Penner J (2023)
Publication Language: English
Publication Type: Thesis
Publication year: 2023
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.
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.
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