On the false positives and false negatives of the Jacobian matrix in kinematically redundant parallel mechanisms
File(s)
Accepted version
Author(s)
Baron, Nicholas
Philippides, Andrew
Rojas, Nicolas
Type
Journal Article
Abstract
The Jacobian matrix is a highly popular tool for the control and performance analysis of closed-loop robots. Its usefulness in parallel mechanisms is certainly apparent, and its application to solve motion planning problems, or other higher level questions, has been seldom queried, or limited to non-redundant systems. In this paper, we discuss the shortcomings of the use of the Jacobian matrix under redundancy, in particular when applied to kinematically redundant parallel architectures with non-serially connected actuators. These architectures have become fairly popular recently as they allow the end-effector to achieve full rotations, which is an impossible task with traditional topologies. The problems with the Jacobian matrix in these novel systems arise from the need to eliminate redundant variables when forming it, resulting in both situations where the Jacobian incorrectly identifies singularities (false positive), and where it fails to identify singularities (false negative). These issues have thus far remained unaddressed in the literature. We highlight these limitations herein by demonstrating several cases using numerical examples of both planar and spatial architectures.
Date Issued
2020-06
Date Acceptance
2019-12-28
Citation
IEEE Transactions on Robotics, 2020, 36 (3)
ISSN
1552-3098
Publisher
Institute of Electrical and Electronics Engineers
Journal / Book Title
IEEE Transactions on Robotics
Volume
36
Issue
3
Copyright Statement
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
https://ieeexplore.ieee.org/document/8979308
Subjects
Science & Technology
Technology
Robotics
Jacobian matrices
Rigidity
Actuators
Parallel robots
Transmission line matrix methods
End effectors
Kinematics
parallel robots
redundant robots
singularity analysis
SINGULARITY ANALYSIS
Industrial Engineering & Automation
0801 Artificial Intelligence and Image Processing
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2020-02-03