Integrable quadratic Hamiltonians on the Euclidean group of motions

Biggs, J. D. and Holderbaum, W. ORCID: https://orcid.org/0000-0002-1677-9624 (2010) Integrable quadratic Hamiltonians on the Euclidean group of motions. Journal of Dynamical and Control Systems, 16 (3). pp. 301-317. ISSN 1573-8698 doi: 10.1007/s10883-010-9094-8

Abstract/Summary

In this paper, we discuss 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 whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an 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 extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/17001
Item Type	Article
Refereed	Yes
Divisions	Life Sciences > School of Biological Sciences > Department of Bio-Engineering
Uncontrolled Keywords	sub-Riemannian curves; Euclidean group of motions; Hamiltonian systems; motion planning
Publisher	Springer
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