Multi-Obstacle Muscle Wrapping Based on a Discrete Variational Principle - Penner, Johann; Leyendecker, Sigrid (Progress in Industrial Mathematics at ECMI 2018, 2018)
Simulations of biomechanical multibody systems actuated by Hill-type muscles are established as a major tool for investigating human motion. In addition to the activation level, typically, muscle actuated systems require to compute muscle paths, their length and their rates of length change to determine the muscle force. In particular, the muscle force direction is influenced by the muscle path. Assuming that the muscles are always under tension, their path is often modelled as a locally length minimizing curve that wraps over moving obstacles representing anatomical structure of the human body. This work is based on a mechanical analogue to find the shortest path on general smooth surfaces, using a discrete variational principle. In this context, the geodesic path is reinterpreted as the force-free motion of a particle in n dimensions under holonomic constraints. The muscle path is then a G1-continuous combination of geodesics on adjacent obstacle surfaces. It can be described as a shortest path boundary value problem with G1-continuous transitions across a certain number of obstacles. This contribution focuses on the technical details of the proposed method for multiple obstacles, while specific biomechanical applications will be presented in the future. In the given form, the formulation avoids nested loops and is well suitable to be used in an optimal control framework based on the direct transcription method DMOCC (Discrete mechanics and optimal control for constrained systems). Examples show the application of the given wrapping method to a certain number of general smooth surfaces. <