KD trees and Delaunay-based linear interpolation for function learning: a comparison to neural networks with error backpropagation

Abstract

We illustrate how a KD tree data structure with Delaunay triangulation can be used for function learning. The example function is the inverse kinematics of a three degree-of-freedom (DOF) robot. The result can subsequently be used for kinematic control. The KD tree is used to efficiently extract a set number of nearest neighbors to a query point. Delaunay triangulation provides a good criterion for constructing a continuous linear approximation to the true function from neighborhood points of the query. For comparison purposes we solve the same problem with a neural network trained with error backpropagation. We conclude that the KD/Delaunay approach, in comparison to neural networks, can potentially yield a massive reduction in training time and significantly improve function estimate performance.