COMPARISON OF SOME NEURAL-NETWORK AND SCATTERED DATA APPROXIMATIONS -THE INVERSE MANIPULATOR KINEMATICS EXAMPLE

This paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a nu mber of joint angle/Cartesian coordinate training pairs. The first met hod is a standard feedforward neural network with error backpropagatio n learning. The next two methods are derived from an extended Kohonen Map algorithm that we combine with Shepard interpolation for the forwa rd computation, We compare the method of Ritter et al. for the learnin g of the extended Kohonen Map to our own scheme based on gradient desc ent optimization. We also study three scattered data approximation alg orithms. They include two variants of the Radial Basis Function (RBF) method: Hardy's multiquadrics and gaussian RBE We further develop our own Local Polynomial Fit method that could be considered as a modifica tion of McLain's method. We propose extensions to the considered scatt ered data approximation algorithms to make them suitable for vector-va lued multivariable functions, such as the mapping of Cartesian coordin ates into joint angle coordinates.