Structurally dynamic wavelet networks for adaptive control of robotic systems

The practical applicability of recently developed adaptive neurocontrol algorithms for poorly modelled robotic systems depends crucially upon the accuracy and efficiency of the neural network used to approximate the functions required for accurate control of the system. Recently, drawing upon results from multiresolution approximation theory, an algorithm has been developed which dynamically varies the actual structure of the network concurrently with its associated parameters, and, in the process, stably evolves a minimal network which still provides the required accuracy. In this paper, we extend these ideas to the adaptive control of robot manipulators, providing a formal proof of the stability and convergence properties of our new algorithm. A main feature of the proof is the demonstration that the stability properties of the algorithm are independent of the specific mechanism used to vary the structure of the network, allowing great flexibility in the design of the structure adaptation mechanism. A specific structural adaptation mechanism is suggested, representing a real-time approximation to a new nonparametric estimation technique, and its performance is then demonstrated on a simulation of a free-floating space robotic manipulator.