# Bounded-Curvature Shortest Paths through a Sequence of Points using Convex Optimization

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of $n$ points in the plane in a given order. This problem is a sub-problem of the Dubins Traveling Salesman Problem and also arises naturally in path planning for point car-like robots in the presence of polygonal obstacles. We show that when consecutive waypoints are distance at least four apart, this question reduces to a family of convex optimization problems over polyhedra in $\mathbb{R}^n$.
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Journal articles

Cited literature [33 references]

https://hal.inria.fr/hal-00927100
Contributor : Sylvain Lazard <>
Submitted on : Friday, January 10, 2014 - 7:06:40 PM
Last modification on : Monday, June 24, 2019 - 12:32:04 PM

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### Citation

Xavier Goaoc, Hyo-Sil Kim, Sylvain Lazard. Bounded-Curvature Shortest Paths through a Sequence of Points using Convex Optimization. SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2013, 42 (2), pp.662-684. ⟨10.1137/100816079⟩. ⟨hal-00927100⟩

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