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.
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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