Exploiting critical points to reduce positioning error for sensor-based navigation

This paper presents a planner that determines a path such that the robot does not have to heavily rely on odometry to reach its goal. The planner determines a sequence of obstacle boundaries that the robot must follow to reach the goal. Since this planner is used in the context of a coverage algorithm already presented by the authors, we assume that the free space is already, completely or partially, represented by a cellular decomposition whose cell boundaries are defined by critical points of Morse functions (isolated points at obstacle boundaries). The topological relationship among the cells is represented by a graph where nodes are the critical points and edges connect the nodes that define a common cell (i.e., the edges correspond to the cells themselves). A search of this graph yields a sequence of cells that directs the robot from a start to a goal. Once a sequence of cells and critical points are determined, a robot traverses each cell by mainly following the boundary of the cell along the obstacle boundaries and minimizes the accumulated dead-reckoning error at the intermediate critical points. This allows the robot to reach the goal robustly even in the presence of dead-reckoning error.