Speeding up the learning of robot kinematics through function decomposition

The main drawback of using neural networks or other example-based learning procedures to approximate the inverse kinematics (IK) of robot arms is the high number of training samples (i.e., robot movements) required to attain an acceptable precision. We propose here a trick, valid for most industrial robots, that greatly reduces the number of movements needed to learn or relearn the IK to a given accuracy. This trick consists in expressing the IK as a composition of learnable functions, each having half the dimensionality of the original mapping. Off-line and on-line training schemes to learn these component functions are also proposed. Experimental results obtained by using nearest neighbors and parameterized self-organizing map, with and without the decomposition, show that the time savings granted by the proposed scheme grow polynomially with the precision required.

I. Introduction

A robot manipulator is a multifunctional and reprogrammable articulated mechanism able to move in a given workspace. It usually consists of several bodies linked by joints, and it is commanded by providing values to some of these joints. Thus, when moving, the robot can be thought of as realizing a mapping from joint space to workspace coordinates, which is referred to as the forward kinematics mapping. Robot programming, however, is most easily carried out in terms of the Cartesian coordinates of the workspace, leaving to the controller the task of translating such specification into joint variables. Thus, robot control critically depends on the so-called inverse kinematics mapping (IKM), i.e., that providing joint coordinates as a function of the desired position and orientation of the robot end-effector in the workspace.