Compliant Interaction Control of Lower-Limb Exoskeletons Via Fractional-Order Admittance and Phase-Modulated Proximal Policy Optimization

Abstract

Lower-limb rehabilitation exoskeletons must track motion while accommodating user-generated interaction torque. This study evaluates a fractional-order admittance outer loop in which six joint-specific mass, damping, and stiffness coefficients and two shared derivative orders are adjusted by proximal policy optimization (PPO). Gait-phase modulation scales policy exploration, while a previously published fractional-order sliding-mode controller and disturbance observer provide the inherited inner tracking loop. To ensure a traceable evaluation, the controller was independently implemented from the reported equations and parameter settings and assessed across 20 held-out randomized gait and user-impedance scenarios using three training seeds. Relative to standard PPO, phase-modulated PPO reduced normalized parameter variation by 22.2% (paired mean difference −0.0654, 95% bootstrap confidence interval $[-0.0765,-0.0545]$ ; Holm-adjusted $p=3.05\times 10^{-5}$ ). Differences in tracking root mean square error, RMS interaction torque, and peak interaction torque were not detected after multiplicity correction. Relative to fixed fractional admittance, it reduced RMS and peak interaction torque, without a supported tracking advantage. These simulation results support smoother parameter adaptation, but do not establish closed-loop stability, hardware safety, or clinical effectiveness.