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In-Hand Manipulation with Synergistic Actuated Robotic Hands: An MPC-Based Approach
No full textIn-hand manipulation, or dexterous manipulation, is one of the most complex challenges in robotics as it requires the accurate coordination of multiple degrees of freedom. While several solutions have been presented for fully actuated hands, less work has focused on underactuated grippers. Synergies can be interpreted as a method for coupling joint motions, constraining the hand's degrees of freedom, and thereby reducing the number of control inputs. In this paper, we propose a model predictive control scheme (MPC) that integrates synergies to implement dexterous in-hand manipulation with robotic hands. In the MPC formulation, synergies can either be considered as constraints on the joint variables or are directly inserted in the system function with a reallocation of the input variables acting on the joints. Through several sets of simulations we compare these two approaches and show their main features
Modellprädiktive Interaktionsregelung von Robotersystemen
Full text linkIn this thesis, a model predictive control based method is presented for handling physical robot-environment interactions. The optimization-based approach enables a modular and flexible control scheme for force control, compliance control, motion control, and hybrid forms thereof. The method is based on the prediction of the behavior of the robot motion as well as the forces and moments on the end-effector. For the latter, a linear-elastic model is used, which takes the compliance of the environment as well as of the underlying controller into account. The geometrically serial configuration of the two elasticities results in an upper bounded stiffness in the linear-elastic prediction model even in the case of a contact with a rigid environment. This also allows to handle the interaction with rigid objects.
In the first part of this thesis, the methodology of model predictive interaction control (MPIC) is derived. Model predictive control is based on the cyclic solution of an optimization problem. The individual components of the optimization problem, namely system dynamics, cost functional and constraints, have different tasks in order to implement a desired control behavior. The system dynamics describes the motion behavior of the robot as well as the behavior of the end-effector forces and torques. The control objective is defined by the cost functional. For this purpose, the deviation from an operating point or reference trajectory is penalized.
Robot-specific and eventual task-specific conditions can be taken into account via inequality constraints.
A special focus of this work is on the practical implementation of model predictive control on real robot systems. For this purpose, the application of the methodology on a seven-degrees-of-freedom robot is considered. Therefore, the concrete problem formulations for motion control in joint and Cartesian space, force control, compliance control, and hybrid force and motion control are presented and evaluated.
Robot tasks usually consist of a sequence of several individual tasks. This implies that a robot task cannot be solved by a single control objective.
For this reason, this thesis develops a concept that exploits the flexibility of MPIC to realize different elementary primitives via a single control scheme. The basis is a hierarchical framework for a structured description of the robot task. The lowest level is formed by so-called manipulation primitives, which can be realized by an appropriate parameterization of the optimization problem using MPIC. This results in a framework that enables the implementation of extensive robot tasks by varying a few parameters. The framework is evaluated in simulation as well as on a force-locking non-grip-based manipulation task on a seven-degree-of-freedom robot.
Another aspect of this thesis is the control of robot hands. For this purpose, the methodology developed for the single-arm robot is adapted for the requirements of robot hands. The focus in this field of application is on the consideration of force-specific constraints in order to realize force closure grasps or to restrict internal grasp forces. These are necessary to stabilize a force closure grasp or to detect contact with an unknown object.
In addition, a force closure manipulation of a sphere with an anthropomorphic robotic hand is demonstrated. Furthermore, a link to the framework for robot tasks is established in order to realize holistic grasping tasks. Three exemplary grasp types are discussed and evaluated.In dieser Arbeit wird ein auf der modellprädiktiven Regelung basierendes Verfahren zur Handhabung physischer Roboter-Umgebungs-Interaktionen vorgestellt. Der optimierungsbasierte Ansatz ermöglicht ein modulares und flexibles Regelungsschema für die Kraftregelung, Nachgiebigkeitsregelung, Bewegungsregelung sowie hybride Formen davon. Das Verfahren fußt auf der Prädiktion des Verhaltens der Roboterbewegung sowie der Kräfte und Momente am Roboterendeffektor. Für letzteres wird ein linear-elastisches Modell verwendet, welches die Nachgiebigkeit der Umgebung sowie des unterlagerten Reglers berücksichtigt. Die geometrisch serielle Anordnung der beiden Elastizitäten führt dazu, dass selbst im Grenzfall eines Kontakts mit starrer Umgebung eine nach oben hin beschränkten Steifigkeit im linear-elastischen Prädiktionsmodell resultiert. Damit lässt sich auch die Interaktion mit starren Objekten handhaben.
