Scalable variational integrators for constrained mechanical systems in generalized coordinates

Elliot R. Johnson; Todd D. Murphey

doi:10.1109/TRO.2009.2032955

Scalable variational integrators for constrained mechanical systems in generalized coordinates

Elliot R. Johnson, Todd D. Murphey

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

57 Scopus citations

Abstract

We present a technique to implement scalable variational integrators for generic mechanical systems in generalized coordinates. Systems are represented by a tree-based structure that provides efficient means to algorithmically calculate values (position, velocities, and derivatives) needed for variational integration without the need to resort to explicit equations of motion. The variational integrator handles closed kinematic chains, holonomic constraints, dissipation, and external forcing without modification. To avoid the full equations of motion, this method uses recursive equations, and caches calculated values, to scale to large systems by the use of generalized coordinates. An example of a closed-kinematic-chain system is included along with a comparison with the open-dynamics engine (ODE) to illustrate the scalability and desirable energetic properties of the technique. A second example demonstrates an application to an actuated mechanical system.

Original language	English (US)
Article number	5306102
Pages (from-to)	1249-1261
Number of pages	13
Journal	IEEE Transactions on Robotics
Volume	25
Issue number	6
DOIs	https://doi.org/10.1109/TRO.2009.2032955
State	Published - Dec 2009

Funding

Dr. Murphey is the recipient of a National Science Foundation CAREER Award. Manuscript received November 16, 2008; revised May 16, 2009 and August 7, 2009. First published October 30, 2009; current version published December 8, 2009. This paper was recommended for publication by Associate Editor K. Yamane and Editor J.-P. Laumond upon evaluation of the reviewers’ comments. This work was supported by the National Science Foundation under CAREER Award CMS-0546430. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This paper was presented in part at the IEEE International Conference on Robotics and Automation, Pasadena, CA, May 2008.

Keywords

Animation and simulation
Dynamics
Variational integrators

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TRO.2009.2032955

Cite this

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abstract = "We present a technique to implement scalable variational integrators for generic mechanical systems in generalized coordinates. Systems are represented by a tree-based structure that provides efficient means to algorithmically calculate values (position, velocities, and derivatives) needed for variational integration without the need to resort to explicit equations of motion. The variational integrator handles closed kinematic chains, holonomic constraints, dissipation, and external forcing without modification. To avoid the full equations of motion, this method uses recursive equations, and caches calculated values, to scale to large systems by the use of generalized coordinates. An example of a closed-kinematic-chain system is included along with a comparison with the open-dynamics engine (ODE) to illustrate the scalability and desirable energetic properties of the technique. A second example demonstrates an application to an actuated mechanical system.",

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Scalable variational integrators for constrained mechanical systems in generalized coordinates

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