Robot Kinematics

Abstract

This chapter presents the formulation of robot manipulator kinematics within the geometric algebra framework. In this algebraic system, the 3D Euclidean motion of points, lines, and planes can be advantageously represented using the algebra of motors. The computational complexity of direct and indirect kinematics and other problems concerning robot manipulators are dependent on the robot’s degrees of freedom as well on its geometric characteristics. Our approach makes possible a direct algebraic formulation of the concrete problem in such a way that it reflects the underlying geometric structure. This is achieved by describing parts of the problem based on motor representations of points, lines, planes, circles, and spheres where necessary.