A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions

Mueller, Andreas and Terze, Zdravko and Pandža, Viktor (2016) A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions. = A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions. In: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 21-24.08.2016., Charlotte, North Carolina, USA.

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Official URL: https://www.bib.irb.hr/863790

Abstract

Quaternions are favorable parameters to describe spatial rotations of rigid bodies since they give rise to simple equations governing the kinematics and attitude dynamics in terms of simple algebraic equations. Dual quaternions are the natural extension to rigid body motions. They provide a singularity-free purely algebraic parameterization of rigid body motions, and thus serve as global parameters within the so-called absolute coordinate formulation of MBS. This attractive feature is owed to the inherent redundancy of these parameters since they must satisfy two quadratic conditions (unit condition and Plcker condition). Formulating the MBS kinematics in terms of dual quaternions leads to a system of differential-algebraic equations (DAE) with index 3. This is commonly transformed to an index 1 DAE system by replacing the algebraic constraints with their time derivative. This leads to the well-known problem of constraint violation. A brute force method, enforcing the unit constraint of quaternions, is to normalize them after each integration step. Clearly this correction affects the overall solution and the dynamic consistency. Moreover, for unit dual quaternions the two conditions cannot simply be enforced in such a way. In this paper a non- redundant formulation of the motion equations in terms of dual quaternions is presented. The dual quaternion constraints are avoided by introducing a local canonical parameterization. The key to this formulation is to treat dual unit quaternions as Lie group. The formulation can be solved with any standard integration scheme. Examples are reported displaying the excellent performance of this formulation regarding the constraint satisfaction as well as the solution accuracy.

Item Type: Conference or Workshop Item (Lecture)
Keywords (Croatian): multibody systems ; singularities ; absolute coordinates ; dual quaternions ; Lie groups ; vector parameterization
Subjects: NATURAL SCIENCES > Mathematics
Divisions: 1300 Department of Aeronautical Engineering > 1320 Chair of Aircraft Dynamics
Indexed in Web of Science: Yes
Indexed in Current Contents: No
Citations JCR: 0 (12.01.2018.)
Citations SCOPUS: 0 (12.01.2018.)
Date Deposited: 12 Jan 2018 09:42
Last Modified: 12 Jan 2018 09:43
URI: http://repozitorij.fsb.hr/id/eprint/8218

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