Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
Scattered data interpolation in three or more variables
Mathematical methods in computer aided geometric design
Neural networks: an introduction
Neural networks: an introduction
Maximum likelihood competitive learning
Advances in neural information processing systems 2
A resource-allocating network for function interpolation
Neural Computation
Universal approximation using radial-basis-function networks
Neural Computation
Generalization properties of radial basis functions
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
A practical Bayesian framework for backpropagation networks
Neural Computation
Predicting the future: Advantages of semilocal units
Neural Computation
Fast learning in networks of locally-tuned processing units
Neural Computation
DOA estimation based on the database retrieval technique with nonuniform quantization and clustering
Digital Signal Processing
Inverse kinematics in robotics using neural networks
Information Sciences: an International Journal
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This paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a number of joint angle/Cartesian coordinate training pairs. The first method is a standard feedforward neural network with error backpropagation learning. The next two methods are derived from an extended Kohonen Map algorithm that we combine with Shepard interpolation for the forward computation. We compare the method of Ritter et al. for the learning of the extended Kohonen Map to our own scheme based on gradient descent optimization. We also study three scattered data approximation algorithms. They include two variants of the Radial Basis Function (RBF) method: Hardy's multiquadrics and gaussian RBF. We further develop our own Local Polynomial Fit method that could be considered as a modification of McLain's method. We propose extensions to 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.