Motor algebra approach for computing the kinematics of robot manipulators

This article presents the formulation of the robot manipulator kinematics i n the geometric algebra framework. In this algebraic system the three-dimen sional Euclidean motion of points, lines, and planes can be advantageously represented using the algebra of motors. The computational complexity of th e direct and indirect kinematics and other problems concerning robot manipu lators depend on their degrees of freedom as well as on their geometric cha racteristics. Our approach makes possible a direct algebraic formulation of the problem in such a way that it reflects the underlying geometric struct ure. This is achieved by switching where necessary to a description of part s of the problem based on motor representations of points, lines, and plane s. This article presents the formulation and computation of closed-form sol utions of the direct and indirect kinematics of standard robot manipulators and a simple example of a grasping task. The flexible method presented her e is new, and it widens the current standard point or line representation-b ased approaches for the treatment of problems related to robot manipulators . (C) 2000 John Wiley gr Sons, Inc.