2026· IEEE Transactions on Automation Science and Engineering· Vol 23, pp. 13796-13811· 0 citations· 42 references
Computer Science
Abstract
Upper-limb rehabilitation exoskeleton systems are characterized by strong coupling, high nonlinearity, parametric uncertainties, and unknown disturbances. Furthermore, conventional prescribed-performance methods usually impose fixed and strict error constraints during the convergence process, which may limit the flexibility of transient response. To address these issues, the core innovation of this paper lies in the introduction of an adaptive-boundary prescribed performance mechanism, which enables the constraint boundaries to be dynamically adjusted online according to tracking errors, thereby simultaneously improving both transient flexibility and steady-state convergence accuracy. Specifically, a model-free system representation is first established by combining an ultra-local model with time-delay estimation. Subsequently, a gain-adaptive super-twisting sliding mode observer is developed to estimate and compensate for time-delay estimation errors and lumped uncertainties in real time. On this basis, by introducing a fixed-time nonsingular terminal sliding mode surface and a novel hyperbolic-cosine barrier Lyapunov function, a prescribed-performance fixed-time sliding mode controller is constructed to ensure that the system states achieve fixed-time convergence while strictly satisfying the prescribed performance constraints. Finally, numerical simulations comparing different methods demonstrate that the proposed approach exhibits superior comprehensive performance in tracking accuracy, convergence speed, and robustness. Subsequent visual simulations further verify the effectiveness and practical application potential of the proposed method. Finally, experiments are implemented in the wear-able exoskeleton experimental platform, experiment results demonstrate the effectiveness of the proposed scheme. Note to Practitioners—This work is motivated by the need for safer and more flexible assistance in upper-limb rehabilitation exoskeletons. In clinical training, patients may show different movement abilities, muscle stiffness, fatigue levels, or involuntary motions. Therefore, a fixed tracking boundary may be too strict for some patients at the beginning of training, while a loose boundary may reduce rehabilitation accuracy. The proposed method allows the error boundary to change online according to the tracking error, so that the exoskeleton can tolerate larger transient deviations during difficult movements and gradually provide stricter tracking assistance as the motion becomes stable. For practical use, the initial boundary should be selected according to the patient’s initial motion error and safety range, and the steady-state boundary should be chosen according to the required rehabilitation accuracy. The controller does not require an accurate dynamic model of the exoskeleton, which may reduce the modeling burden for engineers. However, before clinical application, further extensive hardware tests and multi-subject evaluations should be conducted.
In this paper, we propose an assist-as-needed (AAN) backstepping control scheme for a lower-limb exoskeleton with nonlinear dynamics and uncertain human–robot interactions. The main objective is to achieve a good trajectory tracking capability while adaptively controlling the assistance of the robot according to the user’s effort. The adopted dynamic model is nonlinear, which includes joint dynamics and external human interaction torque. This allows for the derivation of the tracking error formulation. The backstepping control law, formulated based on the filtered tracking error, ensures stable closed-loop performance with bounded tracking errors. We incorporate an AAN scaling framework based on estimated human effort to regulate the overall control torque as a convex combination of the nominal backstepping torque and the impedance-based assistance torque. The proposed controller was tested by numerical simulations and was compared with the sliding mode control (SMC) and the proportional–integral–derivative (PID) control. The overall root-mean-square tracking error for the proposed controller was 0.0962 rad, while for the SMC controller and PID controller, it was 0.0819 rad and 0.1246 rad, respectively. Moreover, the proposed controller reduced the peak human–robot interaction torque to 14.68 N·m compared to 15.36 N·m for SMC and 15.81 N·m for PID, adaptively controlling assistance based on the applied effort of the user. The assistance ratio went down from an average of 0.7988 in the low-effort condition to 0.6960 in the higher-effort condition, indicating effective adaptation while maintaining stable tracking performance. Although the PID controller achieved the lowest torque-variation index, the proposed controller achieved a more favorable trade-off among tracking accuracy, adaptive assistance, and acceptable torque smoothness. Finally, the proposed AAN backstepping controller achieved a practical trade-off between tracking accuracy, adaptive assistance, torque smoothness, and interaction safety, suggesting its potential in rehabilitation and assistive exoskeleton applications.
Muktar Fatihu Hamza, A. I. Isa, Abdulrahman Alqahtani et al.· Applied Sciences· 0 citations
This paper presents a novel fast fixed-time nonsingular sliding mode controller designed to enhance target tracking accuracy and reduce vibrations in flexible-link manipulators. The core innovation lies in simultaneously addressing model uncertainties, external disturbances, and actuator saturation by incorporating them into the system’s dynamics, thereby overcoming the inherent complexity and design challenges. Beyond this simultaneous handling, the proposed sliding surface itself incorporates new functions that improve upon previous sliding mode designs. Furthermore, actuator saturation, uncertainties, and disturbances are all explicitly considered within the dynamic equations themselves, not added as afterthoughts. The proposed paper integrates three key contributions. First, a new nonsingular fast terminal sliding surface is designed, which uses improved functions to ensure rapid convergence of tracking errors while avoiding singularity issues. Second, a nonlinear extended state observer (NESO) is combined with an auxiliary function to actively estimate and compensate for aggregated disturbances, model uncertainty, and input saturation. Third, an adaptive mechanism is embedded to eliminate the requirement for prior knowledge of uncertainty bounds, making the controller more practical and robust in real-world applications. The proposed method is compared with intelligent control strategies. Closed-loop stability is guaranteed using Lyapunov theory, with theoretical proof of fixed-time tracking error convergence to zero, independent of initial conditions. Effectiveness and robustness are validated via comparative simulations against a state-of-the-art benchmark and experiments on a Speedgoat real-time machine.
