Modeling and Pose Control of Robotic Manipulators and Legs using Conformal Geometric Algebra

Oscar Carbajal-Espinosa¹, Luis González-Jiménez², Jose Oviedo-Barriga³, Bernardino Castillo-Toledo⁴, Alexander Loukianov ⁴, Eduardo Bayro-Corrochano⁴

¹ Instituto Tecnológico y de Estudios Superiores de Monterrey, Guadalajara, México. oscar.carbajal@itesm.mx

² Instituto Tecnológico y de Estudios Superiores de Occidente, Guadalajara, México. luis.gonzalez@iteso.mx

³ Universidad Veracruzana, Ciudad Mendoza, México. luoviedo@uv.mx

⁴ Centro de Investigación y De Estudios Avanzados del I.P.N., Guadalajara, México. toledo@gdl.cinvestav.mx, louk@gdl.cinvestav.mx, edb@gdl.cinvestav.mx

Article received on 03/12/2014.
Accepted on 16/04/2015.

Abstract

Controlling the pose of a manipulator involves finding the correct configuration of the robot's elements to move the end effector to a desired position and orientation. In order to find the geometric relationships between the elements of a robot manipulator, it is necessary to define the kinematics of the robot. We present a synthesis of the kinematical model of the pose for this type of robot using the conformal geometric algebra framework. In addition, two controllers are developed, one for the position tracking problem and another for the orientation tracking problem, both using an error feedback controller. The stability analysis is carried out for both controllers, and their application to a 6-DOF serial manipulator and the legs of a biped robot are presented. By proposing the error feedback and Lyapunov functions in terms of geometric algebra, we are opening a new venue of research in control of manipulators and robot legs that involves the use of geometric primitives, such as lines, circles, planes, spheres.

Keywords: Serial manipulators, pose control, motors, conformal geometric algebra.

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Acknowledgements

This work was supported in part by Project SEP-CONACYT "Métodos Geométricos y Cognitivos para la percepción, aprendizaje, control y acción de humanoides" under Grant 82084 and PhD scholarships No. 219316 and No. 28824.

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