Research on kinematics and fractional order active disturbance rejection control of skating training robot

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

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.

Research on adaptive robust control of lower limb rehabilitation exoskeleton

In order to improve the trajectory tracking accuracy of the lower limb rehabilitation exoskeleton robot, this paper proposes an adaptive robust error compensation control method (ARCEC) based on RBF neural network. First, the dynamics of the single-leg swing phase of the lower-limb exoskeleton are modeled using Lagrange’s equations, taking into account factors such as joint friction, flexible transmission, and the torque arising from human–robot interaction. Subsequently, nominal model compensation, online approximation via RBF neural networks, and nonlinear error feedback are integrated to mitigate the impact of model uncertainty and external disturbances on trajectory tracking performance. Simulation and experimental results demonstrate that compared to traditional PID control and sliding mode control (SMC), the ARCEC method exhibits significant advantages in trajectory tracking accuracy. It achieves up to a 30% reduction in tracking error, enabling the lower-limb exoskeleton to precisely track human gait curves.

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.

Original Research Article Model-Based Predictive Command of a 5-DoF Robotic Manipulator using Dynamics Mathematics

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

Improving trajectory-following accuracy remains a central issue in lower-limb rehabilitation exoskeletons, especially when joint motion is affected by nonlinear coupling, parameter drift, and interaction disturbances during repetitive gait training. To address this problem, this study develops an adaptive trajectory-tracking method driven by an RBF neural network. A single exoskeleton leg is first represented as a two-degree-of-freedom planar double-link mechanism in the sagittal plane, and the swing-phase dynamics are formulated via the Lagrange approach. On this basis, a nominal-model decomposition framework is introduced so that uncertain dynamics and external perturbations can be approximated online by the RBF network. A joint-space controller is then constructed to improve tracking stability and robustness. MATLAB simulations and prototype experiments are further carried out, with conventional PID control used for comparison. The results indicate that the proposed approach yields faster error attenuation, smaller steady-state oscillation, along with improved resistance to disturbances in the hip and knee motions. Overall, the proposed approach is effective for accurate gait-following control in rehabilitation exoskeletons.