Motion planning amidst fat obstacles
نویسنده
چکیده
The complexity of exact motion planning algorithms highly depends on the complexity of the robot’s free space, i.e., the set of all collision-free placements of the robot. Theoretically, the complexity of the free space can be very high. In practice, the complexity of the free space tends to be much smaller. We show that, under some realistic assumptions, the complexity of the free space of a robot moving amidst fat obstacles is linear in the number of obstacles. The complexity results lead to efficient algorithms for motion planning amidst fat obstacles: we show that theO(n5) motion planning algorithm by Schwartz and Sharir runs in O(n2) time if the obstacles are fat. Finally, we modify the algorithm to improve the running time toO(n log2 n).
منابع مشابه
Efficient Algorithms for Exact
The complexity of exact motion planning algorithms highly depends on the complexity of the robot’s free space, i.e., the set of all collision-free placements of the robot. Theoretically, the complexity of the free space can be very high. In practice, the complexity of the free space tends to be much smaller. We show that, under some realistic assumptions, the complexity of the free space of a r...
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