Discrete and continuous mechanics for tree representations of mechanical systems

Elliot R. Johnson, Todd D. Murphey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

We use a tree-based structure to represent mechanical systems comprising interconnected rigid bodies. Using this representation, we derive a simple algorithm to numerically calculate forward kinematic maps, body velocities, and their derivatives. The algorithm is computationally efficient and scales to large systems very well by using recursion to take advantage of the tree structure. Moreover, this method is less prone to modeling errors because each element of the graph is simple. The tree representation provides a natural framework to simulate mechanical dynamics with numeric computations rather than large symbolically-derived equations. In particular, the representation allows one to simulate systems in generalized coordinates using Lagrangian dynamics without symbolically finding the equations of motion. This method also applies to the relatively new variational integrators which numerically integrate dynamics in a way that preserve momentum and other symmetries. We show how to implement both integration schemes for an arbitrary system of interconnected rigid bodies in a computationally efficient way while avoiding symbolic equations of motion. We end with an example simulating a marionette; a mechanically complex, high degree-of-freedom system.

Original languageEnglish (US)
Title of host publication2008 IEEE International Conference on Robotics and Automation, ICRA 2008
Pages1106-1111
Number of pages6
DOIs
StatePublished - 2008
Event2008 IEEE International Conference on Robotics and Automation, ICRA 2008 - Pasadena, CA, United States
Duration: May 19 2008May 23 2008

Publication series

NameProceedings - IEEE International Conference on Robotics and Automation
ISSN (Print)1050-4729

Other

Other2008 IEEE International Conference on Robotics and Automation, ICRA 2008
Country/TerritoryUnited States
CityPasadena, CA
Period5/19/085/23/08

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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