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A consistent direct transcription method for optimal control problems in multibody dynamics
Author(s) -
Siebert Ralf,
Betsch Peter
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110028
Subject(s) - integrator , multibody system , robustness (evolution) , control theory (sociology) , equations of motion , generalized coordinates , computer science , context (archaeology) , numerical integration , optimal control , algebraic number , mathematics , control (management) , mathematical optimization , classical mechanics , mathematical analysis , physics , computer network , biochemistry , chemistry , paleontology , bandwidth (computing) , artificial intelligence , biology , gene
The present work deals with optimal control problems governed by differential‐algebraic equations (DAEs). In particular, the control effort, which is necessary for moving a multibody system from one configuration to another, will be minimized. The orientation of the rigid bodies will be described using directors, which facilitates the integration of the equations of motion with an energy‐momentum consistent time‐stepping scheme [1]. This type of structure‐preserving integrators offer outstanding numerical stability and robustness properties in comparison to the often applied generalized coordinates formulation. In the context of optimal control, other kinds of consistent integrators have been applied previously in [2] and [3]. We will test the different formulations with two numerical examples, a 3‐link manipulator and a satellite. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)