Affiliation:
1. Technion, Israel Institute of Technology, Haifa, 32000, Israel
Abstract
This paper classifies common mobile robot on-line motion planning problems according to their competitive complexity. The competitiveness of an on-line algorithm measures its worst case performance relative to the optimal off-line solution to the problem. Competitiveness usually means constant relative performance. This paper generalizes competitiveness to any functional relationship between on-line performance and optimal off-line solution. The constants in the functional relationship must be scalable and may depend only upon on-line information. Given an on-line task, its competitive complexity class is a pair of lower and upper bounds on the competitive performance of all on-line algorithms for the task, such that the two bounds satisfy the same functional relationship. The paper classifies the following on-line motion planning problems into competitive classes: area coverage, navigation to a target, and on-line search for an optimal path. In particular, it is shown that navigation to a target whose position is either apriori known or recognized upon arrival belongs to a quadratic competitive complexity class. The hardest on-line problem involves navigation in unknown variable traversibility environments. Under certain restriction on traversibility, this last problem belongs to an exponential competitive complexity class.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
1 articles.
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