RBF-Based Adaptive Sliding-Mode Control for Isokinetic Rehabilitation Under Continuous Interaction Loads

Abstract

Time-varying interaction loads and uncertain actuator dynamics complicate isokinetic velocity regulation. This study evaluates a hierarchical controller combining nominal compensation, measured-load feedforward, posture-aware radial basis function (RBF) residual compensation, and adaptive sliding-mode feedback. The RBF network uses offline initialization, bounded online updates, and domain-gated output. Closed-loop boundedness is discussed under stated disturbance and actuator assumptions. Under a 40 N·m, 0.5 Hz periodic load, the complete controller achieved a velocity RMSE of 0.9938°/s, with reductions of 55.75% and 86.88% relative to the tested fixed-gain SMC and ASMC configurations, respectively. Independent validation showed a decrease in mean robust gain from 9.0492 to 3.8409 rad/s2. In five prototype trials per controller and load, C3 achieved RMSE values of 1.380 ± 0.049°/s at 12.5 kg and 1.984 ± 0.067°/s at 25 kg. Repeated-load tests revealed peak-error deterioration in five of nine conditions and substantial out-of-domain exposure at higher loads. The results support the complete compensation module under the tested conditions but do not isolate the incremental benefit of online updating or establish patient-level safety.