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

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 stiffness- and damping-matched so improvements cannot be attributed to higher impedance. Under a motion-opposing $15\unit{Nm}$ step, classical impedance and MPC without estimation produce about $500\unit{mrad}$ steady-state error, whereas Kalman-augmented interaction MPC reduces this to $1.17\unit{mrad}$ at 100Hz and $0.70\unit{mrad}$ at 500Hz; the 500~Hz peak is $7.27\unit{mrad}$. In 30 randomized trials, the 95th-percentile peak is $21.57\unit{mrad}$. Bounded Assist-as-Needed scheduling, a corrective-channel energy tank, inequality-constrained 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 interaction-dynamics framework while separating it from clinical intent recognition, full-system passivity, safety certification, hardware trials, and free-standing multi-joint validation.