Edwin Kreuzer - Academia.edu (original) (raw)
Papers by Edwin Kreuzer
Monitoring missions in confined underwater environments such as nuclear storage ponds or industry... more Monitoring missions in confined underwater environments such as nuclear storage ponds or industry tanks call for highly maneuverable fully autonomous micro underwater robots. In this work, we target this challenging scenario with the new low-cost open-source HippoCampusX platform. We present a modular software and hardware architecture which is easily adaptable to mission specific requirements. Our system is part of the PX4-environment [1] and constitutes PX4’s first underwater extension including a SITL simulation. We conduct a series of experiments to demonstrate HippoCampus’ agile maneuvering capabilities and validate the derived dynamic model.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
Container cranes belong to the class of underactuated systems for which the design of control law... more Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally.
Journal of Vibration and Control, Feb 18, 2019
Underactuated mechanical systems are frequently encountered in several industrial and real-world ... more Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input-multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.
arXiv (Cornell University), May 23, 2022
This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The ... more This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The adopted approach is based on sliding mode control and enhanced by an artificial neural network to cope with modeling inaccuracies and external disturbances that can arise. The sliding surfaces are defined as a linear combination of both actuated and unactuated variables. A radial basis function is added to compensate the performance drop when, in order to avoid the chattering phenomenon, the sign function is substituted by a saturation function in the conventional sliding mode controller. An application of the proposed scheme is introduced for an inverted pendulum, in order to illustrate the controller design method, and numerical results are presented to demonstrate the improved performance of the resulting intelligent controller.
Springer eBooks, Sep 14, 2006
Almost all offshore structures have to be modeled as multibody systems. Only ships or single pont... more Almost all offshore structures have to be modeled as multibody systems. Only ships or single pontoons can be modeled as a single rigid body. The dynamic behavior of the multibody system is significantly influenced by fluid-structure interactions. So far, most available methods for analyzing these interactions are restricted to single bodies, small wave amplitudes and body motions, or both. In the present paper a two-dimensional boundary integral approach with fully nonlinear boundary conditions on the free surface is used to simulate the behavior of elastically coupled floating multibody systems in gravity waves. This method will be applied to analyze the dynamics of two floating bodies moored to a quay. The results of numerical simulations for selected configurations are shown.
The Twentieth International Offshore and Polar Engineering Conference, 2010
Konstruktion, 2017
Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fe... more Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fertigung von Prototypen ermöglicht. Wie bei jedem Fertigungsverfahren gibt es auch bei generativen Fertigungsverfahren „Best-Prac- tices”. Während allgemeine Richtlinien zum 3D-Druck- gerechten Konstruieren einen guten allgemeinen Überblick bieten, fehlen bislang Konstruktionsrichtlinien für die Dichtheit der gedruckten Teile. Einflussfaktoren wie Druck oder auch die Materialeigenschaften beeinflussen die Dichtheit eines Systems aus 3D-gedruckten Komponenten. Dieser Beitrag stellt eine Vorgehensweise für das 3D-Druck-gerechte Konstruieren vor, um 3D-gedruckte Systeme und Module zu dichten. Die Methoden werden anhand eines Mikro-Autonomen-Unterwasserfahrzeugs aufgezeigt.
The importance of remotely operated underwater vehicles for construction, inspection, and mainten... more The importance of remotely operated underwater vehicles for construction, inspection, and maintenance of off-shore structures has been continuously increasing in the recent years. Especially oil prospecting in water depths inaccessible for human divers (>300m) needs unmanned vehicles. For a great variety of tasks a robust positioning control of the vehicle is required. This control is complicated not only due to nonlinearities involved in the system including the umbilical and parameter uncertainties [1,7] but also because of the lack of precise position information. The positioning problem can be split into two domains: the region far from the structure, where the navigation from the basis ship to the structure takes place and the region close to the structure, where the position of the vehicle relative to the structure must be kept for a task to be performed.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode obs... more We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
The stochastic equation of motion for a heaving cylinder subject to irregular sea waves is solved... more The stochastic equation of motion for a heaving cylinder subject to irregular sea waves is solved numerically with the polynomial chaos framework. Thereby, the stochastic forcing is expressed by a truncated Karhunen-Loève expansion and the hydrodynamic radiation is formulated as a state space model. We obtain the mean and the variance of the cylinder heave motion.
The aim of this book is to present important software tools, basic concepts, methods, and highly ... more The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.
