An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
On the Movement of Robot Arms in Two Dimensional Bounded Regions
On the Movement of Robot Arms in Two Dimensional Bounded Regions
The impact of robotics on computer science
Communications of the ACM
On the geodesic Voronoi diagram of point sites in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Moving a ladder in three dimensions: upper and lower bounds
SCG '87 Proceedings of the third annual symposium on Computational geometry
A methodology of autonomous navigation in 3-D space under location uncertainty
IEA/AIE '88 Proceedings of the 1st international conference on Industrial and engineering applications of artificial intelligence and expert systems - Volume 1
Motion planning in the presence of moving obstacles
Journal of the ACM (JACM)
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
Planning the shortest path for a disc in O(n2log n) time
SCG '85 Proceedings of the first annual symposium on Computational geometry
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Pseudo approximation algorithms, with applications to optimal motion planning
Proceedings of the eighteenth annual symposium on Computational geometry
Signal Processing - Special issue: Fractional signal processing and applications
The visibility-Voronoi complex and its applications
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots
International Journal of Robotics Research
Flexible Path Planning Using Corridor Maps
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A variational approach to path planning for hyper-redundant manipulators
Robotics and Autonomous Systems
Indicative routes for path planning and crowd simulation
Proceedings of the 4th International Conference on Foundations of Digital Games
Robotics and Autonomous Systems
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The two-dimensional Movers' Problem may be stated as follows: Given a set of polygonal obstacles in the plane, and a two-dimensional robot system B, determine whether one can move B from a given placement to another without touching any obstacle, and plan such a motion when one exists. Efficient algorithms are presented for the two special cases in which B is either a disc or a straightline segment, running respectively in time 0(n log n) and 0(n2 log n). To solve the problem for a disc one uses the planar Voronoi diagram determined by the obstacles; in the case of a line-segment one generalizes the notion of Voronoi diagram to the 3-dimensional configuration space of the moving segment.