A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Algorithmic motion planning in robotics
Handbook of theoretical computer science (vol. A)
An exact algorithm for kinodynamic planning in the plane
Discrete & Computational Geometry
Journal of the ACM (JACM)
Motion planning in the presence of moving obstacles
Journal of the ACM (JACM)
Motion planning for a steering-constrained robot through moderate obstacles
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Robot Motion Planning
Approximation Algorithms for Curvature-Constrained Shortest Paths
SIAM Journal on Computing
Curvature-Constrained Shortest Paths in a Convex Polygon
SIAM Journal on Computing
Approximation of Curvature-Constrained Shortest Paths through a Sequence of Points
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
A Complete Approximation Algorithm for Shortest Bounded-Curvature Paths
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n^2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment.