On Information Invariants in Robotics

Abstract

We consider the problem of determining the information requirements to perform robot tasks, using the concept of information invariants. This paper represents our attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity. We also provide a first approximation to a purely operational theory that addresses a narrow but interesting special case. We discuss several measures for the information complexity of a task: (a) How much internal state should the robot retain? (b)How many cooperating agents are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We consider how one might develop a kind of "calculus" on (a) - (e) in order to compare the power of sensor systems analytically. To this end, we attempt to develop a notion of information invariants. We develop a theory whereby one sensor can be "reduced" to another (much in the spirit of computation-theoretic reductions), by adding, deleting and reallocating (a) - (e) among collaborating autonomous agents.