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

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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SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2013, 42 (2), pp.662-684. 〈10.1137/100816079〉
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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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