Robust Iterative Learning Control Algorithm for lower limb

rehabilitation proactive human-robot collaboration

JINGPINHG GING XIAN 1, SAMBA AIME HERVE 2

Intelligent Robot Research Center, Zhejiang Lab, Hangzhou, China 1

Po. Box 356, Hangzhou, China

National Higher Polytechnic School, University of Douala, Douala, Cameroon 2

Po. Box 1872, Douala, CAMEROON

Abstract: At present, the motion control algorithms of lower limb exoskeleton robots have errors in tracking the

desired trajectory of human hip and knee joints, which leads to poor follow-up performance of the human-machine

system. Therefore, an iterative learning control algorithm is proposed to track the desired trajectory of human hip

and knee joints. In this paper, the experimental platform of lower limb exoskeleton rehabilitation robot is built,

and the control system software and hardware design and robot prototype function test are carried out. On this

basis, a series of experiments are carried out to verify the rationality of the robot structure and the feasibility

of the control method. Firstly, the dynamic model of the lower limb exoskeleton robot is established based on

the structure analysis of the human lower limb; secondly, the servo control model of the lower limb exoskeleton

robot is established based on the iterative learning control algorithm; finally, the exponential gain closed-loop

system is designed by using MATLAB software. The relationship between convergence speed and spectral radius

is analyzed, and the expected trajectory of hip joint and knee joint is obtained. The simulation results show that

the algorithm can effectively improve the gait tracking accuracy of the lower limb exoskeleton robot and improve

the follow-up performance of the human-machine system.

Key-Words: lower limb exoskeleton robots, iterative learning control algorithm , knee joints,human-machine

system

Received: August 29, 2021. Revised: April 21, 2022. Accepted: May 23, 2022. Published: June 30, 2022.

1 Introduction

With the coming of the 21st century, the aging of the

population is becoming more and more serious. Some

diseases and injuries lead to functional disorders of

lower limb movement. Lower limb assisted ex-

oskeleton robot is a wearable human-computer inte-

grated equipment, which can complete various high-

intensity tasks through the guidance of human lower

limbs [1]. The equipment provides assistance for hu-

man walking, enhances human walking ability and

speed, and relieves human fatigue under high load and

long-time walking. Motion control algorithm is the

core part of the control system of exoskeleton robot

[22]. The key technology of the control algorithm is

to recognize the gait information of the wearer and

detect the wearer’s motion intention. The research

team of Berkeley University of California developed

a lower extremity exoskeleton robot (BLEEX) using a

hybrid control algorithm of position control and sen-

sitivity amplification control [3]. The exoskeleton

robot (hal-5) developed by the University of Tsukuba,

Japan, judges the wearer’s movement intention by

collecting biological current on human skin and con-

trols the exoskeleton machine. The results show that

the lower limb rehabilitation exoskeleton will follow

the wearer to exercise [4]; the lower limb rehabili-

tation exoskeleton developed by the State Key Lab-

oratory of Fluid Transmission and Control of Zhe-

jiang University uses the analysis and decisionmaking

method of fuzzy logic to identify the wearer’s move-

ment intention [5]; the fuzzy adaptive PID (proportion

integral) is adopted by Shanghai Jiaotong University.

The application of derivative control algorithm to hy-

brid lower limb exoskeleton robot increases the load

capacity of human body.

As we all know, many controlled objects in the

actual control system are nonlinear, and the motion

process has periodicity, such as robot control system.

Although we hope to understand the characteristics

of the controlled object clearly in the actual control,

so as to obtain the accurate mathematical model to

realize the accurate motion control, it is difficult to

achieve because of the complexity of the system. PID

control, which is widely used in industrial field, can

control the nonlinear system [6]. However, it often

takes a lot of time to adjust PID parameters, and it may

not achieve good control effect and control efficiency.

