A discrete variational approach to muscle wrapping in musculoskeletal optimal control simulations

Penner J (2023)


Publication Language: English

Publication Type: Thesis

Publication year: 2023

Abstract

This work shows the development of a simulation method for musculoskeletal

models used for in-silico human posture experiments. Here, the application of

discrete variational calculus to muscle wrapping problems allows the prediction

of the action and path of muscles around joints, in conjunction with skeletal

movements represented as a multibody system. Specifically, we tread the

multibody system’s motion and the muscle’s action in a variational context.

The resulting simulation model reflects the human anatomical structure with

Hill-type muscle actuation. This muscle model requires the calculation of the

muscle paths, their lengths, and changes in length during the movement, which

are determined by the muscle wrapping problem. In the sequel, we refer to

the combination of the multibody system and Hill-type muscle actuation as a

musculoskeletal model and approximate the action of the muscle as a geodesic

curve between the muscle’s origin and insertion. In order to solve the geodesic

path problem and the skeletal equation of motion, we transfer principles of

the calculus of variations to their discrete counterparts. The Hill-type muscle

forces and the forces acting on the skeleton are discretized analogously. A

vital advantage of the variational formulation is that the structure-preserving

properties of the integrator enable the simulation to account for large, rapid

changes in muscle paths at relatively moderate computational costs. In particular,

the derived muscle wrapping formulation does not rely on special

case solutions, has no nested loops, has a modular structure, and is entirely

described by algebraic equations. Furthermore, we consider applications in

which a musculoskeletal model is intended to perform specific movement tasks

while information about the corresponding required muscle activities and forces

are of interest. Modeling this simulation task as an optimal control problem

and approximating its solution numerically is a well-suited procedure to obtain

such information. The optimal control formulation in this work is based on

the direct transcription method DMOCC and comprises the minimization of

an objective function subject to the fulfillment of the discrete Euler-Lagrange

equations. To solve this problem, we also focus on the numerical tools needed

to solve a large-scale non-linear constrained optimization problem. Finally, we

show simulation results for specific motion tasks and their ad-hoc validation

through motion capture.


Authors with CRIS profile

How to cite

APA:

Penner, J. (2023). A discrete variational approach to muscle wrapping in musculoskeletal optimal control simulations (Dissertation).

MLA:

Penner, Johann. A discrete variational approach to muscle wrapping in musculoskeletal optimal control simulations. Dissertation, 2023.

BibTeX: Download