CDS 280/CIMMS Lunchtime Talk: Discrete mechanics, optimal control and formation flying spacecraft

Dr. Oliver Junge, Munich University of Technology, Germany

A new approach to the solution of optimal control problems for mechanical systems is proposed.  It is based on a direct discretization of the Lagrange-d'Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints).  The resulting forced discrete Euler-Lagrange equations then serve as constraints for the optimization of a given cost functional.  We numerically illustrate the method by optimizing a low thrust satellite orbit transfer, the reconfiguration of a group of hovercraft in the plane and of a group of formation flying spacecraft as motivated by the Darwin (ESA) and TPF (NASA) space missions. This is joint work with Jerry Marsden and Sina Ober-Bloebaum (Paderborn).