Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Closed-Loop SEA Outer-Loop Study
Abstract
Safe rehabilitation is an interaction-dynamics problem: the controller must regulate a prescribed motion while absorbing involuntary spasm, voluntary effort, actuator compliance, and model mismatch as disturbances. This paper instantiates the predictive interaction-dynamics framework of the base pHRI formulation on a SEA knee joint. SEA feedforward reduces the gravity-compensated knee to the same scalar double integrator as the base framework, while a dynamic-residual measurement from spring deflection supplies an interaction-disturbance observation. A steady-state target converts the estimated disturbance into a cancelling input, and a finite-horizon quadratic program regulates deviations from that target under range-of-motion, torque, and velocity constraints. The evaluation matches stiffness and damping across controllers so gains cannot be attributed to higher impedance. Under a motion-opposing 15unitNm step, classical impedance and MPC without estimation produce about 500unitmrad steady-state error, whereas Kalman-augmented interaction MPC reduces this to 1.17unitmrad at 100~Hz and 0.70unitmrad at 500~Hz; the 500~Hz peak is 7.27unitmrad. In 30 randomized trials, the 95th-percentile peak is 21.57unitmrad. Bounded Assist-as-Needed scheduling, a corrective-channel energy tank, constrained OSQP stress cases, direct MuJoCo execution, and a posture-clamped MyoSuite knee slice are implemented. The framework holds on a single-mass, closed-inner-loop SEA approximation; an explicit two-mass plant with a finite-bandwidth, pole-placed inner torque loop (Section~VIII) confirms this for nominal tracking but shows delivered torque can overshoot the commanded bound by 21.7\% near saturation. Scope excludes clinical intent recognition, full-system passivity, safety certification, hardware trials, and multi-joint validation.
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BibTeX
@misc{cao2026interaction,
title = {{Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Closed-Loop SEA Outer-Loop Study}},
author = {Yongyan Cao and Jinshan Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.13485},
eprint = {2606.13485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13485},
}
RIS
TY - UNPB
TI - Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Closed-Loop SEA Outer-Loop Study
AU - Yongyan Cao
AU - Jinshan Tang
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2606.13485
UR - https://arxiv.org/abs/2606.13485
AB - Safe rehabilitation is an interaction-dynamics problem: the controller must regulate a prescribed motion while absorbing involuntary spasm, voluntary effort, actuator compliance, and model mismatch as disturbances. This paper instantiates the predictive interaction-dynamics framework of the base pHRI formulation on a SEA knee joint. SEA feedforward reduces the gravity-compensated knee to the same scalar double integrator as the base framework, while a dynamic-residual measurement from spring deflection supplies an interaction-disturbance observation. A steady-state target converts the estimated disturbance into a cancelling input, and a finite-horizon quadratic program regulates deviations from that target under range-of-motion, torque, and velocity constraints. The evaluation matches stiffness and damping across controllers so gains cannot be attributed to higher impedance. Under a motion-opposing 15unitNm step, classical impedance and MPC without estimation produce about 500unitmrad steady-state error, whereas Kalman-augmented interaction MPC reduces this to 1.17unitmrad at 100~Hz and 0.70unitmrad at 500~Hz; the 500~Hz peak is 7.27unitmrad. In 30 randomized trials, the 95th-percentile peak is 21.57unitmrad. Bounded Assist-as-Needed scheduling, a corrective-channel energy tank, constrained OSQP stress cases, direct MuJoCo execution, and a posture-clamped MyoSuite knee slice are implemented. The framework holds on a single-mass, closed-inner-loop SEA approximation; an explicit two-mass plant with a finite-bandwidth, pole-placed inner torque loop (Section~VIII) confirms this for nominal tracking but shows delivered torque can overshoot the commanded bound by 21.7\% near saturation. Scope excludes clinical intent recognition, full-system passivity, safety certification, hardware trials, and multi-joint validation.
ER -