The ILC strategy is suitable for the control of such

periodic nonlinear systems because of its model inde-

pendent characteristics and strong self-learning abil-

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ity, which also lays the foundation for the rapid devel-

opment of ILC. Miao et al. [7] did a lot of research

on various control laws of iterative learning, such as

the study of control algorithm theory and application,

made a detailed explanation, and made clear the con-

cept of ILC. Since then, research teams around the

world have conducted extensive research on ILC, in-

cluding the design of learning control law, algorithm

stability analysis, and robustness analysis of learn-

ing control and convergence rate [8]. The research

on the theoretical basis of these algorithms provides

a good theoretical basis for the application of ILC in

various fields. At present, ILC has been widely used

in industrial control, such as robot repetitive opera-

tion control. Due to the excellent self-learning ability

of ILC to the controlled system, it has also been ap-

plied to exercise rehabilitation with periodic move-

ment characteristics in recent years. For example,

Ghanbari et al. [9] used a phase ahead ILC algorithm

in the upper limb rehabilitation based on NMES to

reconstruct the motor function of the affected limb.

In addition, ILC is also used to control and obtain

the desired ankle movement to achieve foot drop cor-

rection. The process of iterative learning is to make

the trajectory tracking error of the controlled system

smaller and smaller by repeatedly running the control

system. Through repeated learning of the controlled

system, the controller makes the actual trajectory ap-

proach the expected trajectory continuously. ILC is

characterized by strict mathematical description and

low requirements for controlled system. -erefore, ILC

is usually suitable for nonlinear systems

The Swiss Federal Institute of Technology Zurich

has developed a gait rehabilitation training robot

LOKOMAT that can be put on the market [?]. The

rehabilitation robot has four degrees of freedom and

is used with a weight-reducing device and a treadmill

to drive patients to reciprocate gait movement. The

exoskeleton uses a DC servo motor to drive the lead

screw to drive the upper and lower legs to swing in

the sagittal plane. In addition, in the follow-up study,

the posture control of the exoskeleton stepping on the

joint was increased, which can prevent the foot injury

caused by the patient’s toe drop. At the same time,

in order to realize the active and passive rehabilita-

tion training of patients, strategies such as PD control,

impedance control, force/position hybrid control, and

adaptive control were, respectively, proposed. The

experiment proved the effectiveness of the control

strategy [11]. At present, although LOKOMAT has

been put into use in some world-renowned rehabilita-

tion centers and hospitals, it is still unacceptable for

most rehabilitation hospitals due to its high price.

In this paper, based on the poor tracking perfor-

mance of lower limb exoskeleton robot following hu-

man motion, iterative learning control algorithm is

suitable for repeated work in limited time and can

achieve the desired trajectory tracking. Therefore,

based on iterative learning control algorithm, this pa-

per puts forward the following control model of lower

limb exoskeleton robot; through the analysis of hu-

man lower limb structure, establishes the dynamic

model of lower limb exoskeleton robot; uses itera-

tive learning control algorithm to design the motion

control system and carries out convergence analysis;

and uses MATLAB software to analyze the human

hip. Tracking the desired gait trajectory of the joint

and knee joint verifies the superiority of the iterative

learning control algorithm and shows good applica-

tion value.

2 Dynamic Modeling of Lower Limb

Exoskeleton Robot

Biomechanical simulation and experimental studies

show that the power consumed by human body in

sagittal plane is equivalent to the sum of frontal plane

and horizontal plane. From the control point of view,

robot belongs to multivariable nonlinear automatic

control system, and each control task itself is a dy-

namic system. Robot dynamics is the basis of robot

technology research. Studying robot dynamics is to

pave the way for better solving control problems.

2.1 Structural Analysis of Human Lower

Limbs

After a lot of simplifications to the dynamics of the

musculoskeletal system, the modeling process is still

extremely complicated, with many model parame-

ters. The process of musculoskeletal system produc-

ing joint motion is highly nonlinear, such as the pro-

cess of muscle fiber recruitment and joint viscoelas-

ticity. In addition, the time-varying characteristics of

the parameters of the musculoskeletal system of the

human body are also very obvious, and the related pa-

rameters may change in different time periods and dif-

ferent posture measurements [12], and under the ac-

tion of electrical stimulation, the acceleration of mus-

cle fatigue will also bring about physiological param-

eters. These factors not only bring great difficulty to

the identification of model parameters, but also the ac-

curacy of parameter identification cannot be guaran-

teed, which brings a lot of challenges to model-based

joint motion control. Therefore, in order to obtain a

good control effect, the control target of the control

system must be the self-learning and adaptive capa-

bilities of the musculoskeletal system.

