Preliminary Results on Controllability of Serial Robot-Manipulators in Singular Configurations

Mir Mamunuzzaman, Jörg Mareczek

2023

Abstract

We develop a standard system representation and analyse controllability properties for velocity kinematics of robot-manipulators located on singularities. These are positions where the Jacobian loses rank. Since its column vectors span the set of admissible workspace velocity directions, it is still a widespread misunderstanding that some directions would be locked on singularities and thus had to be bypassed as far as possible. We will show that this does not generally hold: On some types of singularities, the kinematic shows local redundancy, which can be used to generate paths crossing the singularity in any desired workspace velocity direction. To further analyse controllability properties, we develop an SVD-based method to represent the Jacobian-based velocity kinematics in standard system description of control theory without the need for inverse kinematics (IK). In many cases, IK do not offer a unique solution on singularities and, therefore, cannot be used. Furthermore, we present a modification of the SVD-based method for which the analytical calculation effort is feasible. The resulting system description has the advantage of being a simple decoupled set of single-integrators where the system states are divided into one set describing admissible workspace motions and a second set describing possible internal motions, also called nullspace motion. Based on this standard system representation, we determine local controllability and local accessibility for two different types of singularities. Finally, we illustrate our methods by means of a simple 3-DoF SCARA-type manipulator.

Paper Citation

in Harvard Style

Mamunuzzaman M. and Mareczek J. (2023). Preliminary Results on Controllability of Serial Robot-Manipulators in Singular Configurations. In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-670-5, SciTePress, pages 327-334. DOI: 10.5220/0012238000003543

in Bibtex Style

@conference{icinco23,
author={Mir Mamunuzzaman and Jörg Mareczek},
title={Preliminary Results on Controllability of Serial Robot-Manipulators in Singular Configurations},
booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2023},
pages={327-334},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012238000003543},
isbn={978-989-758-670-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Preliminary Results on Controllability of Serial Robot-Manipulators in Singular Configurations
SN - 978-989-758-670-5
AU - Mamunuzzaman M.
AU - Mareczek J.
PY - 2023
SP - 327
EP - 334
DO - 10.5220/0012238000003543
PB - SciTePress