On shortest paths in polyhedral spaces
SIAM Journal on Computing
Plane-sweep algorithms for intersecting geometric figures
Communications of the ACM
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Simultaneous containment of several polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion planning in the presence of movable obstacles
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient motion planning for an L-shaped object
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Collision Detection of a Moving Polygon in the Presence of Polygonal Obstacles in the Plane
IEEE Transactions on Pattern Analysis and Machine Intelligence
Translating a convex polyhedron over monotone polyhedra
Computational Geometry: Theory and Applications
A solution to the Path Planning problem using angle preprocessing
Robotics and Autonomous Systems
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We state and prove a theorem about the number of points of local nonconvexity in the union of m. Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Al,…, Am, following a basic approach suggested by Lozano-Perez and Wesley. Assuming that the number of corners of B is fixed, the algorithm developed here runs in time &Ogr;(n log2n), where n is the total number of corners of the Al's.