Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Kinetic maintenance of context-sensitive hierarchical representations for disjoint simple polygons
Proceedings of the eighteenth annual symposium on Computational geometry
Terrain Polygon Decomposition, with Application to Layered Manufacturing
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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Any practical model of robotic motion must cope with the uncertainty and imprecision inherent in real robots. One important model is compliant motion, in which a robot that encounters an obstacle obliquely may slide along the obstacle. The authors start by investigating the geometry of compliant motion in the plane under perfect control and find a compact data structure encoding all paths to a goal. When the authors introduce uncertainty in control and position sensing, the same data structure allows them to find efficiently a compliant motion that reaches the goal, if one exists, to compute the boundary of the nondirectional backprojection of the goal, and to compute multistep plans for sensorless robots. This "preprocessing and query" approach has advantages of speed for online queries and flexibility for considering robots with different capabilities or initial positions in the same environment.