Singularities of Serial Robots: Identification and Distance Computation Using Geometric Algebra

Isiah Zaplana, Hugo Hadfield and Joan Lasenby
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Isiah Zaplana: Department of Mechanical Engineering, KU Leuven, 3000 Leuven, Belgium
Hugo Hadfield: Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
Joan Lasenby: Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK

Mathematics, 2022, vol. 10, issue 12, 1-27

Abstract: The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and motion planning strategies. While classical approaches entail the computation of the determinant of either a 6 × n or n × n matrix for an n -degrees-of-freedom serial robot, this work addresses a novel singularity identification method based on modelling the twists defined by the joint axes of the robot as vectors of the six-dimensional and three-dimensional geometric algebras. In particular, it consists of identifying which configurations cause the exterior product of these twists to vanish. In addition, since rotors represent rotations in geometric algebra, once these singularities have been identified, a distance function is defined in the configuration space C , such that its restriction to the set of singular configurations S allows us to compute the distance of any configuration to a given singularity. This distance function is used to enhance how the singularities are handled in three different scenarios, namely, motion planning, motion control and bilateral teleoperation.

Keywords: serial robotic manipulators; singularity identification; geometric algebra; rotor group; distance to a singularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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