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Optimal control problems on parallelizable riemannian manifolds : theory and applications

Ram V. Iyer; Raymond Holsapple; David Doman — 2006

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group $S E (3),$ which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...

Optimal control problems on parallelizable Riemannian manifolds: theory and applications

Ram V. Iyer; Raymond Holsapple; David Doman — 2005

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group which is also a parallelizable Riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing...

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