Feedback Can Reduce the Specification Complexity of Motor Programs
Egerstedt, Magnus B.
Brockett, Roger W.
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In this paper, we show that when it is possible to use feedback in the specification of "motor programs," the length of the descriptions of the instruction sequences for carrying out a given task can be reduced by a factor that reflects the richness of the available feedback signals. The model on which this work is based is that of a finite automaton, modified in such a way that instruction processing is akin to the way in which difference or differential equations "process" piecewise constant inputs. In terms of such "free-running" automata, we show that when feedback is available the length of the shortest description can be reduced by a factor depending on the ratio of the size of the entire state space to the size of the set of states for which feedback is locally effective.