High order variational integrators in the optimal control of mechanical systems
Cédric M. Campos Sina Ober-Blöbaum Emmanuel Trélat
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are momentum preserving and symplectic. In this article, we develop two high order variational integrators which distinguish themselves in the dimension of the underling space of approximation and we investigate their application to finite-dimensional optimal control problems posed with mechanical systems. The convergence of state and control variables of the approximated problem is shown. Furthermore, by analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that, for these particular integrators, dualization and discretization commute.
keywords: high order Optimal control commutation property. direct methods geometric integration Runge-Kutta mechanical systems variational integrator
Symmetry exploiting control of hybrid mechanical systems
Kathrin Flasskamp Sebastian Hage-Packhäuser Sina Ober-Blöbaum
Symmetry properties such as invariances of mechanical systems can be beneficially exploited in solution methods for control problems. A recently developed approach is based on quantization by so called motion primitives. A library of these motion primitives forms an artificial hybrid system. In this contribution, we study the symmetry properties of motion primitive libraries of mechanical systems in the context of hybrid symmetries. Furthermore, the classical concept of symmetry in mechanics is extended to hybrid mechanical systems and an extended motion planning approach is presented.
keywords: mechanical systems optimal control Symmetry motion planning. hybrid systems

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