Journal of Applied Mathematics and Mechanics, Nov 1, 2001
We present a method to analyze dynamical systems undergoing random perturbations based on the cel... more We present a method to analyze dynamical systems undergoing random perturbations based on the cell mapping approach. Analytical expressions are derived for the transition probabilities from the evolution operator of the system. Thus there is no need for simulation of randomness and the numerical approximations are safe, i.e., we approximate attractors and their basins from within and give lower bounds for exit times. For additively perturbed systems the transition probabilities can be expressed in terms of the transition probabilities of the unperturbed system and the properties of the perturbation. The numerical details concerning the perturbation terms are discussed and their application is shown with an example.
Springer eBooks, 1990
In mechanical systems nonlinear effects due to stick slip and backlash are often observed. If suc... more In mechanical systems nonlinear effects due to stick slip and backlash are often observed. If such systems are harmonically driven, then besides well known bifurcation phenomena also sudden changes of the chaotic dynamics occur. These types of qualitative change of system’s behavior, the so-called crises, result from a collision between an unstable periodic orbit and a chaotic attractor. Different crises phenomena are discussed and it is demonstrated how the occurrence of crises can be determined numerically.
Computer Methods in Applied Mechanics and Engineering, Nov 1, 1986
Based upon Poincare maps, the generalized cell mapping theory has been developed for the global a... more Based upon Poincare maps, the generalized cell mapping theory has been developed for the global analysis of nonlinear dynamical systems. The mathematical description of an autonomous generalized cell mapping leads to a finite, discrete, stationary Markov chain where the transition probability matrix completely determines the behavior of the system. Although analytical methods for analyzing Markov chains are highly developed, efficient numerical algorithms for the analysis of Markov chains with a very large number of states are rare. Restricting ourselves to the determination of absorption probabilities and the expected absorption times of transient states, we describe an algorithm for an efficient numerical treatment of Markov chains to obtain these quantities.
The Proceedings of the 1st European Nonlinear Oscillations Conference contain invited contributio... more The Proceedings of the 1st European Nonlinear Oscillations Conference contain invited contributions of mathematicians engaged in the development of analytical and numerical methods and of scientists working on vibration problems in mechanics, physics, and other fields.
Der vorliegende Band ist der zweite in der Reihe "Hamburger Akademievorträge", in welcher die Aka... more Der vorliegende Band ist der zweite in der Reihe "Hamburger Akademievorträge", in welcher die Akademie der Wissenschaften in Hamburg Vorlesungsreihen und Einzelvorträge aus den breit gefächerten Akademie-Aktivitäten dokumentiert und im Open Access online zugänglich macht. Der Band fasst die Vorträge der Akademievorlesungsreihe "Reformation im Diskurs" zusammen, die vom Auftakt des Reformationsjahres im Oktober 2016 bis zum Januar 2017 in den Baseler Hof Sälen in Hamburg stattfanden. Die Beiträge werden ergänzt durch den Festvortrag "Martin Luther, Erneuerer der christlichen Religion", den unser Ordentliches Mitglied Johannes Schilling auf der Jahrfeier unserer Akademie im November 2016 gehalten hat. Johannes Schilling war es auch, der als langjähriger Präsident der Luther-Gesellschaft und an den Vorbereitungen zum offiziellen Reformationsjubiläum maßgeblich Beteiligter der Akademie bereits 2015 vorschlug, eine Vortragsreihe anlässlich des Reformationsjubiläums zu veranstalten. Die Reformation ist eng verknüpft mit dem Namen Martin Luther, dessen Veröffentlichung von 95 Thesen am 31. Oktober 1517 als ihr Auslöser gilt. Die Reformation war eine kirchliche Erneuerungsbewegung, die Geschichte, Gesellschaft, Wirtschaft und Kultur nicht nur in Europa tief und nachhaltig geprägt hat. Die Reformatoren wollten keine neue Kirche gründen oder die alte spalten, aber: ohne Reformation keine evangelischen Kirchen, keine Gegenreformation, keine Hugenottenkriege, kein Dreißigjähriger Krieg. So wirkmächtig und vielschichtig wie die Reformation war auch die Persönlichkeit Luthers. Für jeden, der sich mit ihm in den vergangenen Jahrhunderten beschäftigte, ist eine Facette dabei: die des abtrünnigen
Numerische Untersuchung nichtlinearer dynamischer Systeme, 1987
Monitoring missions in confined underwater environments such as nuclear storage ponds or industry... more Monitoring missions in confined underwater environments such as nuclear storage ponds or industry tanks call for highly maneuverable fully autonomous micro underwater robots. In this work, we target this challenging scenario with the new low-cost open-source HippoCampusX platform. We present a modular software and hardware architecture which is easily adaptable to mission specific requirements. Our system is part of the PX4-environment [1] and constitutes PX4’s first underwater extension including a SITL simulation. We conduct a series of experiments to demonstrate HippoCampus’ agile maneuvering capabilities and validate the derived dynamic model.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
Container cranes belong to the class of underactuated systems for which the design of control law... more Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally.
