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Main Title: Simulation of Multibody Systems with Servo Constraints through Optimal Control
Author(s): Altmann, Robert
Heiland, Jan
Type: Research Paper
Abstract: We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path. Modelling the system using Newton's second law - "The force acting on an object is equal to the mass of that object times its acceleration." - and enforcing the servo constraints directly leads to differential-algebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5 which already poses high regularity conditions. Also, common approaches for the numerical time-integration will likely fail. If one relaxes the servo constraints and considers the system from an optimal control point of view, the strong regularity conditions vanish and the solution can be obtained by standard techniques. By means of a spring-mass system, we illustrate the theoretical and expected numerical difficulties. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.
Subject(s): servo constraints
inverse dynamics
high-index DAEs
optimal control
underactuated mechanical systems
Issue Date: 26-Nov-2015
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 70Q05 Control of mechanical systems
65L80 Methods for differential-algebraic equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2015, 27
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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