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Table 1. Performance indicators of the three controllers
Controllers RMSE of hip MAE of hip MTE of hip RMSE of knee MAE of knee MTE of knee
AFOFTSMC (Proposed) 0.0056 rad 0.0026 rad 0.0300 rad 0.0075 rad 0.0057 rad 0.0529 rad
CSMC [26] 0.0066 rad 0.0056 rad 0.0174 rad 0.0189 rad 0.0166 rad 0.0529 rad
FTSMC [27] 0.0056 rad 0.0370 rad 0.0253 rad 0.0128 rad 0.0105 rad 0.0529 rad

erate the convergence of system errors and make adaptive adjustments to control law parameters. Compared
with the traditional control methods, AFOFTSMC has better potential to be applied to the actual exoskeleton
rehabilitation robot and help patients to carry out rehabilitation training in the early stage of rehabilitation.
In addition to the field of rehabilitation robots, the algorithm can also be extended to other fields to achieve
better control effects, such as chaotic systems, robot manipulators, and quadrotor UAVs.

5. CONCLUSIONS
In this paper, we study a human gait trajectory-tracking control issue of lower limb exoskeleton rehabilitation
robot. Firstly, the dynamic properties of the lower limb exoskeleton rehabilitation robot were analyzed. Then,
a new AFOFTSMC algorithm was developed for the lower limb exoskeleton robot with uncertain parameters
and unknown external interference, where the fractional order fast terminal sliding mode function was intro-
duced to achieve rapid convergence in finite time. Particularly, the unknown dynamic part of the exoskeleton
was processed by adaptive law, and the width of the quasi-sliding mode band was adjusted in real-time to en-
sure that the sliding mode variables quickly enter the quasi-sliding mode band. Moreover, the stability of the
whole control system was verified in the Lyapunov sense. To illustrate the effectiveness of the proposed con-
troller, we compared the simulation results of CSCM, FTSMC, and AFOFTSMC on the MATLAB-Opensim
co-simulation platform. The simulation results showed that the adaptive fractional order fast terminal slid-
ing mode controller has the characteristics of high precision, fast response, and strong robustness for robot
trajectory tracking.

DECLARATIONS
Authors’ contributions
Implemented the methodologies presented and wrote the paper: Zhou Y, Sun Z
Performed oversight and leadership responsibility for the research activity planning and execution, as well as
developed ideas and evolution of overarching research aims: Sun Z, Chen B, Wang T
Performed critical review, commentary, and revision, as well as providing technical guidance: Sun Z, Chen B,
Wu X, Huang G
All authors have revised the text and agreed to the published version of the manuscript.

Availability of data and materials
Not applicable.

Financial support and sponsorship
ThisworkwassupportedbythePrimaryResearchandDevelopmentPlanof ZhejiangProvince(No. 2022C03029)

Conflicts of interest
All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate
Not applicable.