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 network systems analytically. To this end, we attempt to develop a notion of information invariants. We develop a theory whereby one sensor network can be “reduced” to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a)-(e) among collaborating autonomous agents.
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