On minimum-time paths of bounded curvature with position-dependent constraints
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Frazzoli_On minimum-time.pdf
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Author(s)
Sanfelice, Ricardo G.
Yong, Sze Zheng
Frazzoli, Emilio
Date Issued
December 2013
Journal
Automatica
Publisher
Elsevier
Citation
Sanfelice, Ricardo G.; Yong, Sze Zheng and Frazzoli, Emilio. “On Minimum-Time Paths of Bounded Curvature with Position-Dependent Constraints.” Automatica 50, no. 2 (February 2014): 537–546 © 2013 Elsevier Ltd
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Author's final manuscript
Abstract
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a “refraction” law at the boundary of the regions that generalizes the so-called Snell’s law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.automatica.2013.11.016
