A Tuning-Free Variational Framework for Muscle Redundancy Resolution: Torque Fiber Proximal Dynamics with Active-Set Switching and EMG-Validated Activation Prediction

Abstract

Muscle redundancy can be formulated as a constrained selection on a time-varying convex set of feasible activations. We introduce Torque Fiber Proximal Dynamics (TFPD), where activation evolves as the Euclidean projection of the previous state onto a convex polytope defined by torque equality and physiological bounds. TFPD is equivalent to a backward-Euler discretization of a sweeping process and a variational inequality with a maximal monotone normal cone operator. Within this framework, antagonist recruitment emerges naturally under a projection-based control hypothesis as a structural consequence of active-set transitions induced by the geometry, not as an imposed cost. We derive sufficient KKT-based conditions for antagonist activation under generic moment-arm asymmetry, linking boundary projection, strict complementarity, and torque coupling. We validate TFPD on a three-muscle elbow model using exact quadratic programming, benchmark it against five classical methods and a random baseline, and achieve a Pearson correlation of 0.68-0.73 with triceps EMG envelopes across ten subjects without any tunable cost-weight parameters. Sensitivity analysis and a three-dimensional activation trajectory visualization demonstrate robustness. TFPD connects neuromuscular coordination to proximal point theory, variational inequalities, and projected dynamical systems.