Im ersten Teil der Arbeit wird die Methodik der modellprädiktiven Interaktionsregelung oder kurz MPIC (engl. model predictive interaction control) hergeleitet. Die modellprädiktive Regelung basiert auf der zyklischen Lösung eines Optimierungsproblems. Dabei haben die einzelnen Bestandteile des Optimierungsproblems, nämlich Systemdynamik, Kostenfunktional und Beschränkungen, verschiedene Aufgaben, um ein gewünschtes Regelverhalten umzusetzen. Die Systemdynamik beschreibt das Bewegungsverhalten des Roboters sowie das Verhalten der Endeffektorkräfte und -momente. Das Regelziel wird über das Kostenfunktional definiert. Dabei wird die Abweichung zu einem Arbeitspunkt oder einer Referenztrajektorie bestraft.
Roboterspezifische und etwaige aufgabenspezifische Einschränkungen können über Ungleichungsbeschränkungen berücksichtigt werden.
Ein besonderer Fokus dieser Arbeit liegt auf der praktischen Umsetzung der modellprädiktiven Regelung an realen Robotersystemen. Hierzu wird im ersten Teil die Anwendung der Methodik an einem Sieben-Freiheitsgrade-Roboter betrachtet. Dazu werden die konkreten Problemformulierungen für die Regelziele der Bewegungsregelung im Gelenk- und Arbeitsraum, die Kraftregelung, die Nachgiebigkeitsregelung sowie die hybride Regelung von Kraft und Bewegung vorgestellt und evaluiert.
Roboteraufgaben bestehen üblicherweise aus einer Abfolge mehrerer Einzelaufgaben. Dies impliziert, dass eine Roboteraufgaben nicht durch ein einzelnes Regelungsziel gelöst werden kann. Aus diesem Grund wird in dieser Arbeit ein Rahmenwerk entwickelt, dass die Flexibilität der MPIC ausnützt, um verschiedene elementare Primitive über ein einzelnes Regelungsverfahren zu realisieren. Die Grundlage bildet ein hierarchisches Modell zur strukturierten Beschreibung der Roboteraufgabe. Die unterste Ebene baut auf sogenannten Manipulationsprimitiven auf, die durch eine entsprechende Parametrierung des Optimierungsproblems mithilfe der MPIC realisiert werden können. Daraus entsteht ein Rahmenwerk, welches durch die Variation weniger Parametern die Umsetzung von umfangreichen Roboteraufgaben ermöglicht. Das Rahmenwerk wird in der Simulation sowie an einer kraftschlüssigen nicht-griffbasierten Manipulationsaufgabe an einem Sieben-Freiheitsgrade-Roboter evaluiert.
