Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This project proposes two computationally efficient formulations for solving these dynamic optimization problems using direct collocation optimal control methods. Both formulations rely on implicit representation of the contraction dynamics and use either muscle length or tendon force as state variable.

This project provides Matlab code for solving the muscle redundancy problem based on both formulations using direct collocation. This project also provides OpenSim models and necessary input data for solving the muscle redundancy problem in the leg during walking and running trials with different models.

From v1.1, an implicit formulation of the muscle activation dynamics is available.
From v2.1, an open-source version of the code is available.