Polyhedral mixture of linear experts for many-to-one mapping inversion and multiple controllers

Feed-forward control schemes require an inverse mapping of the controlled system. In adaptive systems this inverse mapping is learned from examples. The biological motor control is very redundant, as are many robotic systems, therefore the mapping is many-to-one and the inverse problem is ill posed. In this paper we present a novel architecture and algorithms for the approximation and inversion of many-to-one functions. The proposed architecture retains all the possible solutions available to the controller in real time. This is done by a modified mixture of experts architecture, where each expert is linear and more than a single expert may be assigned to the same input region. The learning is implemented by the hinging hyperplanes algorithm. The proposed architecture is described and its operation is illustrated for some simple cases. Finally, the virtue of redundancy and its exploitation by multiple controllers are discussed.