Control of a Manipulator with a Minimum Number of Motion Primitives

Recent experiments on sensory-motor systems of frogs and rats have revealed that those systems have a modular structure. Apparently, control actions form a vector space with a handful of elementary controls as a basis. The reduction of admissible controls to a vector space plays in control theory a similar role to PCA in learning and recognition applications. Inspired by these observations, we first propose a mathematical model of the experimentally observed modular structure. We then show how to choose elementary control actions so as to make the system reach any desired final state. Finally, we determine the minimum number of elementary control actions to perform reaching.