Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3

In this paper we develop, study, and test a Lie group multisymplectic integra- tor for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions.Comment: Article in press. 22 pages, 18 figures. Received 20 November 2013, Received in revised form 26 February 2014, Accepted 27 February 2014. Communications in Nonlinear Science and Numerical Simulation. 201

Numerical methods for the inverse dynamics simulation of underactuated mechanical systems

The present work deals with the inverse dynamics simulation of underactuated multibody systems. In particular, the study focuses on solving trajectory tracking control problems of differentially flat underactuated systems. The use of servo constraints provides an approach to formulate trajectory tracking control problems of underacutated systems, which are also called underactuated servo constraint problems

Numerical methods for the inverse dynamics simulation of underactuated mechanical systems

In der vorliegenden Dissertation wird die Simulation der inversen Dynamik unteraktuierter Mehrkörpersysteme behandelt. Insbesondere werden Steuerungsprobleme der Bahnverfolgung für differentiell flache unteraktuierte Systeme untersucht. Mit Hilfe von Servobindungen werden die Steuerungsprobleme der Bahnverfolgung für unteraktuierte Systeme formuliert. Die betrachteten Probleme werden unteraktuierte Servobindungsprobleme genannt. Minimalkoordinaten, abhängige oder redundante Koordinaten werden zur Formulierung unteraktuierter Servobindungsprobleme verwendet. Die Formulierung ergibt differential-algebraische Gleichungen mit hohem Index. Die diskrete Nullraum-Methode ermöglicht den Übergang von redundanten Koordinaten zu Minimalkoordinaten. Da die numerische Lösung der differential-algebraischen Gleichungen mit hohem Index anspruchsvoll ist und die flachheitsbasierte analytische Lösung für komplizierte unteraktuierte Systeme nicht praktikabel ist, werden Methoden zur Indexreduktion vor der direkten Zeitdiskretisierung eingesetzt. Eine spezielle Projektionsmethode wird angewendet, um den Index von fünf auf drei zu reduzieren. Die Methode erfordert die Berechnung von Projektionsmatrizen, die in der redundanten Koordinaten Formulierung konstant und in der Minimalkoordinaten Formulierung zeitabhängig sind. Eine neue Methode, Indexreduktion durch minimale Erweiterung genannt, wird in dieser Dissertation entwickelt und für Servobindungsprobleme unteraktuierter Systeme verwendet. Die beiden Methoden werden auf repräsentative numerische Beispiele angewandt. Insbesondere wird schon gezeigt, dass sich die neu entwickelte Indexreduktionsmethode zur Lösung involvierter Probleme eignet, die bislang mit der Projektionsmethode nicht gelöst werden konnten

Evolution of the DeNOC-based dynamic modelling for multibody systems

Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

ROBOTRAN: a powerful symbolic gnerator of multibody models

The computational efficiency of symbolic generation was at the root of the emergence of symbolic multibody programs in the eighties. At present, it remains an attractive feature of it since the exponential increase in modern computer performances naturally provides the opportunity to investigate larger systems and more sophisticated models for which real-time computation is a real asset. <br><br> Nowadays, in the context of mechatronic multibody systems, another interesting feature of the symbolic approach appears when dealing with enlarged multibody models, i.e. including electrical actuators, hydraulic devices, pneumatic suspensions, etc. and requiring specific analyses like control and optimization. Indeed, since symbolic multibody programs clearly distinguish the modeling phase from the analysis process, extracting the symbolic model, as well as some precious ingredients like analytical sensitivities, in order to export it towards any suitable environment (for control or optimization purposes) is quite straightforward. Symbolic multibody model portability is thus very attractive for the analysis of mechatronic applications. <br><br> In this context, the main features and recent developments of the ROBOTRAN software developed at the Université catholique de Louvain (Belgium) are reviewed in this paper and illustrated via three multibody applications which highlight its capabilities for dealing with very large systems and coping with multiphysics issues

Use of Penalty Formulations in Dynamic Simulation and Analysis of Redundantly Constrained Multibody Systems

[Abstract] The determination of particular reaction forces in the analysis of redundantly constrained multibody systems requires the consideration of the stiffness distribution in the system. This can be achieved by modelling the components of the mechanical system as flexible bodies. An alternative to this, which we will discuss in this paper, is the use of penalty factors already present in augmented Lagrangian formulations as a way of introducing the structural properties of the physical system into the model. Natural coordinates and the kinematic constraints required to ensure rigid body behaviour are particularly convenient for this. In this paper, scaled penalty factors in an index-3 augmented Lagrangian formulation are employed, together with modelling in natural coordinates, to represent the structural properties of redundantly constrained multibody systems. Forward dynamic simulations for two examples are used to illustrate the material. Results showed that scaled penalty factors can be used as a simple and efficient way to accurately determine the constraint forces in the presence of redundant constraints