Abstract
A mobile robot usually estimates its position and orientation by a dead reckoning system. However under several kinds of uncertainties, e.g. inner/outer sensor errors and/or a slip, a mobile robot unfortunately misunderstands true position and orientation in a real world as false position and orientation in a computer world. Due to the difference, a mobile robot governed by sensor-based navigation sometimes gets lost in an unknown 2-D environment. On the observation, in this paper, we firstly improve previous metric sensor-based navigation algorithms in order for a mobile robot to deal with such uncertainties. Secondly, we name a class of errors a homeomorpic error, where true and false positions in real and computer worlds are projected each other by the homeomorphism. Finally, we theoretically show that generation of the homeomorpic error is the necessary and sufficient condition for a mobile robot not to enter into any limit cycle in every type of sensor-based navigation algorithm.
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