Differential and inverse kinematics of robot devices using conformal geometric algebra

  • Authors:

  • Eduardo Bayro-Corrochano;Julio Zamora-esquivel

  • Affiliations:

  • Electrical Engineering and Computer Science Department, GEOVIS Laborator, Centro de Investigación y de Estudios Avanzados, Guadalajara, Jalisco 44550, Mexico E-mail: jzamora@gdl.cinvestav.mx;Electrical Engineering and Computer Science Department, GEOVIS Laborator, Centro de Investigación y de Estudios Avanzados, Guadalajara, Jalisco 44550, Mexico E-mail: jzamora@gdl.cinvestav.mx

  • Venue:
  • Robotica
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, the authors use the conformal geometric algebra in robotics. This paper computes the inverse kinematics of a robot arm and the differential kinematics of a pan–tilt unit using a language of spheres showing how we can simplify the complexity of the computations. This work introduces a new geometric Jacobian in terms of bivectors, which is by far more effective in its representation as the standard Jacobian because its derivation is done in terms of the projections of the involved points onto the line axes. Furthermore, unlike the standard formulation, our Jacobian can be used for any kind of robot joints. In this framework, we deal with various tasks of three-dimensional (3D) object manipulation, which is assisted by stereo-vision. All these computations are carried out using real images captured by a robot binocular head, and the manipulation is done by a five degree of freedom (DOF) robot arm mounted on a mobile robot. In addition to this, we show a very interesting application of the geometric Jacobian for differential control of the binocular head. We strongly believe that the framework of conformal geometric algebra can generally be of great advantage for visually guided robotics.