Toward the design and analysis of blind, bouncing robots

What kind of tasks are robots with extremely simple control laws capable of performing? Consider a point robot that navigates by aligning itself to a certain fixed angle relative to the environment boundary, then driving in a straight line. Even without knowing the robot's exact location, basic, noisy odometry and counting sensors can be used to narrow down the robot's possible locations over time. This paper describes methods of determining the possible locations of the robot after the robot has moved a sufficient distance or has impacted the boundary a sufficient number of times.