Adaptive RBF neural network control for gait trajectory following in a rehabilitation exoskeleton

Performance Comparison of Classical and Robust Control Strategies for a Lower-Limb Rehabilitation Exoskeleton

Lower-limb rehabilitation exoskeletons have emerged as a promising complementary technology to conventional therapy, enabling repetitive, intensive, and personalized gait training. However, achieving accurate trajectory tracking while maintaining robustness against parametric uncertainties, external disturbances, and unpredictable human–robot interaction remains a significant control challenge due to the highly nonlinear dynamics of coupled human–exoskeleton systems. This paper presents an experimental performance comparison of five control strategies for gait rehabilitation exoskeletons, including a classical proportional–integral–derivative (PID) controller, a model-based proportional–derivative controller with gravity compensation (PD+G), a computed torque sliding mode controller (CT-SMC), a computed torque–super-twisting sliding mode controller (CT–ST-SMC) and a hybrid backstepping–super-twisting sliding mode controller (BS–ST-SMC). All the controllers were implemented on the same lower-limb rehabilitation exoskeleton under identical operating conditions. The experimental results demonstrate that the proposed BS–ST-SMC architecture outperforms classical and traditional robust approaches, particularly in mitigating chattering and managing human–robot interaction uncertainties. Specifically, the BS–ST-SMC achieved the highest tracking precision with a mean squared position error (MSEp) of 1.32×10−3rad2 and effectively synchronized with the user by reducing the phase lag to just 4.22° at the knee joint. Their overall performance was evaluated using the following metrics: mean squared position error (MSEP), mean squared velocity error (MSEv), peak error, phase lag, jerk index, peak torque, and peak power.

Adaptive SMC for Lower Limb Rehabilitation Robots Using a Sliding Mode Hyperbolic ESO

Dynamics-Based Collaborative Control for an Exoskeleton-Walker System via Deterministic Learning

Lower limb exoskeletons and mobile robots hold great potential in improving motor function rehabilitation for patients with limb dysfunction. However, their widespread application is limited by the substantial time and effort investment required from professional rehabilitation therapists. A significant challenge in achieving autonomous and intelligent rehabilitation lies in addressing the coordinated control between the exoskeleton and the robotic walker. This paper proposes a novel collaborative learning control strategy based on deterministic learning, which aims to achieve high-performance coordinated control through precise closed-loop dynamics modeling of the exoskeleton-walker system. First, radial basis function neural networks (RBFNNs) are employed to approximate the system dynamics during the coordinated control process. Utilizing deterministic learning theory, it is rigorously demonstrated that, under persistent excitation conditions, the unknown dynamics of the system can be accurately approximated and stored as constant neural networks. Subsequently, an experience-based collaborative learning controller is designed, enabling autonomous coordinated control of the human-robot system and offering a viable approach for its broader application. The effectiveness and superior performance of the proposed control strategy are validated through experiments conducted on the CoppeliaSim robotic platform. Note to Practitioners—This work is intended for researchers and engineers working on rehabilitation robotics, particularly those focusing on lower limb exoskeletons and mobile robotic walkers. One of the main barriers to the practical deployment of these systems is the reliance on continuous assistance from rehabilitation professionals during use. To address this, we propose a deterministic learning-based collaborative control strategy that enables accurate modeling and reuse of system dynamics, ultimately achieving autonomous coordination between the exoskeleton and robotic walker. This reduces reliance on manual intervention and opens up the possibility for long-term, high-performance rehabilitation training in clinical and home environments. Practitioners can leverage this approach to develop smarter, more adaptive rehabilitation systems that respond to patient needs with greater precision and autonomy.

Design and Control of an Enhanced Self-Reconfigurable Parallel Ankle Rehabilitation Exoskeleton

Design, modeling, and experimental validation of a self-reconfigurable parallel ankle rehabilitation platform demonstrate the approach’s feasibility, demonstrating stable trajectory tracking and setpoint regulation under practical conditions, with minor deviations attributable to actuator and mechanical nonlinearities.

Assist-As-Needed Backstepping Control of Lower-Limb Exoskeletons with Human Effort Estimation and Comparative Evaluation Against Sliding Mode and PID Controllers

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.

Model-Free Fixed-Time Sliding Mode Control for Wearable Exoskeletons With Adaptive-Boundary Prescribed Performance

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.