Fast Marching methods for Curvature Penalized Shortest Paths

Abstract : We introduce numerical schemes for computing distances and shortest paths with respect to several planar paths models, featuring curvature penalization and data-driven velocity: the Dubins car, the Euler/Mumford elastica, and a two variants of the Reeds-Shepp car. For that purpose, we design monotone and causal discretizations of the associated Hamilton-Jacobi-Bellman PDEs, posed on the three dimensional domain R2 × S1. Our discretizations involves sparse, adaptive and anisotropic stencils on a cartesian grid, built using techniques from lattice geometry. A convergence proof is provided, in the setting of discontinuous viscosity solutions. The discretized problems are solvable in a single pass using a variant of the Fast-Marching algorithm. Numerical experiments illustrate the applications of our schemes in motion planning and image segmentation.
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https://hal.archives-ouvertes.fr/hal-01538482
Contributor : Jean-Marie Mirebeau <>
Submitted on : Thursday, November 9, 2017 - 11:09:16 AM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM
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Jean-Marie Mirebeau. Fast Marching methods for Curvature Penalized Shortest Paths. 2017. ⟨hal-01538482v3⟩

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