Using backprojections for fine motion planning with uncertainty
International Journal of Robotics Research
Visibility of disjoint polygons
Algorithmica
On moving and orienting objects
On moving and orienting objects
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
The complexity of planar compliant motion planning under uncertainty
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Error detection and recovery in robotics
Error detection and recovery in robotics
Plane-sweep algorithms for intersecting geometric figures
Communications of the ACM
Manipulator Grasping and Pushing Operations
Manipulator Grasping and Pushing Operations
On Motion Planning with Uncertainty
On Motion Planning with Uncertainty
A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Landmark-based robot navigation
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
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Uncertainty in the execution of robot motion plans must be accounted for in the geometric computations from which plans are obtained, especially in the case where position sensing is inaccurate. We give an &Ogr;(n2 log n) algorithm to find a single commanded motion direction which will guarantee a successful motion in the plane from a specified start to a specified goal whenever such a one-step motion is possible. The plans account for uncertainty in the start position and in robot control, and anticipate that the robot may stick on or slide along obstacle surfaces with which it comes in contact. This bound improves on the best previous bound by a quadratic factor, and is achieved in part by a new analysis of the geometric complexity of the backprojection of the goal as a function of commanded motion direction.