Algebraic verification for parameterized motion planning libraries

Anirudha Majumdar, Mark Tobenkin, Russ Tedrake

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

8 Scopus citations

Abstract

Recent progress in algorithms for estimating regions of attraction and invariant sets of nonlinear systems has led to the application of these techniques to motion planning in complex environments. In most instances, the verification occurs offline as the algorithms are still too computationally demanding for realtime implementation; as a result any online planner is restricted to applying the finite set of motion plans that were verified offline. In this paper we attempt to present a partial remedy by algebraically verifying families of parameterized feedback controllers. We provide a specific example using LQR controllers parameterized by their goal or nominal motion. We formulate this verification using robust region of attraction techniques in sums-of-squares optimization, and show that perturbations of a Lyapunov or Riccati equation can be used to provide algebraically parameterized Lyapunov candidates. The resulting verified funnels then provide a parameterized motion library that can be used efficiently in online planning. We present a number of numerical examples to demonstrate the effectiveness of our approach.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages250-257
Number of pages8
ISBN (Print)9781457710957
DOIs
StatePublished - Jan 1 2012
Externally publishedYes
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Majumdar, A., Tobenkin, M., & Tedrake, R. (2012). Algebraic verification for parameterized motion planning libraries. In 2012 American Control Conference, ACC 2012 (pp. 250-257). [6315544] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2012.6315544