Figure 1 shows the phase diagram of human gait

cycle. For unilateral lower limb, a gait cycle can be

divided into two phases: support phase and swing

phase. Among them, the support phase accounts for

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60% of the whole movement period, including the sin-

gle foot support state and the bipedal support state,

and the swing phase accounts for 40% of the whole

swing period [13].

Therefore, in the man-machine coupling system,

the rotation of the hip joint and knee joint in the single

foot support state drives the swing of the thigh, leg,

and foot to realize the posture movement of the human

lower limbs. -is article attempts to apply the ILC algo-

rithm to the design of the NMES joint motion control

system, in order to use the ILC algorithm to achieve

stable and accurate joint motion control without rely-

ing on the characteristics of the precise model and the

powerful self-learning ability. Theerefore, this sec-

tion first explains the theoretical basis of ILC and then

designs an iterative learning control joint motion con-

trol system and simulates based on the musculoskele-

tal system model established in the previous section

to verify the feasibility and effectiveness of the algo-

rithm.

According to the normal movement space of hu-

man body, the degree of freedom of human lower limb

movement includes thigh flexion and extension, in-

ternal rotation, external rotation, and adduction and

abduction; leg flexion and extension; foot flexion and

extension, internal rotation, external rotation, and ad-

duction and abduction. As the main form of human

movement, walking completes the body movement

through the alternate support of two feet. In the pro-

cess of human walking, it is stipulated that a complete

gait cycle starts from one foot following the ground

and ends with another landing on the same side.

2.2 Dynamic Model of Lower Limb

Exoskeleton Robot

The dynamic equation of lower limb exoskeleton

robot mainly describes the relationship between robot

motion and control force. The movement of walking

posture mainly occurs in the sagittal plane. A com-

plete support phase can be divided into one-foot sup-

port state and two-foot support state. In the stage of

single foot support, the driving torque of hip joint and

knee joint of swinging leg is larger than that of bipedal

support state; because the ankle joint mainly adjusts

the direction of human motion in the horizontal plane,

the joint driving torque provided in the sagittal plane

is smaller [14]. Therefore, the swing leg of lower limb

exoskeleton robot can be simplified into the swing leg

model as shown in Figure 2 in sagittal plane. As-

suming that the mass of the connecting rod is concen-

trated in the center of the link, the simplified swing leg

model of the exoskeleton robot is analyzed. The man-

machine system is taken as the research object by the

Lagrange method. The kinetic energy and potential

energy of the human-machine system are analyzed,

and the dynamic equation is obtained:

Figure 1: Phase diagram of human gait cycle.

τ−T a =A(p)p+B(p, p)p+C(p)(1)

In equation (1), define the joint angular dis-

placement pθ1

θ2, inertial force matrix A(p) =

m11 m12

m21 m22 , and

m12 =m21 = 0.25a2L2

2+ 0.5a2L1L2cosθ2,

m11 = 0.25a1L2

1+a2L2

1+ 0.25a2L2

a2L1L2cosθ2,

m22 = 0.25a2L2(2)

Centrifugal force matrix is

B(p, p) = b11 b12

b21 b22 (3)

b11 =−a2L1L2sinθ2,

b12 =−0.5a2L1L2sinθ2,

b21 = 0.5a2L1L2sinθ2,

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b22 =a2L1L2sinθ2(4)

Define the gravity vector:

C(p) = c1

c2

c1= 0.5a1gL1cosθ1+a2gL1cosθ1+

0.5a2gL2cos(θ1+θ2),

c2= 0.5a2gL2cos(θ1+θ2),(5)

Figure 2: Swing leg model.

Among them,a1and a2represent the mass of thigh

and lower leg, respectively, L1and L2represent the

length of thigh and lower leg in man-machine system,

and θ1and θ2represent the motion angles of hip joint

and knee joint, respectively.

