Competitive Disconnection Detection in On-Line Mobile Robot Navigation

This paper is concerned with 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 it generates 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 a doubly competitive algorithm in terms of path stability.