ

In formula (9), tend is the duration of the algorithm, and a5Hz low-pass filter is used to filter yðtÞ to obtain f ðtÞ. Theparameter smooth factor (SF) indicates whether the data issmooth or not. In the course of human gait walking, the pre-dicted sensor data is smooth and stable to match the actualwalking data. Therefore, the smaller the SF is, the closer thepredicted sensor data is to the sensor data measured by theactual gait walking. Since the data actually collected in thealgorithm is discrete, when calculating the SF, formula (12)is usually discretized to the following formula:

SF ŷ tð Þð Þ = 1N max ŷ tð Þð Þ −min ŷ tð Þð Þð Þ〠

N

i=0f ið Þ − ŷ ið Þj j:

ð10Þ

The parameters affecting the prediction effect of theTakens algorithm are as follows: (i) the predicted duration(T), (ii) historical reconstruction delay vector length (P),(iii) optimal matching reconstruction vector number (M),and (iv) embedding dimension (N).

We introduced PSO (Particle Swarm Optimization) onthe basis of Takens prediction algorithms, which is a swarmintelligence optimization algorithm in addition to an ant col-ony algorithm and a genetic algorithm in the field of com-puter intelligence. It originated from the study of birdpredation behavior, and the basic idea is to solve and cooper-ate with individuals in the group to achieve the search for theoptimal solution in a complex space [16]. Compared withother intelligent adjustment algorithms [17–18], such asderivative-based or derivative-based (or gradient-based)(e.g., backpropagation (BP), Levenberg-Marquardt (LM),Kalman filter, least square methods, and sliding-mode learn-

ing algorithm), hybrid learning methods, it belongs to thederivative-free method and does not need to update complexparameter equations, making it more suitable for nonlinearoutput situations. Meanwhile, it has the advantages of strongglobal search ability and easy implementation and has strongconvergence and robustness in the process of solving. In thePSO algorithm, each particle represents a potential solution,and the velocity of the particle represents the direction anddistance of each potential solution, which can be used to seekthe optimal value in the multidimensional space.

The PSO-Takens algorithm flow chart is shown inFigure 3.

Step 1. Initialize a swarm of particles (population size m),including the random position and velocity, and limit theupper and lower limits of the particle’s velocity and position.The optimized parameters in the Takens algorithm are asfollows: historical vector dimension P, optimal matchingnumberM, and embedding dimension N ; therefore, the pop-ulation of particles is fx1, x2, x3⋯ Xmg, and the position ofthe i-th particle is fXPi, XMi, XNig, The velocity of the i-thparticle is fVPi, VNi, VMig.

Step 2. Use the evaluation function to calculate the fitness ofeach particle.

Step 3. For each particle, comparing its fitness with the opti-mal value pbest, it has passed through. If the current value isbetter than pbest, the pbest will be set to the current value,and the position of pbest is set as the current position inthe n-dimensional space.

Step 4. For each particle, comparing its fitness value with thebest position gbest, all particles passed through. If the currentvalue is better, the current position will be regarded as thebest position gbest.

Step 5. After updating the local and global optimal values ofthe current iteration, the particle adjusts its velocity and posi-tion through the following formulas.

Vi+1 =Vi + c1 × randðÞ × pbesti − xið Þ + c2 × randðÞ× gbesti − xið Þ,

xi+1 = xi + Vi+1: ð11Þ

When the inertia factor is added, the velocity expressionbecomes

Vi+1 = ωVi + c1 × randðÞ × pbesti − xið Þ + c2 × randðÞ× gbesti − xið Þ:

ð12Þ

Step 6. If the condition to terminate the iteration is notreached, go to Step2, until the iteration termination condi-tion is met.

According to the specific issue, the iteration terminationcondition is generally to reach the maximum iteration num-ber Gk or the optimal value of the evaluation function to


meet the established threshold. The condition for the algo-rithm to stop iteration is as follows: the number of iterationsover 50, or the fitness calculated by the evaluation functionover 100. The fitness (Yef ) evaluation function expression isfollows:

Yef =w1 ×1SF +w2 × PR: ð13Þ

In formula (15), w1 and w2 are constants (0.5), whichmeans that we believe that the accuracy of data is as impor-tant as the smooth factor in the human lower limb predictionalgorithm. The goal of the PSO-Takens prediction algorithmis to adjust the complex parameter tuning problem of theTakens algorithm in gait prediction, so as to achieve the opti-mal prediction effect.

