A Hamiltonian conserving indirect optimal control method for multibody dynamics

In the past, a lot of effort has gone into the development of structure-preserving time-stepping schemes for forward dynamic problems. This is due to the superior numerical stability of these integrators. Guided by previous developments in the design of energy-momentum integrators for forward dynamic problems, a Hamiltonian conserving indirect optimal control method will be introduced. For the state equations, a consistent variant of the midpoint evaluation introduced in [1] will be applied. Based on this specific discretization of the state equations, a discretization of the costate equations will be introduced, which is based on the notion of a discrete derivative and which leads to the algorithmic conservation of the discrete Hamiltonian. The newly developed method will be compared with a direct transcription method. We will test the newly proposed method within two numerical examples, which are the optimal control of a particle in a gravitational field and a 3-link manipulator. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)