Journal of Vibration and Control, Feb 18, 2019
Underactuated mechanical systems are frequently encountered in several industrial and real-world ... more Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input-multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.
arXiv (Cornell University), May 23, 2022
This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The ... more This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The adopted approach is based on sliding mode control and enhanced by an artificial neural network to cope with modeling inaccuracies and external disturbances that can arise. The sliding surfaces are defined as a linear combination of both actuated and unactuated variables. A radial basis function is added to compensate the performance drop when, in order to avoid the chattering phenomenon, the sign function is substituted by a saturation function in the conventional sliding mode controller. An application of the proposed scheme is introduced for an inverted pendulum, in order to illustrate the controller design method, and numerical results are presented to demonstrate the improved performance of the resulting intelligent controller.
Springer eBooks, Sep 14, 2006
Almost all offshore structures have to be modeled as multibody systems. Only ships or single pont... more Almost all offshore structures have to be modeled as multibody systems. Only ships or single pontoons can be modeled as a single rigid body. The dynamic behavior of the multibody system is significantly influenced by fluid-structure interactions. So far, most available methods for analyzing these interactions are restricted to single bodies, small wave amplitudes and body motions, or both. In the present paper a two-dimensional boundary integral approach with fully nonlinear boundary conditions on the free surface is used to simulate the behavior of elastically coupled floating multibody systems in gravity waves. This method will be applied to analyze the dynamics of two floating bodies moored to a quay. The results of numerical simulations for selected configurations are shown.
The Twentieth International Offshore and Polar Engineering Conference, 2010
Konstruktion, 2017
Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fe... more Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fertigung von Prototypen ermöglicht. Wie bei jedem Fertigungsverfahren gibt es auch bei generativen Fertigungsverfahren „Best-Prac- tices”. Während allgemeine Richtlinien zum 3D-Druck- gerechten Konstruieren einen guten allgemeinen Überblick bieten, fehlen bislang Konstruktionsrichtlinien für die Dichtheit der gedruckten Teile. Einflussfaktoren wie Druck oder auch die Materialeigenschaften beeinflussen die Dichtheit eines Systems aus 3D-gedruckten Komponenten. Dieser Beitrag stellt eine Vorgehensweise für das 3D-Druck-gerechte Konstruieren vor, um 3D-gedruckte Systeme und Module zu dichten. Die Methoden werden anhand eines Mikro-Autonomen-Unterwasserfahrzeugs aufgezeigt.
The importance of remotely operated underwater vehicles for construction, inspection, and mainten... more The importance of remotely operated underwater vehicles for construction, inspection, and maintenance of off-shore structures has been continuously increasing in the recent years. Especially oil prospecting in water depths inaccessible for human divers (>300m) needs unmanned vehicles. For a great variety of tasks a robust positioning control of the vehicle is required. This control is complicated not only due to nonlinearities involved in the system including the umbilical and parameter uncertainties [1,7] but also because of the lack of precise position information. The positioning problem can be split into two domains: the region far from the structure, where the navigation from the basis ship to the structure takes place and the region close to the structure, where the position of the vehicle relative to the structure must be kept for a task to be performed.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode obs... more We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
The stochastic equation of motion for a heaving cylinder subject to irregular sea waves is solved... more The stochastic equation of motion for a heaving cylinder subject to irregular sea waves is solved numerically with the polynomial chaos framework. Thereby, the stochastic forcing is expressed by a truncated Karhunen-Loève expansion and the hydrodynamic radiation is formulated as a state space model. We obtain the mean and the variance of the cylinder heave motion.
The aim of this book is to present important software tools, basic concepts, methods, and highly ... more The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.