The control system of the lower limb exoskele-

ton rehabilitation robot involves human-computer in-

teraction. The impact of the patient is in the cir-

cuit. In order to consider the safety of the patient and

the interference of the patient’s exoskeleton control,

the control system should have high real-time perfor-

mance and good robustness. In addition, because the

lower extremity exoskeleton rehabilitation robot in-

teracts with the patient and the patient sends out an

active movement intention as an input signal for the

exoskeleton control, the human-computer interaction

control algorithm is indispensable. In order to pre-

vent the affected limb from confronting the exoskele-

ton due to abnormal muscle activities (such as spasm),

interactive control should be able to provide a safe and

active and flexible training method [14]. At the same

time, in order to encourage patients to actively partic-

ipate in rehabilitation training, so that patients have

a sense of success, interactive control will obtain the

patient’s active movement intention from sensor sig-

nals to achieve active training.

3 Control of Lower Limb

Exoskeleton Robot

Lower extremity exoskeleton robots assisting pa-

tients with gait rehabilitation training have become

the mainstream trend of adjuvant therapy for patients

with hemiplegia caused by spinal cord injury such as

stroke. It can replace part of the therapist, increase

training intensity, delay training time, etc. There-

fore, how to effectively control the lower extremity

exoskeleton rehabilitation robot to assist patients in

completing gait rehabilitation training has become a

main focus of research at home and abroad. It can be

known from the theory of rehabilitation that when the

patient is suffering from paresis (pre-rehabilitation),

the muscle strength of the patient is very small. Pas-

sive rehabilitation is mainly used to improve the mus-

cle tension of the patient and inhibit abnormal muscle

movement. In the passive training mode, the lower

limb exoskeleton orthosis drives the patient’s lower

limbs to make a fixed gait movement according to the

reference trajectory according to the fitted experimen-

tal data, without adjusting the trajectory [15]. How-

ever, with the continuous deepening of the rehabili-

tation training process, the patient’s muscle strength

continues to improve, and the patient is willing to ac-

tively participate in the rehabilitation training. In pa-

tientassisted gait rehabilitation training, the gait train-

ing trajectory of the exoskeleton robot can be ad-

justed by the interaction between the patient and the

exoskeleton, so that the walking gait is determined

jointly by the exoskeleton robot and the patient in-

stead of one rigid gait improving patient participation

and sense of success. Therefore, for the above dif-

ferent rehabilitation stages, this section proposes the

control algorithms for passive and active auxiliary re-

habilitation training for patients.

Exoskeleton robot has the dynamic characteris-

tics of high nonlinearity, strong coupling, and time-

varying. When designing the controller, due to the

uncertainty of the mathematical model, the designed

controller may lead to the system performance insta-

bility. Iterative learning control (ILC) is character-

ized by simple learning algorithm and independent

of the detailed model of the controlled system. It is

suitable for the controlled object with repetitive mo-

tion in finite time interval. On the basis of establish-

ing the dynamics model of lower limb exoskeleton

robot, the tracking error is adjusted to the learning

signal to improve a certain control target and realize

the tracking of the desired trajectory. Reference [17]

used high-speed camera to carry out clinical gait ex-

perimental analysis and obtained the expected joint

motion curves of hip joint and knee joint of lower

limb exoskeleton robot in sagittal plane as shown in

Figure 3. Through the cftool data fitting toolbox of

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MATLAB 2020b, the expected motion trajectory of

the lower limb exoskeleton robot in the hip joint and

knee joint is defined as

Phip(x) = 21.39.sin(4.27x−0.58) + 8.92 (6)

Pknee(x) = 43.14sin(2.74x−0.65)+31.4sin(4.8x+8.91)

(7)

where phip(x)and pknee(x)denote the expected

motion angle of hip joint and knee joint, respectively,

and X represents the exercise time. The expected joint

trajectory of lower limb exoskeleton robot in sagittal

plane is shown in Figure 3.

3.1 Basic Principles of Iterative Learning

Control

In this control technology, iterative learning always

starts from an initial point, and almost all convergence

proofs require the same initial conditions [18]. When

designing an iterative learning system, in order to en-

sure the convergence of the system, the initial value of

the iteration at the beginning of each iteration should

be consistent with the expected initial value [19]:

yi(0) = yk(0)i= 0,1, ...k, (8)

where yi(0) represents the initial value of iteration

and yk(0) is the expected initial value. At the be-

ginning of learning, the initial state of the system is

y0(0). The λk+1(x)motion error εk+1(x)is reduced

by learning the control law. It is shown in the struc-

ture diagram of D-type learning law system. Its con-

trol method is as follows: the K+1 control λk+1(x)is

equal to the correction term of the kth control λk(x)

plus the output error εk(x)of the kth time [13], and

the iterative learning control law is

λk+1(x) = λk(x) + µk(x)Γεk(x)(9)

where λk+1(x)denotes the K+ 1 control, t∈

[0, t],Krepresents the number of iterations, µk(x)>

1, and Γrepresents the learning gain coefficient.

