Time parametrized motion planning

Taylor, S. ORCID: https://orcid.org/0009-0009-3408-340X, Linton, C. ORCID: https://orcid.org/0000-0002-9900-7274, Biggs, J. and Holderbaum, W. ORCID: https://orcid.org/0000-0002-1677-9624 (2024) Time parametrized motion planning. Mathematics, 12 (21). 3404. ISSN 2227-7390 doi: 10.3390/math12213404

Abstract/Summary

Time can be treated as a free parameter to isotropically stretch the tangent space. A trajectory, which matches the boundary conditions on its configuration, is adjusted so that velocity conditions are met. The modified trajectory is found by substitution, without the computational cost of re-integrating the velocity function. This concept is extended to stretch the tangent space anisotropically. This method of time parametrization especially applies to Geometric Control, where the Pontryagin Maximum Principle minimizes some cost function and matches the boundary configuration constraints but not the velocity constraints. The optimal trajectory is modified by the parametrization so that the cost function is minimized if the stretching is stopped at any time. This is a theoretical contribution, using a wheeled robot example to illustrate the modification of an optimal velocity under multiple parametrizations.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/119385
Identification Number/DOI	10.3390/math12213404
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
Publisher	MDPI AG
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