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Competitive disconnection detection in on-line mobile robot navigation. (English) Zbl 1188.93062

Akella, Srinivas (ed.) et al., Algorithmic foundation of robotics VII. Selected contributions of the seventh international workshop on the algorithmic foundations of robotics (WAFR 2006), New York, NJ, USA, July 16–18, 2006. Berlin: Springer (ISBN 978-3-540-68404-6/hbk; 978-3-540-68405-3/ebook). Springer Tracts in Advanced Robotics 47, 253-267 (2008).
Summary: This paper concerns target unreachability detection during on-line mobile robot navigation in an unknown planar environment. Traditionally, competitiveness characterizes an on-line navigation algorithm in cases where the target is reachable from the robot’s start position. This paper introduces a complementary notion of competitiveness which characterizes an on-line navigation algorithm in cases where the target is unreachable. The disconnection competitiveness of an on-line navigation algorithm measures the path length generated in order to conclude target unreachability relative to the shortest off-line path that proves target unreachability from the same start position. It is shown that only competitive navigation algorithms can possess disconnection competitiveness. A competitive on-line navigation algorithm for a disc-shaped mobile robot, called CBUG, is described. This algorithm has a quadratic competitive performance, which is also the best achievable performance over all on-line navigation algorithms. The disconnection competitiveness of CBUG is analyzed and shown to be quadratic in the length of the shortest off-line disconnection path. Moreover, it is shown that quadratic disconnection competitiveness is the best achievable performance over all on-line navigation algorithms. Thus CBUG achieves optimal competitiveness both in terms of connection and disconnection paths. Examples illustrate the usefulness of connection-and-disconnection competitiveness in terms of path stability.
For the entire collection see [Zbl 1155.93004].

MSC:

93C85 Automated systems (robots, etc.) in control theory
93B40 Computational methods in systems theory (MSC2010)
93B27 Geometric methods
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