2.4. Follow-Up Control Design

2.4.1. Dynamic Model of Swing Leg. The movement of thelower limbs of the human body can be regarded as a combi-nation of swing phase and support phase. Usually, the swingphase accounts for 60% of the gait cycle and the supportphase accounts for 40% [19]. For the swinging phase, theswinging legs of the human body can be regarded as aninverted two-link with uniform mass distribution. Duringthe support phase, the leg and the upper body of the humanbody can be regarded as three links fixed at the bottom. Thisdivision method can simplify the complexity of torque calcu-lation in inverse dynamics, making it easy to implement onembedded systems.

The lower limb-assisted exoskeleton single leg model isshown in Figure 4. L0 and L1 are the length of thigh andshank, and the ankle joint is omitted.

Assuming that the mass distribution of the exoskeletonlower limb members is uniform, the centroid coordinatesGiðxi, ziÞ of the exoskeleton thigh and shank are as follows:

x0 = a0 sin q0,z0 = −a0 cos q0,

(ð14Þ

x1 = L0 sin q0 + a1 sin q1,z1 = − L0 cos q0 + a1 cos q1ð Þ:

(ð15Þ

The kinetic energy of the two connecting rods of lowerlimb swing is the sum of the rotational kinetic energy and

START

Initializingparticles

Evaluate particlesand get global optimum

Satisfy the enditeration condition?

NO

Update the speed andposition of each particle

Update the historical optimalposition of each particle

Renew the global optimallocation of the population

Get the optimization parameters.Applied in the prediction algorithm

END

Evaluate the fitnessof each particle

YES

Figure 3: Flow chart of the PSO-Takens algorithm.

x0

q0

m0

m1

x1 q1

z1

z0

a0

L0

a 1L 1

Figure 4: Lower extremity exoskeleton leg’s simplified second linkkinetic model.


kinetic energy of the connecting rod, which can be expressedas follows:

E = 12 〠1

i=0Ii€qi +mi _zi2 + _xi2

� � !: ð16Þ

In formula (16), Ii is the moment of inertia when the exo-skeleton is the i-th lower extremity connecting rod rotating

around the sagittal plane of the joint. The expressionis Ii = ð1/3ÞmiL2i , and €qi is the angular acceleration of thejoint. _zi and _xi are the velocities of the linkage in the x and zdirections, and the total potential energy of the lower limblinkage is as follows:

P = 〠1

i=0migzi: ð17Þ

Human Inertial sensor

Position sensor

Takensprediction Controller

Motordriver EXO

q

q

qd 𝜏

Figure 5: Follow-up control strategy block diagram of the exoskeleton.

0 5 10 15Time (s)

–20

0

20

Deg

(deg

)

Human hip angleEXO hip angle

(a)

Human knee angleEXO knee angle

0 5 10 15Time (s)

0

20

40

60

80

Deg

(deg

)

(b)

Figure 7: Joint angle deviation between human and exoskeleton.

que

¨

qd

qd

EXO

+

H(q) ++

+Kds + Kp

C(q, q)q + G(q).

+

–

𝜏

Figure 6: Control block diagram of calculate torque method.


By defining the Lagrangian function L = E − P and theLagrangian formula, the expression of the joint torque inthe two-link can be expressed as

H qð Þ€qi + C q, _qð Þ _q +G qð Þ = τi: ð18Þ

In formula (18), τi is the joint torque between the links,HðqÞ is the inertia matrix, Cðq, _qÞ is the friction matrix, andGðqÞ is the gravity vector. The expressions of the matrix HðqÞ, Cðq, _qÞ, and the gravity vector GðqÞ are as follows:

H qð Þ =712m0l

20 +m1l21 m1l0l1 cos q0 + q1ð Þ

0 712m1l21

2664

3775,

C q, _qð Þ =0 −m1l0l1 sin q0 + q1ð Þ

−m1l0l1 sin q0 + q1ð Þ 0

" #,

G qð Þ =12m0gl0 sin q0 +m1gl0 sin q0

12m1gl1 sin q1

2664

3775:

ð19Þ

2.4.2. Follow-Up Control Strategy. After obtaining the inversedynamics model of the joint, we use the prediction angleobtained by the prediction algorithm to do Simulink simula-tion of the two-link model in MATLAB. The follow-up con-trol strategy block diagram is shown in Figure 5.