Hamede Karami, F. Bayat, Saleh Mobayen et al.· Journal of Vibration and Con...· 0 citations
Cable-driven manipulators exhibit strong nonlinearities and low structural stiffness, which make precise control challenging under time-varying uncertainties and external disturbances. This paper presents a time-delay-estimation (TDE)-based adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) control strategy for cable-driven robots. A robust controller is constructed within a TDE-based model-free framework by combining fractional-order nonsingular terminal sliding mode error dynamics with a fast terminal sliding mode reaching law. The main contribution is a new adaptive law that introduces an adaptive exponential term into the update gain to form a nonlinear adaptive mechanism. This design improves adaptive regulation under different operating conditions by suppressing noise-induced chattering during smooth tracking while preserving or enhancing the adaptive gain during trajectory reversal. Lyapunov analysis proves the ultimate uniform boundedness of the tracking error. Experimental results show that, compared with the baseline method, the proposed controller reduces RMSE by 34.52% and 31.11%, ITAE by 33.79% and 32.97%, and ISCT by 6.69% and 17.77% for the two joints, respectively. Further comparisons with recently reported adaptive laws demonstrate that the proposed law provides faster adaptive response, more stable gain evolution, and improved chattering suppression. Additional payload tests further verify the robustness and repeatability of the proposed method.
Addressing the inherent low stiffness of flexible manipulators, existing control schemes often face an intrinsic contradiction where rapid convergence leads to increased vibration amplitudes, making it challenging to achieve high-precision trajectory tracking while effectively suppressing elastic vibrations. To tackle this issue, this paper proposes a neural network-based Fixed-Time learning control strategy. This strategy is capable of simultaneously handling output constraints, model uncertainties, and input dead-zone nonlinearities of the system. The designed controller effectively compensates for the adverse effects of the input deadzone, ensuring that all system states converge to a small neighborhood around the origin within a fixed time, thereby significantly improving the system’s convergence speed and transient performance. By introducing a logarithmic Barrier Lyapunov Function (BLF), the prescribed tracking error constraints are strictly guaranteed. Furthermore, high-frequency chattering is mitigated through a smooth approximation of the sign function. Experimental results demonstrate that, compared with the PSF controller, the proposed Fixed-Time control scheme reduces the steady-state tracking errors by 61.9% and 69.2%, respectively. In terms of vibration suppression, the steady-state values of elastic vibrations are reduced by 49.2% and 32.6%, respectively. These results fully validate the superiority and robustness of the proposed control strategy in balancing rapid convergence with vibration suppression.
He-Jia Gao, Tan-Yu Chen, Jiang-Xu Liu et al.· CAAI Artificial Intelligence...· 0 citations
Control systems play a critical role in lower‐limb exoskeletons, directly influencing user safety, comfort, and adaptability to varying physiological conditions. However, achieving fast, robust, and predictable tracking performance remains a significant challenge due to model uncertainties, external disturbances, and human–robot interaction dynamics. In particular, conventional asymptotic, finite‐time, and fixed‐time control strategies do not provide explicit guarantees on convergence time, which is essential for ensuring reliable and user‐friendly assistance in rehabilitation and assistive applications. To address these limitations, this paper proposes a novel Predefined‐time Observer‐based Sliding Mode Control (POSMC) scheme for lower‐limb exoskeleton systems. The dynamics of the human limb and the exoskeleton are modeled and integrated to capture coupled behavior during operation, while interaction forces are explicitly incorporated to reflect realistic usage conditions. The proposed framework combines a state observer and a disturbance observer with predefined‐time stability theory to ensure robust and accurate trajectory tracking within a user‐specified convergence time. The effectiveness of the proposed method is validated through real‐time simulation on a Real‐time Digital Simulator (RTDS) platform under two practical scenarios. Comparative results with finite‐time and fixed‐time sliding mode controllers demonstrate that the proposed POSMC approach achieves faster convergence, improved tracking accuracy, and enhanced robustness against disturbances and modeling uncertainties. These results highlight the potential of the proposed control strategy to improve safety and performance in both rehabilitation and assistive exoskeleton applications.
Ali Soltani Sharif Abadi, Reza Hajiyan, Pouya Heidarpoor Dehkordi et al.· International Journal of Rob...· 0 citations
An adaptive proximate fixed-time terminal sliding mode control (FTTSMC) based on time-delay estimation (TDE) is proposed to ensure high-precision trajectory tracking of robot manipulators subject to unknown dynamics and external disturbances. The controller employs TDE to reconstruct system dynamics online, requiring only the inertia matrix bounds rather than full precise nominal models. Crucially, it replaces the conventional constant bound assumption for the TDE error with a robust state-dependent one, thereby enhancing robustness against discontinuous disturbances. Rigorous Lyapunov stability analysis confirms the fixed-time convergence of the sliding variable and the proximate fixed-time convergence of the tracking error, providing explicit upper bounds on the convergence time. Comparative simulations and experiments on a SCARA robotic platform demonstrate that the developed strategy maintains transient performance comparable to baseline fixed-time approaches while achieving superior steady-state accuracy. Characterized by a compact structure and low computational complexity, the proposed controller exhibits strong potential for high-performance real-time robotic applications.
Pu Yang, Liyin Zhang· Actuators· 0 citations
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