Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Series-Elastic Instantiation

Jul 16, 2026

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Safe rehabilitation is formulated as an interaction-dynamics control task where a robot must track a prescribed motion while rejecting disturbances from patient spasm, voluntary effort, actuator compliance, and model mismatch. The work instantiates a predictive interaction-dynamics framework for a series-elastic-actuated knee: SEA feedforward yields a constant-coefficient double integrator, and dynamic-residual spring-deflection measurements enable disturbance estimation. A steady-state target cancels the estimated disturbance within a finite-horizon QP under ROM, torque, and velocity constraints. Matched-impedance evaluation shows large error reduction versus classical impedance and non-estimating MPC.

LanguageEnglish

CategoryResearch & Report

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Pages9

Reading Time23 min

Introduction

Related Work

Interaction Dynamics, Impedance, and Predictive Control

Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Series-Elastic Instantiation Yongyan Cao and Jinshan Tang arXiv :2606 . 13485v2 [ ee ss . SY] 11 Jul 2026 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 interaction disturbances. This paper instantiates the predictive interaction-dynamics framework of the base pHRI formulation on a series-elastic-actuated knee joint. SEA feedforward reduces the gravity-compensated knee to the same constant-coefficient scalar double integrator used in 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 is stiffnessand damping-matched so improvements cannot be attributed to higher impedance. Under a motion-opposing 15Nm step, classical impedance and MPC without estimation produce about 500mrad steady-state error, whereas Kalman-augmented interaction MPC reduces this to 1. 17mrad at 100 Hz and 0.70mrad at 500 Hz; the 500 Hz peak is 7.27mrad. In 30 randomized trials, the 95th-percentile peak is 21.57mrad. Bounded Assist-asNeeded scheduling, a corrective-channel energy tank, inequalityconstrained OSQP stress cases, direct MuJoCo execution, and a posture-clamped MyoSuite knee-slice run are implemented. The results support the SEA-knee instantiation of the interactiondynamics framework while separating it from clinical intent recognition, full-system passivity, safety certification, hardware trials, and free-standing multi-joint validation. Index Terms—Interaction dynamics, knee rehabilitation, exoskeleton, model predictive control, offset-free MPC, Kalman filter, series elastic actuator, disturbance estimation, impedance control, MuJoCo. I. INTRODUCTION PHYSICAL rehabilitation is not only a trajectory-tracking problem. It is an interaction-dynamics problem in which the robot, the actuator, the patient limb, involuntary spasm, voluntary effort, and unmodeled compliance jointly determine the interface motion. The base pHRI framework [19] shows that, after appropriate feedforward, such interaction dynamics can be represented by a constant-coefficient double integrator with an estimated persistent disturbance. This paper asks whether that representation survives a rehabilitation-specific actuator and sensing stack: a series-elastic-actuated (SEA) knee exoskeleton. The knee setting is a useful stress case for the framework. Fixed-gain impedance control is transparent and clinically familiar, but a constant interaction disturbance produces the Manuscript submitted June 2026 . Y. Cao is with Voryx Robotics, and J. Tang is with George Mason University, Dept. of Health Administration and Policy. Corresponding author: Y. Cao (e-mail: [yongyancao@gmail.com](yongyancao@gmail.com)). equilibrium error e∞ = τh /K. A 15Nm disturbance at K = 30Nm/rad produces 500mrad (28 .6◦ ) error. Increasing stiffness reduces this error but changes the physical interaction and can increase contact load on a recovering joint. A fair evaluation of prediction or disturbance estimation must therefore match the realized stiffness and damping rather than allowing a predictive controller to win by becoming stiffer. Within the interaction-dynamics view, different robots differ mainly in the recovery map from physical coordinates to the normalized residual model. A rigid manipulator uses computed torque or operational-space feedforward; a hydraulic or cable device uses pressure or tension compensation; a quasi-directdrive joint uses current-based torque compensation. For the SEA knee, the inner force loop and gravity/inertia/damping feed

FAQs

Why is the evaluation designed with matched impedance at 100 Hz and 500 Hz?

To ensure improvements are attributable to disturbance estimation and target handling rather than simply increasing impedance stiffness.

Jul 16, 2026

Upload by Patrick