The input of the control system is the angle of the humanjoint qd and the angle sensor placed on the exoskeleton q, andthe joint torque is as the output of the controller and output-ted by the motor driver. It is not necessary and convenient toinstall an angle sensor on the lower limbs of the human body.Since the angle deviation between the exoskeleton and thehuman body is usually a constant value, this means we canpredict the angle of the human body through the positionsensor of the exoskeleton, instead of placing the inertial sen-sor outside the human body, which is the role of the predictalgorithm played in follow-up control strategy.

For the angle data predicted by an algorithm, we used thecalculated torque method for systematic control, aiming atmaking the lower extremity two-link of the exoskeleton fol-low the changing joint curve predicted by the algorithm.Compared with PD control and PD control with gravitycompensation terms, the calculated torque method changes

OriginalTakensPSO-Takens

0 5 10 15Time (s)

–20

0

20

Deg

(deg

)

(a)


0 5 10 15Time (s)

020406080

Deg

(deg

)

(b)

Figure 8: Comparison of Takens and PSO-Takens in prediction of nonstandard gait data. (a) Comparison of hip joint prediction angle. (b)Comparison of knee joint prediction angle.

Table 1: Parameter changes of hip joint prediction algorithm undernonstandard gait data.

# T P M L PR SF Fitness

Takens 10 80 10 300 73.23% 0.2226 38.86

PSO-Takens 10 26 7 644 87.74% 0.2196 46.14

Table 2: Parameter changes of knee joint prediction algorithmunder nonstandard gait data.


Takens 10 80 10 300 71.80% 0.2317 38.05

PSO-Takens 10 48 12 536 85.75% 0.2388 44.97


the lower extremity joints of the exoskeleton into a linear time-invariant system that is easier to control due to the introduc-tion of nonlinear compensation. Huo [20] proved the stabilityof the control method. Based on the inverse dynamics equa-tion, the system can follow the target position well. The con-trol block diagram of this method is shown in Figure 6.

The torque expression calculated by the system controloutput to the hip and knee joints is as follows:

τ =H qð Þ €q + Kd _e + Kpe� �

+ C q, _qð Þ _q + G qð Þ: ð20Þ

In formula (20), the parameters HðqÞ, Cðq, _qÞ, and GðqÞare the matrixes of inverse dynamics in the two-link model;Kd and Kp are diagonal matrices, which are proportionaland differential terms for the tracking error e.

3. Results and Discussion

3.1. Experimental Results

3.1.1. Prediction Algorithm Experiment Result. Figure 7 rep-resents the sensor data of the motion angle data of the jointsin the continuous walking movement. Compared with thesensor data of the wearing exoskeleton, we found that theangle detected from the exoskeleton and the actual motionangle detected from the human body are generally delayedby 200ms, about 10 sampling cycles. Therefore, in a predic-tion algorithm, the sensor data at 200ms after the currentsampling point will be predicted based on EXO historical

data. The angle sensor data obtained by three participants(65 ± 5 kg, 170 ± 5 cm) continuously walking at a speed of3.6 km/h on a treadmill was recorded and predicted. Noneof the participants reported healthy problems in the previousthree months.

From the analysis of the accuracy of the prediction angledata shown in Figure 8 and Tables 1 and 2, for both joints, thePSO-Takens has increased the accuracy of the predictionnearly 14:23 ± 0:5% (n = 3, two-sided paired t-test, p = 0 <0:05), while the smoothing factor is almost unchanged. Dueto the fact that the algorithm needs to store historical data,the algorithm will not immediately predict when the algo-rithm starts to execute. The area where the predicted valueis 0 is the dead zone.

