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Zhang et al. Intell. Robot. 2025, 5(2), 333-54 I http://dx.doi.org/10.20517/ir.2025.17 Page 335

rehabilitation training [28] . Firstly, the setting of motion-restricted areas is a key measure to protect patient
safety. It can prevent excessive joint movement, avoiding potential injuries such as dislocation, sprains, or
pain. Secondly, appropriate motion restrictions can promote the gradual recovery of neuromuscular function,
activating the neuromuscular system through moderate stimulation. Additionally, different patients have dif-
ferent rehabilitation needs and movement capabilities. The establishment of motion-restricted areas can be
adjusted according to the specific circumstances of the patient to provide personalized rehabilitation training
programs. Concomitantly, the establishment of areas subject to movement restrictions facilitates therapists in
closely monitoring patient responses during the training process, enabling timely adjustment or cessation of
the training to prevent further injury. Therefore, it is necessary to flexibly switch between different modes of
normal training and safe stopping in rehabilitation training. Li et al. proposed a hybrid control method, where
thecontroller includesthreeworkingmodes: resistance mode, assistmode, andrestrictionmode, and switches
between the three different modes based on the tracking error performance of the controller output, allowing
the working mode to be automatically adjusted according to the subject’s movement performance [29] . Zhang
et al. proposed a unified control framework, which consists of a mode controller capable of smooth switching
between robot operation modes and a task controller adapted to different training needs [30] . By employing a
motion-related controller with a switching function mode, it achieves seamless and smooth mode switching,
ensuringthesmoothnessandsafetyofthetraining. Wuetal. designedafuzzyproportional-integral-derivative
(PID) controller for the proposed device [31] . Combining fuzzy control with PID control by adjusting the para-
metric PID parameters online according to the control deviation and the deviation change rate, the controller
is able to provide quantifiable assistance for a specific patient based on the error-based self-tuning of the pa-
rameters, but it may lead to a decrease in the system control accuracy and deterioration of the dynamic quality.
To improve accuracy, the number of quantization stages needs to be increased, which increases the amount
of computation and the number of rules. Proietti et al. introduced a controller that adaptively varies the
feedback gain and thus the modulation of the impedance on a task-by-task basis; however, it requires more
accurate modeling of the system and still falls short of the problem of high-frequency unmodelled dynamics
and measurement accuracy [32] .

Sliding mode control (SMC) is an efficient and robust control method that can be combined with the unified
control framework to improve the performance and adaptability of the system. Conventional SMC systems
are mainly based on linear sliding mode surface controllers (LMC), which are easy to implement but have long
convergencetimes. TheterminalSMC(TSMC)strategy [33] hasbeenproposedasasolutiontothefastresponse
problem, aiming to drive the system state to a predefined target state within a finite time. However, in practice,
the TSMC strategy faces the singularity problem; i.e., in some regions of the state space, the control inputs may
require infinitely large values to maintain the desired sliding modes. This problem may lead to discontinuities
in the control inputs, which in turn cause system chattering. In addressing this challenge, researchers have
proposed two approaches: non-singularity TSMC [34] and non-singularity fast TSMC. These approaches offer
a partial solution to the chattering problem by mitigating the effects of controller discontinuities. However,
they do not fully resolve the chattering issue. Zou et al. proposed an improved TSMC manifold design, which
not only ensures the finite-time stability of the system in both the arriving and sliding phases, but also, by
reducing the chattering, improves the overall control performance [35] .

However, existing sliding surface designs primarily focus on attenuating matched disturbances. For mis-
matched disturbances - those that reside in different channels from the control input or whose directions
do not align with the control input - direct compensation via the control input is not feasible. Instead, more
sophisticated control strategies arerequired toaddress these disturbances. Mismatched disturbancesare preva-
lent in various practical systems, and in such cases, the robustness of conventional SMC is seriously affected
by the mismatch uncertainty. Kim et al. constructed a robust sliding hyperplane to deal with structural un-
certainty using Riccati’s inequality [36] . Choi et al. proposed a sliding surface design method based on linear
matrix inequality (LMI) and guaranteed the existence of asymptotically stable sliding surfaces with full-order