Integrable quadratic Hamiltonians on the Euclidean group of motions

James Biggs, William Holderbaum

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper tackles the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular we derive a global result for special sub-Riemannian curves for which their Hamiltonian satisfies a particular condition. The sub-Riemannian curves in this paper are defined in the context of a constrained optimal control problem. The Maximun Principle is then applied to this problem to yield the appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extreme curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.
LanguageEnglish
Pages301-317
Number of pages17
JournalJournal of Dynamical and Control Systems
Volume16
Issue number3
DOIs
Publication statusPublished - 23 Jul 2010

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Hamiltonians
Euclidean
Curve
Motion
Motion planning
Underwater Vehicle
Constrained Control
Motion Planning
Optimal Control Problem
Extremes
Invariant
Computing

Keywords

  • sub-riemannian curves
  • euclidean group of motions
  • hamiltonian systems
  • motion planning

Cite this

Biggs, James ; Holderbaum, William. / Integrable quadratic Hamiltonians on the Euclidean group of motions. In: Journal of Dynamical and Control Systems. 2010 ; Vol. 16, No. 3. pp. 301-317.
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Integrable quadratic Hamiltonians on the Euclidean group of motions. / Biggs, James; Holderbaum, William.

In: Journal of Dynamical and Control Systems, Vol. 16, No. 3, 23.07.2010, p. 301-317.

Research output: Contribution to journalArticle

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