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Fast direct multiple shooting algorithms for optimal robot control. (English) Zbl 1310.70002
Diehl, Moritz (ed.) et al., Fast motions in biomechanics and robotics. Optimization and feedback control. Selected papers based on the presentations at first Ruperto-Carola symposium held at the international science forum (IWH), Heidelberg, Germany, September 7–9, 2005. Berlin: Springer (ISBN 3-540-36118-9/pbk). Lecture Notes in Control and Information Sciences 340, 65-93 (2006).
Summary: In this overview paper, we first survey numerical approaches to solve nonlinear optimal control problems, and second, we present our most recent algorithmic developments for real-time optimization in nonlinear model predictive control.
In the survey part, we discuss three direct optimal control approaches in detail:
(i) single shooting, (ii) collocation, and (iii) multiple shooting, and we specify why we believe the direct multiple shooting method to be the method of choice for nonlinear optimal control problems in robotics. We couple it with an efficient robot model generator and show the performance of the algorithm at the example of a five link robot arm. In the real-time optimization part, we outline the idea of nonlinear model predictive control and the real-time challenge it poses to numerical optimization. As one solution approach, we discuss the real-time iteration scheme.
For the entire collection see [Zbl 1100.70002].

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70E60 Robot dynamics and control of rigid bodies
70Q05 Control of mechanical systems
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
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