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

Björkenstam S, Carlson JS, Linn J, Leyendecker S, Lennartson B (2018)

Publication Language: English

Publication Type: Journal article, Review article

Publication year: 2018

Journal

Journal of Computational and Nonlinear Dynamics American Society of Mechanical Engineers (ASME)

DOI: 10.1115/1.4040780

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.

Authors with CRIS profile

Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

Optimal control of biomechanical MBS-Digital Human Models for simulation in the virtual assembly planning (MKS-Menschenmodelle) Nov. 1, 2015 - March 31, 2018

Involved external institutions

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

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. https://dx.doi.org/10.1115/1.4040780

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).

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