An energy‐momentum conserving method for the optimal control of multibody dynamics

Abstract

The present work deals with inverse multibody dynamics problems, more precisely with optimal control problems for dynamical systems governed by differential‐algebraic equations. The used numerical integration method relies on the Hamilton formulation of the equations of motion. We will apply an energy and momentum conserving time discretization which typically exhibits superior numerical stability properties. The rigid body equations of motion are basically formulated using the director formulation, which requires the implementation of internal constraints. To eliminate the constraints the system will be reduced to its minimal dimension by applying the discrete nullspace method [3]. For the derivation of the necessary conditions of optimality the calculus of variation is used [4]. This approach leads to an indirect transcription method. The arising algorithm yields a sequence of discrete configurations together with a sequence of actuating forces. We test the formulation with the help of representative numerical example problems. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)