Contraction-Relaxation Behavior Inspired Fractional-Order Control for Physical Human-Robot Interaction With Optimized Order

This paper proposes a fractional-order control method for the physical human-robot interaction (pHRI) inspired by the dynamics of muscle contraction-relaxation behavior, which is integrated into a fractional-order sliding mode with variable order and parameters, to achieve fast transient response while guaranteeing high-precision steady-state tracking performance. A sensorless force observer based on fractional calculus is developed to estimate the operator's behavior, enabling a composite control system that guarantees ultimate boundedness of the closed-loop signals. The deep reinforcement learning-based order and parameter optimization mechanism is synthesized into the unified architecture of the composite control system. The effectiveness of the proposed method is validated through numerical simulations and comparative studies, which demonstrate significant improvements in convergence speed on the sliding manifold while maintaining steady-state precision. Experimental results further confirm the feasibility and practical applicability of the framework in a cylindrical docking scenario via visual-reality fusion approach, highlighting its potential for future semi-autonomous human-in-loop missions. Note to Practitioners - This paper was motivated by the problem that the pHRI exhibits significantly rigid motion characteristics, which lack human-like compliance, since the robotic controller design has not taken the laws of human interactive behavior into account. Existing approaches to stabilizing the pHRI generally isolate the robotic controller from the operator, and aim to track a reference trajectory generated from an impedance or admittance structure with the operator's force injected. Hence, the compliant performance of pHRI is dominated by the dynamic response and steady-state performance of the control method, which are challenging to balance with a fixed set of control parameters. This paper suggests a new fractional-order sliding manifold comprising a fractional element and a nonlinear spring to express viscoelastic and elastic movement of the muscle, capturing the time-dependent and dynamic characteristics of contraction-relaxation behavior. The order and control parameters of the proposed composite control system with sensorless force estimation are integrated into a Markov decision process to generate an optimization strategy that accounts for long-horizon compliant performance of pHRI via deep reinforcement learning. In this paper, we mathematically characterize the mechanics of contraction-relaxation behavior for synthesizing the fractional-order control method with order optimization. We then show its effectiveness in simulations. The experimental results suggest that the proposed method is feasible for conducting space haptic operation with the order and parameter strategy.