Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems with Application to Direct Optimal Control

Journal article
(Review article)


Publication Details

Author(s): Björkenstam S, Carlson JS, Linn J, Leyendecker S, Lennartson B
Journal: Journal of Computational and Nonlinear Dynamics
Publication year: 2018
ISSN: 1555-1423
Language: English


Abstract

In this paper, we present efficient algorithms for computation
of the residual of the constrained discrete Euler-
Lagrange equations of motion for tree structured, rigid
multibody systems. In particular, we present new recursive
formulas for computing sensitivities of the kinetic energy.
This enables us to solve the inverse dynamics problem of the
discrete system with linear computational complexity. The
resulting algorithms are easy to implement, and can naturally
be applied to a very broad class of multibody systems
by imposing constraints on the coordinates by means of Lagrange
multipliers. A comparison is made with an existing
software package, which shows a drastic improvement in
computational efficiency. Our interest in inverse dynamics is
primarily to apply direct transcription optimal control methods
to multibody systems. As an example application, we
present a digital human motion planning problem, which we
solve using the proposed method. Furthermore, we present
detailed descriptions of several common joints, in particular
singularity free models of the spherical joint and the rigid
body joint, using the Lie groups of unit quaternions and unit
dual quaternions, respectively.


FAU Authors / FAU Editors

Leyendecker, Sigrid Prof. Dr.-Ing.
Chair of Applied Dynamics


External institutions with authors

Chalmers University of Technology / Chalmers tekniska högskola
Fraunhofer-Chalmers Centre
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) / Fraunhofer Institute for Industrial Mathematics


How to cite

APA:
Björkenstam, S., Carlson, J.S., Linn, J., Leyendecker, S., & Lennartson, B. (2018). Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems with Application to Direct Optimal Control. Journal of Computational and Nonlinear Dynamics.

MLA:
Björkenstam, Staffan, et al. "Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems with Application to Direct Optimal Control." Journal of Computational and Nonlinear Dynamics (2018).

BibTeX: 

Last updated on 2018-16-10 at 11:53