Multi-Obstacle Muscle Wrapping Based on a Discrete Variational Principle

Abstract

This work presents the integration of a discrete muscle wrapping formulation into an optimal control framework based on the direct transcription method DMOCC (discrete mechanics and optimal control for constrained systems (Leyendecker et al., Optim. Control Appl. Meth. 31(6), 505–528, 2010)). The major contribution lies in the use of discrete variational calculus to describe the entire musculoskeletal system, including the muscle path in a holistic way. The resulting coupled discrete Euler-Lagrange equations serve as equality constraints for the nonlinear programming problem, resulting from the discretisation of an optimal control problem. A key advantage of this formulation is that the structure preserving properties of the integrator enable the simulation to account for large, rapid changes in muscle paths at relativity moderate computation coasts. In particular, the derived muscle wrapping formulation does not rely on special case solutions, has no nested loops, a modular structure, and works for an arbitrary number of obstacles. A biomechanical example shows the application of the given method to an optimal control problem with smooth surfaces.