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A geometrical analysis of trajectory design for underwater vehicles

Chyba, Monique, Haberkorn, Thomas, Smith, Ryan N. , & Wilkens, George R. (2009) A geometrical analysis of trajectory design for underwater vehicles. Discrete and Continuous Dynamical Systems-B, 11(2), pp. 233-262.

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Abstract

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.

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4 citations in Scopus
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1 citations in Web of Science®

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103 since deposited on 25 Mar 2011
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ID Code: 40126
Item Type: Journal Article
Keywords: Autonomous Underwater Vehicle, Differential Geometry, Decoupling vector field, Control Theory, Kinematic Reduction
DOI: 10.3934/dcdsb.2009.11.233
ISSN: 1531-3492
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 2009 Please consult the authors.
Deposited On: 25 Mar 2011 02:03
Last Modified: 01 Mar 2012 04:09

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