On information invariants in robotics

Bruce Randall Donald
1995 Artificial Intelligence  
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
more » ... ould 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. Intelligence 72 (1995) 217-304 B.R. Donald/Artijicial Intelligence 72 (1995) 217-304 B.K. Donuld/Artificiul Inrelhgence 72 (1995) 217-304 ' So, p* is the time-resealed trajectory from ,j 1 I9 I. ') For an explicit use of this constant in an actual servo loop, see, for example, [ 44 ] 230 B.R. Donuld/ArtificiuI Intelligence 72 (1995) 217-304 Definition 8.29. Let U and V be sensor systems. We write U <p V if there exists some fixed polynomial function q(n) of the size n of U and V, such that U GyCnI 1/ for all sizes n. So, the assertion "U <p V" is a statement about a family of sensor systems. It says that U reduces to V by permuting V and adding an amount of communication that is polynomial in the size of U and V. In particular, note that if U <p V, then for any i, j E N, i. U <p j V. However, we can say something stronger: Lemma 8.30 (Completeness of polynomial communication). U <p V iJ and only iJ U&V. Proof. "If" is trivial; we show the "only if" direction. If U and V have at most YZ vertices, then global point-to-point communication can be implemented by adding 0(n2) new data-paths. Hence it is always true that U &"z) V. Any additional communication would be superfluous and would not add power to the system. 0
doi:10.1016/0004-3702(94)00024-u fatcat:iw4ftgcz3vfnfdtu4tcen5tbwe