Geometric algebra of points, lines, planes and spheres for computer vision and robotics

Authors:
Eduardo Bayro-Corrochano;Luis Eduardo Falcón
Affiliations:
Centro de Investigación y de Estudios Avanzados Computer Science Department, GEOVIS Lab Guadalajara, Jalisco 45090 (Mexico). E-mail: edb@gdl.cinvestav.mx;Tecnológico de Monterrey Mathematics Department Guadalajara, Jalisco 45201 (Mexico). E-mail: luis.eduardo.falcon@itesm.mx
Venue:
Robotica
Year:
2005

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Differential and inverse kinematics of robot devices using conformal geometric algebra

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Abstract

This paper introduces conformal geometric algebra (CGA) for applications in computer vision and robotics. The authors show that CGA deals with our intuition and insight of the geometry and it helps us to reduce considerably the computational burden of the problems. The CGA can be applied not only to describe the geometry of the space, but to handle the algebra of incidence, as well as conformal transformations, to deal with kinematics or projective geometry problems. The authors show with real and simulated applications that this system can be of great advantage in robotics and computer vision.