On-line deadlock-free path-planning algorithms in the presence of a dead reckoning error

A mobile robot generally calculates its position by the information from its encoders and a magnetic compass. However under some uncertainties of a robot and its environment, e.g., modelling and slipping errors, a robot always accumulates a dead reckoning error, and consequently it sometimes gets lost in a 2D environment. In this paper, we pay attention to a metric error such that the Euclidean distance space is projected into another space each other by the homeomorphism in real and computer worlds. Then we discuss if the previous sensor-based path-planning algorithms keep their deadlock-free characteristics near the goal for a mobile robot with a metric error. In general, all the previous algorithms ensure their deadlock-free characteristics by the metric (distance) condition, the curve (segment) condition, and the nonmetric (topologic) condition, and therefore we should give proofs such that these conditions are still stably against such a dead reckoning error in an unknown world