The complete closed-loop control system includes

control modules, execution modules, feedback mod-

ules, and controlled objects. The specific process is

to use the PC console as the control module to out-

put control commands to the neuromuscular electri-

cal stimulator as the execution module through serial

communication. The electrical stimulator generates

electrical stimulation pulse sequences that act on the

target muscles through stimulation electrodes, while

the feedback module uses angles [20]. The sensor col-

lects the knee joint angle and feeds it back to the con-

sole in real time. The following will briefly introduce

the characteristics and functions of each part of the

hardware system. The PC console is a hardware plat-

form that implements control algorithms and delivers

control instructions to the electrical stimulator. This

research is based on the framework and uses C++ lan-

guage to write software programs to realize the con-

trol algorithm. The software program can realize the

functions of real-time calculation of the required con-

trol amount, data communication with the electrical

stimulator, and control interface display [21]. The

calculation of the control quantity is to obtain the error

information by comparing the actual angle obtained

by the angle sensor with the expected angle and calcu-

late the current required control quantity based on the

control algorithm designed above; the data commu-

nication module is responsible for obtaining the ac-

tual angle from the angle sensor in real time and out-

putting the control amount to the electric stimulator

in real time; the control interface display is used for

the operator to observe the control effect in real time

and evaluate and adjust. The main hardware system

required by the system is shown in Figure 4.

In order for robots to serve humans, the medium

of information exchange between humans and ma-

chines is indispensable. The motion control function

is the core of the lower limb exoskeleton rehabilita-

tion robot to achieve different strategies for the reha-

bilitation mode [?]. Therefore, the quality of the mo-

tion control directly determines whether the robot can

complete tasks efficiently and accurately, as well as

the safety and comfort of the user. The lower limb ex-

oskeleton rehabilitation robot is in direct contact with

the user, and its failure may cause the robot to be de-

stroyed and the user to suffer serious injury. There-

fore, besides realizing basic motion control, its safety

protection function is also very important. Based on

the basic requirements of the above functions, the

control system of the lower limb exoskeleton rehabil-

itation robot is designed.

Figure 3: Expected joint trajectory of lower limb ex-

oskeleton robot in sagittal plane.

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Figure 4: D learning law system structure.

3.2 Design of Motion Control System.

The control task of the lower limb exoskeleton robot

is to track the desired trajectory of repeated gait. After

each iteration cycle, the lower limb exoskeleton robot

returns to its original position. By learning the control

law, λk(x)is designed to reduce the kth motion error

[23].

The convergence of the learning efficiency is de-

termined by the spectral radius of the control law,

that is, the convergence of the learning efficiency

is inversely proportional to the spectral radius, and

the necessary and sufficient condition for the conver-

gence of the exponential variable gain closed-loop D-

type iterative learning control rate is the spectral ra-

dius λ < 1.

The spectral radius of closed-loop D-type con-

troller is shown in Figure 5, where the learning gain

coefficients are 50, 100, and 120, respectively. It can

be seen from Figure 5 that the spectral radius of the

learning gain coefficient of 100 is lower than that of

the other two gain coefficients, and the convergence

speed is faster. It can be clearly seen from Figure

5 that when the learning gain coefficient in the ex-

ponential variable gain closed-loop D-type iterative

learning control rate is 100, after one cycle of iter-

ative learning, the spectral radius decreases rapidly,

and the corresponding convergence speed increases.

