Asymmetric Admittance Control for Compliance to Time-Varying Interaction Force in Dual-Manipulator Rehabilitation System

For passive lower limb rehabilitation using dual-manipulator device in the supine position, accurate trajectory tracking requires high stiffness along the direction of gravity-induced interaction forces. Conversely, a compliant pathway with low stiffness is essential for releasing internal stress, which are often resulting from rehabilitation trajectory mismatches caused by oblique joint axes and their rotations during movement. This asymmetry in the design of admittance parameters poses a non-trivial challenge to traditional impedance/admittance control theories based on stiffness ellipsoids. To address this problem, this paper proposes an asymmetric admittance control method that allows independent adjustment of admittance parameters in the positive and negative directions of each Cartesian dimension, enabling higher stiffness in the direction of gravity-induced interaction forces to enhance trajectory tracking accuracy, and lower stiffness in the opposite direction to release potential internal stress within the dual-manipulator-limb system. Additionally, based on the quasi-static equilibrium equations of the system, this paper proposes an optimization-based identification method for the lower limb parameters, as well as a hierarchical compensation strategy for the time-varying gravity-induced force components of the lower limb. Experimental results demonstrate that the proposed control system can achieve high-precision trajectory tracking and having sufficient compliance in specific directions to release stress within the system.