The Pledge Algorithm Reconsidered under Errors in Sensors and Motion

We consider the problem of escaping from an unknown polygonal maze under limited resources and under errors in sensors and motion. It is well-known that the pledge algorithm always finds a path out of an unknown maze without any means of orientation, provided that such a path exists. The pledge algorithm sums up the turning angles along the boundary of the obstacles and plans its way by using a single counter and no further information. The correctness proof makes use of the fact that motions in the free space and the measurement of turning angles can be done exactly. We consider the case that the free motion of the robot and the computation of turning angles are erroneous. This work is a first attempt to incorporate error assumptions into theoretically sound proofs of online motion planning algorithms.