---
_id: '16630'
abstract:
- lang: eng
text: This paper formulates the dynamical equations of mechanics subject
to holonomic constraints in terms of the states and controls using a constrained
version of the Lagrange-d’Alembert principle. Based on a discrete version of this
principle, a structure preserving time-stepping scheme is derived. It is shown
that this respect for the mechanical structure (such as a reliable computation
of the energy and momentum budget, without numerical dissipation) is retained
when the system is reduced to its minimal dimension by the discrete null space
method. Together with initial and final conditions on the configuration and conjugate
momentum, the reduced time-stepping equations serve as nonlinear equality constraints
for the minimisation of a given cost functional. The algorithm yields a sequence
of discrete configurations together with a sequence of actuating forces, optimally
guiding the system from the initial to the desired final state. The resulting
discrete optimal control algorithm is shown to have excellent energy and momentum
properties, which are illustrated by two specific examples, namely reorientation
and repositioning of a rigid body subject to external forces and the reorientation
of a rigid body with internal momentum wheels.
author:
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Jerrold E.
full_name: Marsden, Jerrold E.
last_name: Marsden
- first_name: Michael
full_name: Ortiz, Michael
last_name: Ortiz
citation:
ama: 'Leyendecker S, Ober-Blöbaum S, Marsden JE, Ortiz M. Discrete Mechanics and
Optimal Control for Constrained Multibody Dynamics. In: Volume 5: 6th International
Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
and C. ; 2007. doi:10.1115/detc2007-34574'
apa: 'Leyendecker, S., Ober-Blöbaum, S., Marsden, J. E., & Ortiz, M. (2007).
Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics. In
Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
and Control, Parts A, B, and C. https://doi.org/10.1115/detc2007-34574'
bibtex: '@inproceedings{Leyendecker_Ober-Blöbaum_Marsden_Ortiz_2007, title={Discrete
Mechanics and Optimal Control for Constrained Multibody Dynamics}, DOI={10.1115/detc2007-34574},
booktitle={Volume 5: 6th International Conference on Multibody Systems, Nonlinear
Dynamics, and Control, Parts A, B, and C}, author={Leyendecker, Sigrid and Ober-Blöbaum,
Sina and Marsden, Jerrold E. and Ortiz, Michael}, year={2007} }'
chicago: 'Leyendecker, Sigrid, Sina Ober-Blöbaum, Jerrold E. Marsden, and Michael
Ortiz. “Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics.”
In Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
and Control, Parts A, B, and C, 2007. https://doi.org/10.1115/detc2007-34574.'
ieee: 'S. Leyendecker, S. Ober-Blöbaum, J. E. Marsden, and M. Ortiz, “Discrete Mechanics
and Optimal Control for Constrained Multibody Dynamics,” in Volume 5: 6th International
Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
and C, 2007.'
mla: 'Leyendecker, Sigrid, et al. “Discrete Mechanics and Optimal Control for Constrained
Multibody Dynamics.” Volume 5: 6th International Conference on Multibody Systems,
Nonlinear Dynamics, and Control, Parts A, B, and C, 2007, doi:10.1115/detc2007-34574.'
short: 'S. Leyendecker, S. Ober-Blöbaum, J.E. Marsden, M. Ortiz, in: Volume 5: 6th
International Conference on Multibody Systems, Nonlinear Dynamics, and Control,
Parts A, B, and C, 2007.'
date_created: 2020-04-16T08:28:13Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1115/detc2007-34574
language:
- iso: eng
publication: 'Volume 5: 6th International Conference on Multibody Systems, Nonlinear
Dynamics, and Control, Parts A, B, and C'
publication_identifier:
isbn:
- 079184806X
publication_status: published
status: public
title: Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics
type: conference
user_id: '15701'
year: '2007'
...