Time Parametrized Motion Planning

Stuart Taylor (), Carol Linton, James Biggs and William Holderbaum
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Stuart Taylor: School of Science, Engineering, and Environment, Salford University, Salford M5 4NT, UK
Carol Linton: School of Systems Engineering, University of Reading, Reading RG6 6AY, UK
James Biggs: School of Science, Engineering, and Environment, Salford University, Salford M5 4NT, UK
William Holderbaum: School of Science, Engineering, and Environment, Salford University, Salford M5 4NT, UK

Mathematics, 2024, vol. 12, issue 21, 1-13

Abstract: 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.

Keywords: geometric control; motion planning; optimization; nonholonomic; time parametrization; wheeled robot (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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