Using backprojections for fine motion planning with uncertainty
International Journal of Robotics Research
Optimal point location in a monotone subdivision
SIAM Journal on Computing
On moving and orienting objects
On moving and orienting objects
Planning, geometry, and complexity of robot motion
Planning, geometry, and complexity of robot motion
On-line construction of the convex hull of a simple polyline
Information Processing Letters
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A fast Las Vegas algorithm for triangulating a simple polygon
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
The complexity of planar compliant motion planning under uncertainty
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Motion Planning with Uncertainty: The Preimage Backchaining Approach
Motion Planning with Uncertainty: The Preimage Backchaining Approach
Structured visibility profiles with applications to problems in simple polygons (extended abstract)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Offline maintenance of planar configurations
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Compliant motion in a simple polygon
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Efficient Algorithms for Two-Center Problems for a Convex Polygon
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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We consider motion planning under the compliant motion model, in which a robot directed to walk into a wall may slide along it. We examine several variants of compliant motion planning for a point robot inside a simple polygon with n sides, where the goal is a fixed vertex or edge. For the case in which the robot moves with perfect control, we build a data structure that lets us in &Ogr;(log n) time determine the range of directions in which the robot can move from a query point to the goal in a single step. This structure lets us solve a variety of other problems: we can find a similar query data structure for multi-step paths; we can solve single-step problems allowing uncertainty in control and position sensing; and we can explicitly compute the set of all points that can reach the goal in a single step, even allowing uncertainty in control. Our algorithms run in &Ogr;(n log n) time and linear space; they use a novel method for maintaining convex hulls of simple paths that may be of independent interest.