Ein weiterer Aspekt dieser Arbeit ist die Regelung von Roboterhänden. Es wird dazu die am Einarm-Roboter entwickelte Methodik für die Gegebenheiten bei Roboterhänden angepasst. Der Fokus liegt in diesem Anwendungsgebiet auf der Berücksichtigung von kraftspezifischen Beschränkungen, um kraftschlüssige Griffe zu realisieren oder innere Griffkräfte zu beschränken. Diese sind notwendig, um beispielsweise einen kraftschlüssigen Griff zu stabilisieren oder bei einem unbekannten Objekt den Kontakt zu detektieren. Neben der Stabilisierung eines Zweifinger-Präzisionsgriffs wird eine kraftschlüssige Manipulation einer Kugel mit einer anthropomorphen Roboterhand gezeigt. Darüber hinaus wird eine Verbindung mit dem Rahmenwerk zur Realisierung von Roboteraufgaben hergestellt, um dadurch ganzheitliche Greifaufgaben umsetzen zu können. Dabei wird die Realisierung von drei beispielhaften Griffen diskutiert und evaluiert
Distributed model predictive control of nonlinear system based on a real-time capable ADMM implementation
No full textParallel erschienen als Druckausgabe bei FAU University Press, ISBN: 978-3-96147-751-7Die vorliegende Dissertation betrachtet die echtzeitfähige Regelung verteilter Systeme. Diese bestehen aus einer großen Zahl an Subsystemen, zwischen denen physikalische oder virtuelle Kopplungen bestehen. Verteilte Systeme halten im Rahmen der Vernetzung von Sensoren und Aktoren zunehmend Einzug in viele Bereiche von Industrie und Alltag. Im Rahmen dieser Dissertation wird ein Regelungskonzept auf Basis der verteilten modellprädiktiven Regelung unter Verwendung des ADMM-Algorithmus vorgestellt, mit dem eine echtzeitfähige Stabilisierung verteilter Systeme möglich ist. Dabei wird die methodische Weiterentwicklung des ADMM-Algorithmus, dessen Implementierung in Form des Softwarepakets GRAMPC-D sowie die Evaluation der methodischen Ergebnisse betrachtet. Zunächst wird aufgezeigt, dass bei Verwendung des Regelungskonzepts die Rechenzeit zur Lösung der lokalen Problemstellungen unabhängig von der Systemgröße sein kann. Weiterhin wird dargelegt, dass das Konvergenzverhalten des ADMM-Algorithmus durch die Ansätze der Nachbarschaftsapproximation sowie der Superagenten verbessert sowie die Kommunikationszeit durch das Konzept der asynchronen Ausführung reduziert werden kann. Zuletzt wird die Echtzeitfähigkeit des Regelungskonzepts im Rahmen einer experimentellen Validierung demonstriert.This thesis considers the real-time capable control of distributed systems. These consist of a large number of subsystems that are physically or virtually coupled. Distributed systems are a growing part of industry and daily life due to the networking of sensors and actuators. The thesis proposes a control concept based on distributed model predictive control using the ADMM algorithm. This concept is capable of controlling distributed systems in real-time. The thesis considers the methodological improvement of the ADMM algorithm, its implementation in the software framework GRAMPC-D, and the evaluation of the methodological results. At first it is shown that the computation effort for solving the local problems can be independent of the network size. It is further presented that the convergence behavior of the ADMM algorithm can be improved by the concepts of neighbor approximation and super agents and that the communication effort can be reduced by using the approach of an asynchronous execution. The real-time capability of the control concept is afterwards demonstrated by an experimental validation
A modular approach for distributed predictive control
No full textModern production systems are increasingly interconnected and are designed in a modular way to allow for flexible reconfiguration. In control engineering terms these systems are often referred to as distributed dynamic systems. A standard approach for the design of the control system for these plants is a central approach. For this approach, the complete dynamic of the distributed system is considered for the control design. Contrary to the central control design is a decentral control design. In this approach, a controller is designed for each modular part of the system and accounts for the interactions with the other parts of the system as disturbances. As a middle ground between these two approaches distributed control has emerged. For this approach, a controller is designed for each part of the system and all controllers exchange information with each other and follow a coordination scheme.
To accomplish complex control tasks with high performance model based control methods are increasingly applied in practical applications, i.e. the controller specifically incorporates a model of the system behavior. Particularly model predictive control (MPC) has become a method of choice for these situations. MPC belongs to the class of optimization based controllers, where the control objective is stated as an optimal control problem (OCP). By solving the optimization problem, the optimal control input for the system is determined. The feedback loop for MPC applications is achieved by repeatedly solving the optimization problem every time a new measurement sample of the system is available and then applying the optimal input until the next sample is available. When MPC is used in a distributed control design, it allows to naturally account for the interaction of all parts of the distributed system in the control design.
In this thesis, a modular approach for a DMPC system will be presented. Each part of the system is controlled by means of an MPC, and the aggregation of the part of the system and the controller is called agent. To preserve the modular structure of the distributed dynamic system within the distributed model predictive control (DMPC), the information exchange between the agents is limited to directly coupled agents. Developing the DMPC system within these constraints allows the configuration of systems with numerous agents, while still keeping the amount of information that a single agent needs to process manageable.
