Page 87 - Read Online

Page 96 Zhou et al. Intell Robot 2023;3(1):95-112 I http://dx.doi.org/10.20517/ir.2023.05

1. INTRODUCTION
In recent years, the aging population of many countries in the world has increased sharply, and the health
[1]
problems of the elderly have been widely concerned by the public . Stroke is a common disease in the el-
derly population, which will lead to the paralysis of the lower limbs of patients. If the patient can get timely
and effective exercise rehabilitation treatment, the patient’s motor function can be restored [1,2] . Traditional
rehabilitation training mainly relies on physical therapists to provide patients with highly repetitive training.
However, the number of therapists is seriously insufficient to meet the social requirements. Furthermore, the
traditional method is a mostly subjective evaluation, which is inefficient and cannot guarantee effectiveness.
In this situation, a lower limb exoskeleton robot is useful for the patient to conduct repetitive rehabilitation
training, greatly reduce the burden of therapists, and assist doctors in accurately observing patients’ rehabil-
itation status. Generally, rehabilitation can be divided into three stages based on the degree of spinal cord
injury: initial, intermediate, and terminal. In the initial stage, due to the weak mobility of the patient, the pa-
tient needs to wear the lower limb exoskeleton robot to accurately follow the predetermined gait trajectory for
rehabilitation training. With the gradual recovery of mobility, the patient can enter the middle and final stages
[2]
of active rehabilitation training . Therefore, the initial stage is crucial for the entire rehabilitation training.
However, the uncertainty and disturbance caused by the unexpected behavior of stroke patients will seriously
impact the initial rehabilitation training.

To improve rehabilitation efficiency at the initial stage and eliminate the influence of external disturbance,
many control algorithms can be applied to exoskeleton robots. For instance, the PID control, adaptive control,
[5]
[6]
[3]
[4]
robust control , fuzzy control , active disturbance rejection control , neural network control , Master-
[8]
[7]
Slave Synchronization , and sliding mode control methods . Among the methods, sliding mode control
has the characteristics of fast response, insensitivity to uncertainties, and easy implementation in motion con-
trol applications. In particular, the sliding mode control can overcome the problems of external disturbances
and uncertainties by constructing the reaching law and sliding mode surface in theory, so that the controlled
[9]
system can achieve higher tracking accuracy. Non-singular terminal sliding mode control and fast terminal
sliding mode control [10] were applied to overcome parameter uncertainty and external disturbances to realize
gait tracking control of lower limb exoskeleton rehabilitation robot, and theoretically analyzed the stability
of controller design and tracking accuracy of trajectory. Sliding mode control technology can also be com-
bined with the neural network, a recurrent neural network-based robust nonsingular sliding mode control
is proposed for the non-holonomic spherical robot, it can enhance the robustness to control the system [11] .
To obtain higher accuracy, fractional order sliding mode control is introduced to deal with uncertainties and
external disturbances. Fractional order sliding mode control has the characteristics of global memory and
elimination of jitter, so it is widely used in industry, such as micro gyroscope [12] , manipulator control [13] ,
and permanent magnet synchronous motor control [14] . In addition, the fractional order control algorithm
can be applied in the field of robot control in combination with other technical methods. For example, a frac-
tional neural integral sliding-mode controller based on the Caputo-Fabrizio derivative and Riemann–Liouville
integral for a robot manipulator mounted on a free-floating satellite [15] and a method based on the nested sat-
urations technique and the Caputo-Fabrizio derivative for a quadrotor aircraft [16] . In chaotic systems, the
application of fractional order can endow the system with more degrees of freedom [17] , help to study the dy-
namic behavior of the system, combined with robust control methods [18] , eliminate external interference, and
effectively solve the synchronization problem of the system [19] . However, the general fractional order sliding
mode control strategy is designed based on the continuous time state of the controlled object and is directly
been tested on the digital computer system, so the design of the controller ignoring the sampling interval will
lead to the loss of the control system precision [20,21] . Moreover, the use of fractional operators to construct
sliding mode functions also introduces the influence of uncertainty. If the fractional operators are defined by
Gr¥ unwald–Letnikov (GL), there are non-physical initial conditions in the experiment. The fractional defini-
tion of Caputo is feasible in engineering applications, but the definition of Caputo can only be implemented
in the approximation method based on the Laplace transform, which will introduce additional approximation