Model Predictive Control-Based Assist-as-Needed Strategy for Reducing Motor Slacking in Robot-Assisted Rehabilitation

This study proposes a model predictive control (MPC)-based Assist-as-Needed (AAN) strategy for upper-limb rehabilitation robots, with particular emphasis on mitigating motor slacking. In conventional error-based AAN approaches, robotic assistance is regulated through a single coefficient tied to the tracking error; thus, a reduction in voluntary effort is absorbed into the assistive channel and remains obscured by a small tracking error. The proposed method decouples this mechanism by introducing a two-channel admittance structure, in which the robotic-assistance gain Ak and the user-participation-reflection gain Bk are jointly optimized within a single convex MPC formulation. The cost function addresses trajectory tracking, participation-aware force alignment, assistance suppression, and passivity, enforced through energy-tank constraints. The controller was validated in two experiments on a mobile upper-limb rehabilitation robot. The first experiment confirmed differential adaptation of Ak and Bk across three instructed contribution levels, with the participation ratio increasing from 0.103 to 0.879 as the contribution shifted from insufficient to appropriate. The second experiment compared the controller with an error-based AAN baseline and a forgetting-factor AAN baseline under an induced motor-slacking condition, in which the task-direction contribution was reduced to 45%. Under an identical synthesized input, the proposed controller yielded a lower aggregate human-contribution ratio of 0.282, compared with 0.595 and 0.535 for the two baselines, respectively. This indicates that the externally imposed reduction in participation was represented more explicitly in the controller allocation, rather than being masked by error-driven assistive compensation. These results suggest that the proposed approach extends AAN control toward a participation-preserving, anti-slacking strategy for robot-assisted rehabilitation.