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A first extension of geometric control theory to underwater vehicles

Chyba, Monique & Smith, Ryan N. (2008) A first extension of geometric control theory to underwater vehicles. In Proceedings of the 2008 IFAC Workshop on Navigation, Guidance and Control of Underwater Vehicles, Elsevier, Lakeside Hotel, Killaloe, Ireland.

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Abstract

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

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ID Code: 40138
Item Type: Conference Paper
Keywords: Autonomous Underwater Vehicle, Geometric Control theory, Decoupling vector field, kinematic reduction
DOI: 10.3182/20080408-3-IE-4914.00015
ISBN: 9783902661357
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Algebraic and Differential Geometry (010102)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Calculus of Variations Systems Theory and Control Theory (010203)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MARITIME ENGINEERING (091100) > Ocean Engineering (091103)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MARITIME ENGINEERING (091100) > Special Vehicles (091106)
Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > Schools > School of Engineering Systems
Copyright Owner: Copyright 2008 Elsevier & IFAC
Deposited On: 25 Mar 2011 08:42
Last Modified: 25 Mar 2011 08:44

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