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Exploiting the virtue of redundancy

Bernstein suggests that redundancy is the main reason for the superb dexterity of human motor control. However, introducing redundancy in an inversely controlled object, results in an ill-posed problem. We suggest learning all the possible solutions and choosing one of them in real time. In this paper we define redundancy and differentiate between finite, countable and uncountable redundancy. We introduce a general concept of multiple controller and describe a specific architecture, the polyhedral mixture of linear experts (PMLE). We extend some notions of learning theory to the case of multiple valued functions and stress the difference between estimated inverse and inverse estimation. Then we show that the multiple inverse PMLE is suitable in serving as a multiple controller.