Journal of Applied Mathematics and Mechanics, Nov 1, 2001
We present a method to analyze dynamical systems undergoing random perturbations based on the cel... more We present a method to analyze dynamical systems undergoing random perturbations based on the cell mapping approach. Analytical expressions are derived for the transition probabilities from the evolution operator of the system. Thus there is no need for simulation of randomness and the numerical approximations are safe, i.e., we approximate attractors and their basins from within and give lower bounds for exit times. For additively perturbed systems the transition probabilities can be expressed in terms of the transition probabilities of the unperturbed system and the properties of the perturbation. The numerical details concerning the perturbation terms are discussed and their application is shown with an example.
Springer eBooks, 1990
In mechanical systems nonlinear effects due to stick slip and backlash are often observed. If suc... more In mechanical systems nonlinear effects due to stick slip and backlash are often observed. If such systems are harmonically driven, then besides well known bifurcation phenomena also sudden changes of the chaotic dynamics occur. These types of qualitative change of system’s behavior, the so-called crises, result from a collision between an unstable periodic orbit and a chaotic attractor. Different crises phenomena are discussed and it is demonstrated how the occurrence of crises can be determined numerically.
Computer Methods in Applied Mechanics and Engineering, Nov 1, 1986
Based upon Poincare maps, the generalized cell mapping theory has been developed for the global a... more Based upon Poincare maps, the generalized cell mapping theory has been developed for the global analysis of nonlinear dynamical systems. The mathematical description of an autonomous generalized cell mapping leads to a finite, discrete, stationary Markov chain where the transition probability matrix completely determines the behavior of the system. Although analytical methods for analyzing Markov chains are highly developed, efficient numerical algorithms for the analysis of Markov chains with a very large number of states are rare. Restricting ourselves to the determination of absorption probabilities and the expected absorption times of transient states, we describe an algorithm for an efficient numerical treatment of Markov chains to obtain these quantities.
The Proceedings of the 1st European Nonlinear Oscillations Conference contain invited contributio... more The Proceedings of the 1st European Nonlinear Oscillations Conference contain invited contributions of mathematicians engaged in the development of analytical and numerical methods and of scientists working on vibration problems in mechanics, physics, and other fields.
Der vorliegende Band ist der zweite in der Reihe "Hamburger Akademievorträge", in welcher die Aka... more Der vorliegende Band ist der zweite in der Reihe "Hamburger Akademievorträge", in welcher die Akademie der Wissenschaften in Hamburg Vorlesungsreihen und Einzelvorträge aus den breit gefächerten Akademie-Aktivitäten dokumentiert und im Open Access online zugänglich macht. Der Band fasst die Vorträge der Akademievorlesungsreihe "Reformation im Diskurs" zusammen, die vom Auftakt des Reformationsjahres im Oktober 2016 bis zum Januar 2017 in den Baseler Hof Sälen in Hamburg stattfanden. Die Beiträge werden ergänzt durch den Festvortrag "Martin Luther, Erneuerer der christlichen Religion", den unser Ordentliches Mitglied Johannes Schilling auf der Jahrfeier unserer Akademie im November 2016 gehalten hat. Johannes Schilling war es auch, der als langjähriger Präsident der Luther-Gesellschaft und an den Vorbereitungen zum offiziellen Reformationsjubiläum maßgeblich Beteiligter der Akademie bereits 2015 vorschlug, eine Vortragsreihe anlässlich des Reformationsjubiläums zu veranstalten. Die Reformation ist eng verknüpft mit dem Namen Martin Luther, dessen Veröffentlichung von 95 Thesen am 31. Oktober 1517 als ihr Auslöser gilt. Die Reformation war eine kirchliche Erneuerungsbewegung, die Geschichte, Gesellschaft, Wirtschaft und Kultur nicht nur in Europa tief und nachhaltig geprägt hat. Die Reformatoren wollten keine neue Kirche gründen oder die alte spalten, aber: ohne Reformation keine evangelischen Kirchen, keine Gegenreformation, keine Hugenottenkriege, kein Dreißigjähriger Krieg. So wirkmächtig und vielschichtig wie die Reformation war auch die Persönlichkeit Luthers. Für jeden, der sich mit ihm in den vergangenen Jahrhunderten beschäftigte, ist eine Facette dabei: die des abtrünnigen
Numerische Untersuchung nichtlinearer dynamischer Systeme, 1987