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This paper is concerned with the problem where a mobile robot of size D has to navigate to a target in an unknown planar environment. The competitiveness of an on-line navigation algorithm measures its path length relative to the length of the optimal off-line path. While competitiveness usually means constant relative performance, it is generalized here to any functional relationship between online performance and optimal off-line solution. This paper describes a new on-line navigationdoi:10.1109/robot.2005.1570409 dblp:conf/icra/GabrielyR05 fatcat:ghxkl5sjtbdoxcl4n57bwar5jy