Comparison of Inverse Manipulator Kinematics Approximations from Scattered Input-Output Data using ANN-Like Methods

We compare the application of five different methods for the approximation of the inverse kinematics of a robot arm from a number of joint angle/Cartesian coordinate training pairs. The first method is a standard feed-forward neural network with error back-propagation learning. The next two methods employ an extended Kohonen Map that we combine with Shepard interpolation for the forward computation. We consider learning of the Kohonen Map with the method of Ritter et al. and compare it to our own method based on steepest descent optimization. We also study two scattered data approximation algorithms, namely Gaussian Radial Basis Function interpolation and a Local Polynomial Fit method that could be considered as a modification of McLain´s method. We propose extensions of the considered scattered data approximation algorithms to make them suitable for vector-valued multivariable functions, such as the mapping of Cartesian coordinates into joint angle coordinates.