To develop the approach, three formulations of nonlinear dynamically coupled systems are introduced and the control problem for the DMPC is stated as an OCP. In the following, two decomposition schemes for the resulting OCPs are presented. The optimality conditions of the OCPs following from both decomposition schemes are derived. The structure of the optimality conditions allows the application of well known duality based decomposition method to split the original problem into a collection of subproblems on a per agent basis that are tied together by coordination variables. While this development is based on the Lagrangian formulation of the decomposable OCPs, additionally the Augmented Lagrangian formulation of the decomposable OCPs is stated. The equivalence of the optimal solution following from the Lagrangian formulation and the augmented Lagrangian formulation is established for the given decomposable OCPs to form the basis for the application of distributed algorithms.
Building on the properties of the decomposable OCP, duality based algorithms can be applied to find the optimal solution. To this end, a Dual Decomposition based method, and three variants of an augmented Lagrangian based method are applied. The algorithms are compared by the application to a toy problem, featuring two coupled water tanks. For the best performing method, i.e. Alternating Direction Method of Multipliers ADMM a convergence prove for the application to the developed OCP is provided.
The chosen decomposition of a given distributed dynamical system, can have a large impact on the performance of ADMM. For two of the developed formulations of the distributed dynamics, it is possible to choose a decomposition that allows each agent to anticipate the reaction of its coupled neighbors to its own actions. The effectiveness of the decomposition scheme is demonstrated comparing it with a standard decomposition scheme when both are applied to a cooperative payload example. In this example system, a four robots are coupled to to payloads and need to collectively carry them to a target location. It is shown that the convergence of ADMM with this scheme can be greatly enhanced.
To highlight challenges of a practical DMPC implementation, a distributed software framework for the agent implementation is developed using the unified modeling language (UML). Using UML the data exchange and configuration of a coupling connection between the agents is modeled. Furthermore, the calculation of basic functions to be used by the optimizing framework is modeled in a modular way, allowing to assemble complex dynamics from modular building blocks based on the current couplings of the agent. The developed framework is then used in an laboratory setup featuring four coupled water tanks. Each tank is equipped with its own computing hardware and connected to a common information exchange bus. The experimental results show the DMPC to control different coupling scenarios of the setup by employing the agent framework. Yet, the performance analysis reveals the communication to take up a large portion of the runtime
Gradient-based nonlinear model predictive control with constraint transformation for fast dynamical systems
No full textModel predictive control (MPC) is a modern control methodology that is based on the repetitive solution of an optimal control problem (OCP) at fixed time instances. The determined state of the system at the current sampling instance is used as initial value for the OCP and the computed control action is then injected to the plant. This procedure is repeated in the next sampling step where the OCP is resolved with the new state of the system.
A model predictive controller provides a number of benefits compared to classic control methods. The desired control objective is formulated in a cost function while constraints are directly taken into account. Additionally, an MPC allows to control nonlinear and multivariable systems. However, the numerical solution of an optimal control problem requires in general a significant computational effort and hence limits the application of a model predictive controller. This is even more severe if an MPC is used to control fast dynamical systems with low sampling times. To this end, efficient algorithms, powerful hardware platforms or a combination of both have to be used to circumvent this difficulty.
This thesis discusses an MPC scheme that is well-suited for controlling fast nonlinear dynamical systems in real-time. This goal is achieved by combining the efficient gradient method with a transformation technique to handle a particular class of constraints in a systematic way allowing to reformulate a constrained optimal control problem into an unconstrained counterpart to reduce the numerical burden. The related systematic and algorithmic conditions and properties are discussed in detail together with convergence and stability results. The performance of the approach is demonstrated in simulation and experimental studies
Nichtlineare modellprädiktive Drehmomentregelung elektrischer Antriebssysteme für hochdynamische Anwendungen
No full textNonlinear model predictive control ((N)MPC) techniques are used more and more frequently for high-performance control of dynamic nonlinear multiple-input and multiple-output systems. A main reason for this is the systematic consideration of (nonlinear) constraints, as they frequently occur in mechatronic systems. Typically, the sampling times of such systems are in the (sub-)millisecond range and the control strategy must be implemented in an embedded system with limited resources. Especially in time-critical applications with small computing power, the real-time implementation of MPC algorithms still poses a challenge.