From the third iterative learning cycle, the spectral

radius reaches the minimum, and the corresponding

convergence speed reaches the fastest, and the spec-

tral radius is in the whole range. During the move-

ment, it is assumed that the speed is a constant, and the

convergence of motion control system is improved

with the increase of movement time. On the basis

of exponential variable gain closed-loop D-type iter-

ative learning control rate, the spectral radius which

affects the convergence rate of motion control system

decreases with the increase of time t, and the conver-

gence rate of iterative learning is inversely propor-

tional to the spectral radius. Therefore, the conver-

gence speed of iterative learning increases gradually.

From the third iteration cycle, the spectral radius is

the smallest and the convergence speed is the fastest,

which realizes the integration of the human computer

system.

Figure 5: Spectral radius of closed-loop controller.

4 Analysis of Simulation Results

4.1 The Proposed Control Targets for

Stormwater Runoff Control in Central

Urban Areas.

The goal of lower limb exoskeleton rehabilitation

robot is to replace rehabilitation doctors to assist pa-

tients with gait rehabilitation training and improve

the efficiency of rehabilitation training and the effect

of rehabilitation treatment. After three-dimensional

modeling, theoretical calculation, simulation analy-

sis, processing, and assembly, the physical prototype

of the lower limb exoskeleton rehabilitation robot is

basically completed. This section mainly introduces

the construction of the system experimental platform,

the hardware integration and debugging in the con-

trol system, and the design of the human-computer in-

teraction interface of the rehabilitation training mode

selection module in the software system [16]. After

the completion of the system, a series of experiments

including functional test, passive rehabilitation train-

ing, and active auxiliary training were carried out.

The experiment not only verifies the feasibility of the

structure and the effectiveness of the algorithm but

also provides a theoretical basis for further proposing

more ideal ontology structure and control strategy.

The exoskeleton must be wearable, so the bone

shape and the distribution of degrees of freedom must

be studied before the configuration design. Though

the study of the mechanism of human lower limb

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bones, the lower limb bones are composed of thigh

bones, calf bones, and foot bones, which are, respec-

tively, formed by three parts of skeletal joints, knee

joints, and step joints, and the entire lower limbs are

formed by two series mechanisms in parallel [17]. In

order to study the movement of the human body, er-

gonomics and clinical medicine usually use the sagit-

tal plane, frontal plane, and horizontal plane to de-

scribe. In terms of the structural form of the joints,

each joint movement is not strictly about the center of

the sphere but is a compound movement of sliding and

rotating. However, considering the relatively small

amount of sliding, it is generally treated as an ideal

spherical pair. The spherical rotation of the joint can

be decomposed into rotation around three two-by-two

orthogonal joint axes, which are abduction/adduction,

extension/flexion, and internal rotation/ external ro-

tation, as shown in Table 1. Due to the limitation

of ligament length, the amplitudes of the rotation an-

gles of the skeleton joint, knee joint, and step joint

in the three directions are quite different. The skele-

tal joint has 3 degrees of freedom, which can realize

abduction/adduction, extension/flexion, and internal

rotation/external rotation; the knee joint has 1 degree

of freedom, which can only achieve extension/flex-

ion movements; the stepping joint has 3 degrees of

freedom, which can achieve abduction/adduction, toe

flexion/dorsiflexion, and internal rotation/external ro-

tation movement. The range of rotation angle of each

joint of the lower limbs can be obtained from the sta-

tistical results of ergonomics.

The lower extremity exoskeleton rehabilitation

robot studied in this subject is a device used for gait

rehabilitation training for patients. The gait is mainly

composed of the flexion/extension movement of each

joint in the sagittal plane, so the movement of other

planes is not studied. The lower extremity exoskele-

ton can be simplified into a 7-bar model with 6 de-

grees of freedom, that is, the left and right leg joints,

knee joints, and step joints each have 1 degree of free-

dom of rotational movement, and the patient’s balance

is maintained by a weight-reducing balance mecha-

nism.

In addition, we take the joint movement angles of

the exoskeleton orthosis shown in Table 2 as the de-

sign index of the lower extremity exoskeleton ortho-

sis.

Because the musculoskeletal system of different

people shows great differences, it is necessary to iden-

tify the parameters of the musculoskeletal system of

different subjects before the formal experiment. The

iteration speed of the model-based ILC algorithm pro-

posed in this paper is related to the accuracy of the

model, so good model parameters can further accel-

erate the iterative learning process when the iteration

speed is already fast. The parameters that need to be

identified include human inertia parameters, joint mo-

tion parameters, and muscle activation and contrac-

tion parameters. This article looks for subjects to par-

ticipate in human joint motion control experiments.

