Motor algebra approach for computing the kinematics of robot manipulators

Abstract

This article presents the formulation of the robot manipulator kinematics in the geometric algebra framework. In this algebraic system the three-dimensional Euclidean motion of points, lines, and planes can be advantageously represented using the algebra of motors. The computational complexity of the direct and indirect kinematics and other problems concerning robot manipulators depend on their degrees of freedom as well as on their geometric characteristics. Our approach makes possible a direct algebraic formulation of the problem in such a way that it reflects the underlying geometric structure. This is achieved by switching where necessary to a description of parts of the problem based on motor representations of points, lines, and planes. This article presents the formulation and computation of closed-form solutions of the direct and indirect kinematics of standard robot manipulators and a simple example of a grasping task. The flexible method presented here is new, and it widens the current standard point or line representation-based approaches for the treatment of problems related to robot manipulators. © 2000 John Wiley & Sons, Inc.