Abstract
The parameterization of a rigid-body motion can be done using multiple algebraic entities. A very important criterion when choosing a parameterization method is the number of algebraic equations and variables. Recently, orthogonal dual tensors and dual quaternion proved to be a complete tool for computing rigid body displacement and motion parameters. The present research is focused on developing new methods for recovering kinematic data when the state of features attached to a body during a rigid displacement is available. The proof of concept is sustained by computational solutions both for the singularity-free extraction of a dual quaternion from feature-based representation of motion and for the recovery algorithms of the dual quaternion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Condurache, D., Burlacu, A.: Dual tensors based solutions for rigid body motion parameterization. Mech. Mach. Theory 74, 390–412 (2014)
Condurache, D., Burlacu, A.: Dual lie algebra representations of the rigid body motion. In: AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper, San Diego (2014)
Pennestri, E., Valentini, P.: Dual quaternions as a tool for rigid body motion analysis: a tutorial with an application to biomechanics. Arch. Mech. Eng. LVII, 187–205 (2010)
Angeles, J.: The application of dual algebra to kinematic analysis. Comput. Methods Mech. Syst. 161, 3–31 (1998)
Dong, H., Hu, Q., Akella, M.R.: Dual-quaternion-based spacecraft autonomous rendezvous and docking under six-degree-of-freedom motion constraints. J. Guidance Control Dyn. 41(5), 1150–1162 (2018)
Leclercq, G., Lefevre, P., Blohm, G.: 3D kinematics using dual quaternions: theory and applications in neuroscience. Front. Behav. Neurosci. 1–25, 7 (2013)
Müller, A.: Coordinate mappings for rigid body motions. J. Comput. Nonlinear Dyn. 12(2), 021010 (2017)
Condurache, D.: A Davenport dual angles approach for minimal parameterization of the rigid body displacement and motion. Mech. Mach. Theory 140, 104–122 (2019)
Sarabandi, S., Perez-Garcia, A., Thomas, F.: On Cayley’s factorization with an application to the orthonormalization of noisy rotation matrices. Adv. Appl. Clifford Algebras 29, 49 (2019)
Condurache, D.: Orthogonal dual tensor method for solving the AX = XB sensor calibration problem. Mech. Mach. Theory 104, 382–404 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Condurache, D. (2021). Singularity-Free Extraction of a Dual Quaternion from Orthogonal Dual Tensor. In: Lenarčič, J., Siciliano, B. (eds) Advances in Robot Kinematics 2020. ARK 2020. Springer Proceedings in Advanced Robotics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-50975-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-50975-0_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-50974-3
Online ISBN: 978-3-030-50975-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)