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Baumgarte stabilisation over the SO(3) rotation group for control

Gros, Sebastien and Zanon, Mario and Diehl, Moritz Baumgarte stabilisation over the SO(3) rotation group for control. In: 54th Conference on Decision and Control, December 15-18, 2015, Osaka, Japan pp. 620-625. ISBN 978-1-4799-7886-1. (2015)

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Representations of the SO(3) rotation group are crucial for airborne and aerospace applications. Euler angles is a popular representation in many applications, but yield models having singular dynamics. This issue is addressed via non-singular representations, operating in dimensions higher than 3. Unit quaternions and the Direction Cosine Matrix are the best known non-singular representations, and favoured in challenging aeronautic and aerospace applications. All nonsingular representations yield invariants in the model dynamics, i.e. a set of nonlinear algebraic conditions that must be fulfilled by the model initial conditions, and that remain fulfilled over time. However, due to numerical integration errors, these conditions tend to become violated when using standard integrators, making the model inconsistent with the physical reality. This issue poses some challenges when non-singular representations are deployed in optimal control. In this paper, we propose a simple technique to address the issue for classical integration schemes, establish formally its properties, and illustrate it on the optimal control of a satellite.

Item Type: Conference or Workshop Item (Paper)
Identification Number: 10.1109/CDC.2015.7402298
Subjects: T Technology > T Technology (General)
Research Area: Computer Science and Applications
Depositing User: Mario Zanon
Date Deposited: 12 Mar 2018 09:23
Last Modified: 12 Mar 2018 09:23
URI: http://eprints.imtlucca.it/id/eprint/4015

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