Multidimensional Online Robot Motion

Details Multidimensional Online Robot Motion Multidimensional Online Robot Motion

2009-03-26

arxiv.org/abs/0903.4696v1

International Journal of Computational Geometry and Applications, 20(6):653-684, 2010

Computer Science

Computational Geometry

26 pages, 5 figures

Scientific paper

10.1142/S0218195910003475

We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-related task in an unknown environment whose geometry is learned by the robot during navigation. The robot is assumed to have tactile and global positioning sensors. We view these problems from the perspective of (non-linear) competitiveness as defined by Gabriely and Rimon. We first show that in 3 dimensions and higher, there is no upper bound on competitiveness: every online algorithm can do arbitrarily badly compared to the optimal. We then modify the problems by assuming a fixed clearance parameter. We are able to give optimally competitive algorithms under this assumption.

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