The complexity of robot motion planning
The complexity of robot motion planning
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Fully dynamic algorithms for maintaining shortest paths trees
Journal of Algorithms
Approximation algorithms
Complexity of the mover's problem and generalizations
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Collision-probability constrained PRM for a manipulator with base pose uncertainty
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
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This paper formulates a new minimum constraint removal (MCR) motion planning problem in which the objective is to remove the fewest geometric constraints necessary to connect a start and goal state with a free path. It describes a probabilistic roadmap motion planner for MCR in continuous configuration spaces that operates by constructing increasingly refined roadmaps, and efficiently solves discrete MCR problems on these networks. A number of new theoretical results are given for discrete MCR, including a proof that it is NP-hard by reduction from SET-COVER. Two search algorithms are described that perform well in practice. The motion planner is proven to produce the optimal MCR with probability approaching 1 as more time is spent, and its convergence rate is improved with various efficient sampling strategies. It is demonstrated on three example applications: generating human-interpretable excuses for failure, motion planning under uncertainty, and rearranging movable obstacles.