A neural network learning of nonlinear mappings with considering their smoothness and its application to inverse kinematics

This paper discusses a learning problem of neural networks for realizing nonlinear mappings on the networks. We propose a learning method such that a neural network represents not only input-output relations of nonlinear mappings itself but also the smoothness of the mappings simultaneously. As a application we discuss a method of solving the inverse kinematics of robot manipulators by using neural networks. An efficient learning algorithm of a neural network such that the network represents the relations of both the positions and velocities from the task space to the joint space simultaneously. It is shown that the proposed methods make it possible to realize a nonlinear mapping on a neural network accurately and to solve the inverse kinematics problem more efficiently and accurately