Journal of the ACM (JACM)
Motion planning for a steering-constrained robot through moderate obstacles
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the twelfth annual symposium on Computational geometry
Curvature-constrained shortest paths in a convex polygon (extended abstract)
Proceedings of the fourteenth annual symposium on Computational geometry
The complexity of the two dimensional curvature-constrained shortest-path problem
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Approximation algorithms for curvature-constrained shortest paths
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Reachability by paths of bounded curvature in convex polygons
Proceedings of the sixteenth annual symposium on Computational geometry
Reachability by paths of bounded curvature in a convex polygon
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
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Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let X denote a sequence of n points. Let s be the length of the shortest curvature-constrained path for B that visits the points of X in the given order. We show that if the points of X are given on-line and the robot has to respond to each point immediately, there is no strategy that guarantees a path whose length is at most f(n)s, for any finite function f(n). On the other hand, if all points are given at once, a path with length at most 5.03s can be computed in linear time. In the semi-online case, where the robot not only knows the next input point but is able to "see" the future input points included in the disk with radius R around the robot, a path of length (5.03 + O(1/R))s can be computed.