Some subjects cannot get rid of their own random

control and other influencing factors, so follow-up ex-

periments are not ideal. Based on the data of human

body size in adult body size and the relative mass dis-

tribution of human body segments, the main sizes and

masses of lower limbs are obtained as shown in Table

Everyone’s height and size are different. If we

want to ensure that the lower limb exoskeleton robot

can meet the physiological characteristics of human

body, we must fully consider this point in the design.

According to the probability distribution research of

ergonomics measurement, it is concluded that there is

a direct proportional relationship between the size of

the lower limb bone and the height of Chinese adults.

According to the established motion control equation

of the lower limb exoskeleton robot, considering the

external interference, the expected trajectory of the

lower limb exoskeleton robot hip joint and knee joint

and the actual tracking trajectory based on iterative

learning control are shown in Figure 6. Due to the in-

fluence of the robot load disturbance, it acts on the ex-

ponential gain closed-loop D-type iterative learning

control rate [18]. Then, according to the error perfor-

mance function between the expected value and the

actual value of the joint, the weight is modified itera-

tively to make the actual tracking of the hip joint and

knee joint closer to the expected trajectory.

The change of gait trajectory tracking error in the

iterative learning control process is shown in Figure

7. By comparing and analyzing the spectral radius of

the closed

Table 1: Range of rotation angle of each joint of lower

limbs.

Joint Extension/ bending Abduction/ adduction

Hip joint 145/25 35/25

Knee joint 0/135 0

Ankle joint 34/25 20/20

5 Conclusion

The joint motion control system is designed based

on the ILC algorithm, and the simulation analysis is

carried out. Aiming at the problem of slow iteration

speed and insufficient accuracy of the traditional ILC

algorithm in the control system, the musculoskeletal

model was introduced, the ILC electrical simulation

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Table 2: Joint motion range of lower limb exoskeleton

orthosis.

Joint Movement Gait angle

Hip flexion/extension 150/235 25/15

Knee joint flexion/extension 0/130 0/55

Ankle joint flexion/extension 30/20 25/30

Table 3: Size and mass of lower limbs.

Body segment name Mass (kg) Length (mm)

Thigh 8.247 542.39

Lower leg 2.942 436.92

Figure 6: Trajectory tracking results based on itera-

tive learning control.

algorithm based on the musculoskeletal model was

designed, and its control effect was verified through

simulation analysis. The joint motion control exper-

iment research was launched, including the complete

design of the joint motion experiment program, the

parameter identification of the musculoskeletal sys-

tem of different subjects, and the development and re-

sult analysis of joint motion control experiments. It is

verified that the ILC electrical simulation algorithm

based on the musculoskeletal model has a good con-

trol effect in human joint motion control.

Aiming at the problem of providing good pos-

ture balance assistance in the rehabilitation process

of lower limb paralysis patients, taking the standing

posture balance as an example, the human posture bal-

ance experimental research has been carried out, in-

cluding the design of experimental schemes, the de-

velopment of experiments, and the analysis of exper-

Figure 7: The change of gait trajectory tracking error

in iterative learning control process.

imental results. Finally, the law of human body pos-

ture balance and the mechanism of lower limb joints

in the process of maintaining posture balance of the

human body are discussed, which has positive signif-

icance for the subsequent design of a lower limb mo-

tor function rehabilitation system that integrates the

ability of posture balance.

In the walking posture of human body with repet-

itive motion, the motion control model of lower limb

exoskeleton robot is established based on iterative

learning control algorithm. The exponential gain

closed-loop D-type motion control system is designed

by MATLAB software, and the expected trajectory

of human lower limb hip joint and knee joint is ob-

tained. The simulation results show that due to the

following response time in the initial stage, there is

a large error in the initial stage of the lower limb ex-

oskeleton robot following the human body. After two

iterations, the expected trajectory tracking error of the

hip joint and knee joint is basically eliminated, which

effectively solves the errors of the human body’s hip

and knee joints’ expected trajectory tracking error and

poor servo performance.

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