Comparing the Power of Robots

Abstract

Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably “more powerful”, in terms of the tasks that they can complete, than others? Can we find meaningful equivalence classes of robot systems? This line of research is inspired by the theory of computation, which has produced similar results for abstract computing machines. Our basic contribution is a dominance relation over robot systems that formalizes the idea that some robots are stronger than others. This comparison, which is based on 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 show that it is directly related to the robots' ability to complete tasks. We give examples to demonstrate the theory, including a detailed analysis of a limited-sensing global localization problem.