A geometric analysis of trajectory design for underwater vehicles | Zendy

Monique Chyba | Zendy; Thomas Haberkorn | Zendy; Ryan N. Smith | Zendy; George R. Wilkens | Zendy

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A geometric analysis of trajectory design for underwater vehicles

Author(s) -

Monique Chyba,

Thomas Haberkorn,

Ryan N. Smith,

George R. Wilkens

Publication year - 2008

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2009.11.233

Subject(s) - concatenation (mathematics) , kinematics , trajectory , actuator , focus (optics) , motion (physics) , computer science , relation (database) , control theory (sociology) , controllability , rank (graph theory) , motion planning , mathematics , mathematical optimization , artificial intelligence , classical mechanics , physics , robot , control (management) , combinatorics , astronomy , database , optics

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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