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A geometric analysis of trajectory design for underwater vehicles

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  • Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning approach using a concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reductions; thereby linking the optimization problem to the inherent geometric framework. Using these kinematic reductions, we provide a solution to the motion planning 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 a concatenation of pure motions.
    Mathematics Subject Classification: Primary: 93C10, 49N90; Secondary: 53A17.

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