Fractional-Order Logarithmic Sliding Mode Control for Sensorless Physical Human-Robot Interaction

This paper explores the application of a fractional-order variable structure control strategy to stabilize the end-effector motion in a sensorless physical human-robot interaction system, considering interaction behaviors and lumped uncertainty. Building upon integer-order calculus, specifically the Caputo definition and comparison principles, the Mittag-Leffler uniformly ultimately bounded stability criterion is employed to analyze the proposed fractional-order logarithmic sliding mode manifold. The convergence set of the tracking error is determined based on the sliding motion on this manifold. To achieve active compliant interaction performance, a fractional-order force observer with an adaptive parameter is utilized to reconstruct the operator's interaction behavior without relying on sensors. Experiments conducted with a 3-DoF Phantom Omni haptic manipulator demonstrate the effectiveness of the proposed framework in terms of both transient and steady-state interaction performance.