Abstract

We study the ratio of the dead-free path length made by a new strategy to the shortest path length in unknown environment containing rectangular and rectilinear obstacles satisfying some limitations on their aspect ratios and side lengths. We show that the ratio is at most arbitrarily close to 1 + 3 5 f , as n grows, if the start point and the target are at the same horizontal level, where the aspect ratio of each obstacle is at most f. We also study the ratio for unknown environment where the start point and the target may be at different levels.

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