Motor algebra approach for visually guided robotics

This paper presents the formulation of the 3D kinematics in the geometric a lgebra framework. We show that this approach is extremely useful for solvin g problems in the field of visual guided robotics. 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 th e direct and indirect kinematics and other problems concerning robot manipu lators depends on its degrees of freedom as well on its geometric character istics. Our approach snakes possible a direct algebraic formulation of the concrete problem in such a way that it reflects the underlying geometric st ructure. This is achieved by switching to a description of parts of the pro blem based on motor representations of points, lines and planes where neces sary. The first robotics task this paper deals with is 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 p oint or line representation based approaches for the treatment of problems related to robot manipulators. The second challenging task presented in thi s paper is the solution of the hand-eye calibration problem when cameras ar e attached to robot arms. The solution of this problem in the motor algebra framework turns to be linear. Both tasks are crucial for visual guided rob otics, that is why we are strongly motivated to present them to show how us eful it is to apply motor algebra for solving geometric problems in visual guided robotics. (C) 2001 Pattern Recognition Society. Published by Elsevie r Science Ltd. All rights reserved.