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Page 350 Zhang et al. Intell. Robot. 2025, 5(2), 333-54 I http://dx.doi.org/10.20517/ir.2025.17

of NFTSMC, closely follows the desired reference trajectory with minimal deviation. In contrast, the TSMC
tracking error plot [Figure 12B], while consistently maintaining a smaller value than NFTSMC, is character-
ized by a continuous fluctuating process. These fluctuations suggest that TSMC, despite having smaller error
values, is unable to achieve the same level of stability and precision as NFTSMC. The sustained oscillations in
the TSMC error curve prevent it from converging to a smaller value. Furthermore, the capacity of NFTSMC to
maintaina lowtracking erroreven whenfaced with parameter changesor external perturbations demonstrates
its enhanced robustness.

Insummary, thecomparativeanalysisofthetrackingerrorplotsrevealsthatNFTSMCnotonlyachieveshigher
tracking accuracy by bringing the system output closer to the desired trajectory but also exhibits better stability
and robustness compared to TSMC. These attributes make NFTSMC a more reliable choice for applications
where precise and stable tracking is paramount.

As can be seen from Figure 13, in the experimental analysis comparing the NFTSMC and NTSMC control
strategies, the system error is intentionally extended over a longer time span to facilitate clearer observation. It
is observed that both methods are capable of steering the system error towards a vicinity of zero within a rela-
tively brief timeframe. However, an examination of the error curves reveals that the NFTSMC exhibits a more
rapid convergence, signifying its superior response time. Additionally, NTSMC encounters specific data con-
straints during experimentation, which may impair its performance in real-world applications. The NTSMC
is prone to singular value issues when managing data, which can result in the instability or diminished efficacy
of the control algorithm. NFTSMC circumvents these challenges by employing a non-singular sliding surface
design, which bolsters the system’s robustness and stability. This design accounts for the dynamic properties
and potential perturbations of the system, ensuring the control strategy’s efficacy amidst uncertainties and
external disturbances. Furthermore, NFTSMC incorporates a rapidly converging sliding surface and an inno-
vative control law, which not only enhances the system’s response velocity but also mitigates the occurrence
of chattering phenomena.

Figures 14 and 15 show the performance of NFTSMC and NTSMC in terms of torque output, respectively.
The torque diagram of NFTSMC shows smoother torque variation than that of NTSMC, which indicates that
NFTSMC generates less chattering during the control process, thus avoiding wear and tear of the actuator and
reduction of energy efficiency caused by chattering. The torque diagram of NFTSMC is more stable than that
of NTSMC. NFTSMC can still maintain stable torque output when facing parameter changes or external dis-
turbances, which indicates that NFTSMC has better robustness. NFTSMC can maintain stable torque output
in the face of parameter changes or external disturbances, which indicates that NFTSMC has better robustness.

5. CONCLUSIONS
This academic paper presents an exhaustive control paradigm for an upper limb exoskeleton rehabilitation
robot, highlighting key factors for the safety and effectiveness of robot-assisted rehabilitation training. The
proposed framework is based on a trajectory planning methodology that combines polynomial interpolation
and the minimum-jerk model to ensure that the training reference trajectory is both smoothly switchable and
close to natural human kinematics.

The control frame includes a motion-switching feature designed to facilitate a seamless transition between two
modes of operation: standard motion and safety stop. This function is crucial for maintaining patient safety
during training, as it significantly reduces the likelihood of abrupt changes, thereby minimizing the potential
for discomfort or injury. The disturbance observer-based NFTSMC design method described in this paper is
capableofaccuratelytrackingthenecessaryjointangles, withtheexoskeletontrackingerrorconvergingtozero