Optimal Gap Navigation for a Disc Robot

This paper considers the problem of globally optimal navigation with respect to Euclidean distance for a disc-shaped, differential-drive robot placed into an unknown, simply connected planar region with piecewise-analytic boundary. The robot is unable to build precise geometric maps or localize itself in any Euclidean frame. Most of the robot’s information comes from a gap sensor, which indicates depth discontinuities and allows the robot to move toward them. A motion strategy is presented that optimally navigates the robot to any landmark in the region. Optimality is proved and the method is illustrated in simulation.