Differential Kinematics Control Using Circles as Bivectors of Conformal Geometric Algebra

Julio Zamora-Esquivel, Alberto Jaimes Pita, Edgar Macias-Garcia, Javier Felip-Leon, David Gonzalez-Aguirre, Eduardo Bayro-Corrochano

2025

Abstract

In this paper, we propose a modern mathematical framework to model a robotic arm and compute the differential kinematics of its end effector, which is represented as a circle in a three-dimensional space. This circle is described using a bi-vector within the context of conformal geometric algebra. By utilizing a circle to characterize the grasping pose on the object and the pose of the end-effector, we develop a differential kinematics-based control law that guides the end-effector to minimize the error between both circles. The circle representation offers three degrees of freedom for the center, two degrees for orientation, and one degree for the radius, allowing us to effectively describe the end-effector pose using a single geometric primitive. Our approach allows for simultaneous adjustment of both the position and orientation of the end effector.

Paper Citation

in Harvard Style

Zamora-Esquivel J., Pita A., Macias-Garcia E., Felip-Leon J., Gonzalez-Aguirre D. and Bayro-Corrochano E. (2025). Differential Kinematics Control Using Circles as Bivectors of Conformal Geometric Algebra. In Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 2: COBOTA; ISBN 978-989-758-770-2, SciTePress, pages 585-592. DOI: 10.5220/0013945500003982

in Bibtex Style

@conference{cobota25,
author={Julio Zamora-Esquivel and Alberto Pita and Edgar Macias-Garcia and Javier Felip-Leon and David Gonzalez-Aguirre and Eduardo Bayro-Corrochano},
title={Differential Kinematics Control Using Circles as Bivectors of Conformal Geometric Algebra},
booktitle={Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 2: COBOTA},
year={2025},
pages={585-592},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013945500003982},
isbn={978-989-758-770-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 22nd International Conference on Informatics in Control, Automation and Robotics - Volume 2: COBOTA
TI - Differential Kinematics Control Using Circles as Bivectors of Conformal Geometric Algebra
SN - 978-989-758-770-2
AU - Zamora-Esquivel J.
AU - Pita A.
AU - Macias-Garcia E.
AU - Felip-Leon J.
AU - Gonzalez-Aguirre D.
AU - Bayro-Corrochano E.
PY - 2025
SP - 585
EP - 592
DO - 10.5220/0013945500003982
PB - SciTePress