Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEs

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Communicated by Bertrand Kerautret
Demo edited by Bertrand Kerautret

Abstract

We introduce a generalized Fast-Marching algorithm, able to compute paths globally minimizing a measure of length, defined with respect to a variety of metrics in dimension two to five. Our method applies in particular to arbitrary Riemannian metrics, and implements features such as second order accuracy, sensitivity analysis, and various stopping criteria. We also address the singular metrics associated with several non-holonomic control models, related with curvature penalization, such as the Reeds-Shepp's car with or without reverse gear, the Euler-Mumford elastica curves, and the Dubins car. Applications to image processing and to motion planning are demonstrated.

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  Software Heritage Archive @softwareversion{sw-ipol.2019.227, title = {{Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEs}}, author = {Jean-Marie Mirebeau, Jorg Portegies}, date = {2018-04-25}, license = {Apache-2.0 GPL-3.0-or-later}, version = {1.0}, swhid = {swh:1:dir:1a45b870420d45e5c1d5eed321b470ba9a8c15e2;origin=https://doi.org/10.5201/ipol.2019.227;visit=swh:1:snp:1a4b2de8059a204e44ef91ecbb4662afb4c4c009;anchor=swh:1:rel:60a083a52336ef08828d062083e1742b3f0ce3ce}, related = {ipol.2019.227}, relatedtype = "Reference article: https://doi.org/10.5201/ipol.2019.227" } % the biblatex-software style extension is recommended for software bibitems
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History

• Note from the editor: the manuscript of the article was modified on 2022-01-01 to include information about its editors. The original version of the manuscript is available here.