Optimal kinematic control of an autonomous underwater vehicle

James Biggs, William Holderbaum

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Abstract

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3) , where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the maximum principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.
Original languageEnglish
Pages (from-to)1623-1626
Number of pages4
JournalIEEE Transactions on Automatic Control
Volume54
Issue number7
DOIs
Publication statusPublished - Jul 2009

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Keywords

  • optimal control
  • underwater vehicle
  • nonholonomic systems
  • control systems
  • kinematic control

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