On Comparing the Power of Mobile Robots

Minimalist models have been studied for a broad array of tasks in robotics. In this paper, we consider the taskcompleting power of robots in terms of the sensors and actuators with which the robot is equipped. Our goal is to understand the relative power of different sets of sensors and actuators and to determine which of these sets enable the robot to complete its task. We define robots as collections of robotic primitives and provide a formal method for comparing the sensing and actuation power of robots constructed from these primitives. This comparison, which is based on the how the robots progress through their information spaces, induces a partial order over the set of robot systems. We prove some basic properties of this partial order and then apply it to a limited-sensing version of the global localization problem.