Efficient Computation of Higher-Order Variational Integrators in Robotic Simulation and Trajectory Optimization

Taosha Fan*, Jarvis Schultz, Todd Murphey

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop O(n) algorithms to evaluate the discrete Euler-Lagrange (DEL) equations and compute the Newton direction for solving the DEL equations, which results in linear-time variational integrators of arbitrarily high order. To our knowledge, no linear-time higher-order variational or even implicit integrators have been developed before. Moreover, an algorithm to linearize the DEL equations is presented, which is useful for trajectory optimization. These proposed algorithms eliminate the bottleneck of implementing higher-order variational integrators in simulation and trajectory optimization of complex robotic systems. The efficacy of this paper is validated through comparison with existing methods, and implementation on various robotic systems—including trajectory optimization of the Spring Flamingo robot, the LittleDog robot and the Atlas robot. The results illustrate that the same integrator can be used for simulation and trajectory optimization in robotics, preserving mechanical properties while achieving good scalability and accuracy.

Original languageEnglish (US)
Title of host publicationSpringer Proceedings in Advanced Robotics
PublisherSpringer Science and Business Media B.V.
Pages689-706
Number of pages18
DOIs
StatePublished - 2020

Publication series

NameSpringer Proceedings in Advanced Robotics
Volume14
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Engineering (miscellaneous)
  • Artificial Intelligence
  • Computer Science Applications
  • Applied Mathematics

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