Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
An efficient and simple motion planning algorithm for a ladder amidst polygonal barriers
Journal of Algorithms
Lower bounds on moving a ladder in two and three dimensions
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangles in space or building (and analyzing) castles in the Air
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Planning algorithm for a convex polygonal object in two-dimensional polygonal space
Discrete & Computational Geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
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We present an algorithm that solves the following motion-planning problem. Given an L-shaped body L and a 2-dimensional region with n point obstacles, decide whether there is a continuous motion connecting two given positions and orientations of L during which L avoids collision with the obstacles. The algorithm requires &Ogr;(n2 log2 n) time and &Ogr;(n2) storage. The algorithm is a variant of the cell-decomposition technique of the configuration space ([SS, LS]) but it employs a new and efficient technique for obtaining a compact representation of the free space, which results in a saving of an order of magnitude. The approach used in our algorithm seems applicable to motion-planning of certain robotic arms whose spaces of free placements have a structure similar to that of the L-shaped body.