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Figure 9: Comparison of Takens and PSO-Takens in prediction of standard gait data. (a) Comparison of hip joint prediction angle. (b)Comparison of knee joint prediction angle.

Table 3: Parameter changes of hip joint prediction algorithm understandard gait data.


Takens 10 120 10 900 77.52% 0.2133 41.10

PSO-Takens 10 69 3 767 88.19% 0.2091 46.48

Table 4: Parameter changes of knee joint prediction algorithmunder standard gait data.


Takens 10 120 15 900 87.14% 0.2063 45.99

PSO-Takens 10 77 15 1296 95.50% 0.2051 50.18


Figure 9 and Tables 3 and 4 show the performance of thetwo prediction algorithms under the standard and fixed fre-quency of the joint angle (data from [21]). The predictionaccuracy in Tables 3 and 4 shows that the accuracy of the pre-diction is improved (hip joint from 77.85% to 88.19%, kneejoint from 87.14% to 95.50%), while the smooth factorremains almost unchanged. Therefore, after the PSO-Takens algorithm is executed, for the movement data of thelower limbs, the prediction algorithm with optimized param-eters becomes accurate and stable.

3.2. Prediction Algorithm Experiment Result. Since the cur-rent pose and the motion-sensing data of the previous period

can only reflect the current motion state, to achieve betterperformance, the exoskeleton system needs to predict theposture data of the following period of time. After processingand analyzing the predicted pose data, the motion intentionwas judged in advance. By predicting the motion angle ofthe human body and introducing it into the control of theexoskeleton, the human-machine coordinated motion pro-cess of the exoskeleton can be more flexible and smoother.

In order to compare the performance of prediction algo-rithms and algorithm optimization in simulation, the jointdata during motion and the predicted joint data wereimported into the two-link model simulation system for acomparative experiment, and the evaluation method of the

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Figure 10: System joint angular output (a). System hip joint angle output (b). System knee joint angle output (c). Hip joint follow controlangle error (d). Knee joint follows control angle error.


algorithm mentioned in the second section was used to eval-uate the performance of the algorithm. The experimentalresults are shown in Figure 10.

It can be found that the predicted data lags behind thesensor data of human motion when the system’s lower limbjoints are controlled to follow the human body at the begin-ning. Over time, the torque control algorithm with gravitycompensation can control the two links to the angle pre-dicted by the two prediction algorithms. When the state orfrequency of the motion changes, the prediction error occurs,but the PSO-Takens algorithm shows a better antidistur-bance ability, and the maximum error during movement isalso better than the original algorithm.

It can be found from Figure 10, in the case of control themovement of the exoskeleton following the lower limbs ofthe human body without using prediction algorithm, due tothe large deviation of the angle, a large interaction force ofhuman-computer interaction force may occur. If the methodof prediction is adopted in the control loop of the exoskele-ton, the movement of the exoskeleton will be at an angle dif-ferent from the actual movement of the human body at theinitial stage. With the increase of time, the two links of thelower limbs of the exoskeleton gradually follow the move-ment of the human body and maintain a high consistencywith the movement of the human body. It is undeniable thatthere is still a deviation between the exoskeleton and the

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Figure 11: System joint angle output for standard gait data input (a). Hip joint angle output (b). Knee joint angle output (c). Hip joint followcontrol angle error (d). Knee joint follows control angle error.


human body. According to formula (8), the accuracy of theprediction using the Takens method for hip joint and kneejoint is 65.10% and 66.71%, while the PSO-Takens hasincreased to 82.13% and 83.03%. When the gait becomes sta-ble, the error of Takens algorithms ranges from -0.13 rad to0.18 rad (hip) and from -0.17 rad to 0.11 rad (knee). Whilethe error of PSO-Takens ranges from -0.04 rad to 0.07 rad(hip) and from -0.05 rad to 0.09 rad (knee).

For standard gait data with a fixed frequency, inappropri-ate parameters of the Takens algorithm will have obviouserrors at the beginning of the prediction, while the PSO-Takens algorithm will not have this problem. Figure 11shows that the error of Takens algorithms ranges from-0.14 rad to 0.10 rad (hip) and from -0.12 rad to 0.09 rad(knee), the error of PSO-Takens algorithms ranges from-0.05 rad to 0.06 rad (hip) and from -0.03 rad to 0.04 rad(knee). According to formula (8), the Takens algorithm pre-diction accuracy rates of the hip and knee joints are calcu-lated as 72.10% and 83.73%, and the PSO-Takens algorithmprediction accuracy rates are 86.07% and 94.01%, which alsoshows the PSO-Takens algorithm performs better in predict-ing such data.

4. Discussion

In the case of ignoring the elasticity coefficient and inertiacoefficient, the human-computer interaction model can besimplified; in this situation, Racine [22] proposed the interac-tion force can be calculated as follows:

Fe = K qh − qeð Þ: ð21Þ

In formula (24), Fe is the human-machine interactionforce and qh, qe represent the human joint angle and EXOjoint angle detected by a sensor, while K equals K0/L0(Nm/rad·m), L0 indicates the distance between the measure-ment point and the joint rotation center, and K0 is a constantthat varies from the system. Formula (24) means that if thereis no angle deviation between the human body and the exo-skeleton, it can be considered that the exoskeleton will nothinder the movement of the human body in the walking stateof the human body, and the human-machine interactionforce will close to 0.

The difficulty of the exoskeleton system controller is howto control the system to move to the target posture of thehuman body at the next moment. Relying on the installationof an inertial sensor on the exoskeleton has hysteresis andcannot judge the posture of the human body at the subse-quent moment. This paper is devoted to the realization ofhuman body motion prediction angle algorithm and intro-duces it to the control system. The simulation experimentresults show that, for the angle prediction of exoskeleton,the PSO-Takens algorithm has the function of improvingalgorithm parameters. Whether it is linear prediction basedon ARMA model LMS, RLS, or DMP [23], the algorithmparameters need to be optimized according to different sys-tems. The PSO-Takens algorithm can deal with periodic dur-ing gait walking data, and when the body’s movement lawchanges, such as from walking to jumping or stopping, the

accuracy of the prediction algorithm will be reduced, whichis the point that the prediction algorithm needs to beimproved in the future study.

5. Conclusions

In this paper, a human motion capture system is designed toacquire human walking joint data, and a method for optimiz-ing parameters of Takens nonlinear prediction algorithm isproposed. Compared with the original Takens predictionalgorithm, the prediction angle obtained by the improvedprediction PSO-Takens algorithm is more closely related tothe actual motion angle data of the human body, with asmaller error rate and smooth features. When the predictedsensor data from the PSO-Takens algorithm were appliedto the joint angle prediction algorithm of the lower extremityexoskeleton, it can improve the accuracy of prediction andenhance the adaptability of the exoskeleton and human body.

Data Availability

The EXO and predicted sensor data based on different algo-rithms used to support the findings of this study are availablefrom the corresponding author upon request.

Conflicts of Interest

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This research is partly supported by the Natural ScienceResearch General Program of Higher Education of JiangsuProvince (16KJB510040). We would like to thank ZhichengQu and Wei Wang for the help with control design.

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Exoskeleton Follow-Up Control Based on Parameter Optimization of Predictive Algorithm1. Introduction1.1. Introduction to Exoskeleton Classification1.2. Introduction to Prediction Algorithm

2. Materials and Methods2.1. Motion Capture System2.2. Takens Prediction Algorithm2.3. PSO-Takens Prediction Algorithm Design2.3.1. Prediction Accuracy Rate (PR)2.3.2. Smooth Factor (SF)

2.4. Follow-Up Control Design2.4.1. Dynamic Model of Swing Leg2.4.2. Follow-Up Control Strategy

3. Results and Discussion3.1. Experimental Results3.1.1. Prediction Algorithm Experiment Result

3.2. Prediction Algorithm Experiment Result

4. Discussion5. ConclusionsData AvailabilityConflicts of InterestAcknowledgments

exoskeleton follow-up control based on parameter ...research article exoskeleton follow-up control...

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