Time parametrized motion planning

Taylor, Stuart; Linton, Carol; Biggs, James; Holderbaum, William

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.

Citation

Taylor, S., Linton, C., Biggs, J., & Holderbaum, W. (2024). Time parametrized motion planning. Mathematics, 12(21), 3404. https://doi.org/10.3390/math12213404

• Journal Article Type: Article
• Acceptance Date: Oct 28, 2024
• Online Publication Date: Oct 31, 2024
• Publication Date: Oct 31, 2024
• Deposit Date: Nov 1, 2024
• Publicly Available Date: Nov 1, 2024
• Journal: Mathematics
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 21
• Article Number: 3404
• Pages: 3404
• DOI: https://doi.org/10.3390/math12213404
• Keywords: 93B27, time parametrization, nonholonomic, motion planning, geometric control, wheeled robot, optimization