Torque control of electrical machines is such a challenging problem with nonlinear dynamics, sampling times in the microsecond range and nonlinear constraints on the phase voltage as well as on the phase and the DC link current. The number of electric servo drives is constantly increasing due to the flexible application in both automotive and industrial environments. The type of machine plays an important role for the application. Traditionally, permanent magnet synchronous machines (PMSMs) are used for precision applications due to their high dynamics, high energy density and good efficiency. Because of improving control strategies, however, induction machines, which are characterized by their robust and inexpensive design, are also increasingly used in more demanding applications. In general, the requirements on the drives with regard to speed and accuracy of torque generation are very high, especially in critical applications such as electric power steering systems or machine tools. Due to increasing environmental awareness and economic considerations, there is also a growing interest in operating the machines as efficiently as possible and to fully exploit their physical limits.
Motivated by the above-mentioned challenges, an MPC approach for fast and energy-efficient torque control of electrical machines is developed in this thesis. A particular focus is on the development of suitable methods to take into account the constraints mentioned at the beginning. On the basis of an augmented Lagrangian approach, the nonlinear constrained optimal control problem is transformed into an unconstrained problem. This allows one to apply a tailored gradient method for solving the unconstrained problem in a time efficient manner. In addition, a fixed point iteration strategy, which further reduces the algorithmic complexity for a certain class of applications. For example, the DC link current constraints, which play an important role in automotive need not always be taken into account.
By seamlessly integrating the solution methods into the augmented Lagrangian framework, an MPC algorithm tailored exactly to the problem at hand is developed. Runtime analyses prove that the torque control for PMSMs with a sampling time of 500µs is real-time feasible even on an electronic control unit (ECU) level. Due to the more complex model structure, the computing time of the induction machines' control is somewhat higher in direct comparison. Nevertheless, real-time feasibility is still achieved on a dSPACE rapid prototyping platform. Another limiting factor for embedded implementation is the memory footprint of the algorithm. For this reason, the developed algorithms are kept streamlined and have an almost negligible memory requirement of less than 10kB.
The basis of the control design is a mathematical model of the machines in the flux-oriented dq-coordinate system. Current-dependent model parameters take saturation effects into account and thus ensure the validity of the model even in case of a significant overload of the machines. At the same time, the complexity of the models is low enough in order to be parameterized using the standard inverter without additional sensors.
In order to increase energy efficiency with regard to copper losses, a new setpoint computation is developed for both the PMSM and the IM. The calculation of the setpoints is based on a hierarchical, static optimization problem and ensures that the setpoints meet all constraints in the stationary case.
Experimental results illustrate the performance of the controls in numerous scenarios. In order to better classify the results, a state--of--the--art field-oriented controller (FOC) is implemented for both machines. The setpoints for these controls are calculated with the methods developed in this thesis, which ensures that the FOC complies with the constraints in the best possible way in order to provide a fair comparison with the MPC methods.Die Dissertation wurde 2020 im Shaker-Verlag unter der ISBN 978-3-8440-7305-8 veröffentlicht
Design of distributed model-based control agents for building automation systems
No full textMany scientific studies stress the importance of the building sector with regard to climate change. The goal is to achieve higher energy efficiencies compared to the state of the art. Although the potential of control approaches such as model predictive control (MPC) to achieve significant reductions in energy demand has been known for years, there is still considerable potential for improvement. Especially the distribution of control tasks to multiple intelligent agents applying distributed MPC (DMPC) is considered promising. The main research question of this thesis is: What are the factors of a suitable design for distributed controllers (agents) that cooperate in building energy systems to reach satisfactory thresholds of energy-efficiency and occupant comfort under uncertainty? In order to answer the question of suitable designs, distributed model-based control algorithms are developed and implemented. According to these algorithms, agents cooperate in various ways and use different kinds of subsystem models. One algorithm follows a sequential scheme and the agents exchange lookup tables. Each agent prepares the lookup tables by solving the subsystem optimization in an explicit MPC manner to provide costs as piecewise linear functions of the coupling variables. In a second algorithm, the agents exchange the coupling variables and the cost gradients that are caused by the coupling in multiple iterations. Among others, entropy balances are used for updating probability distributions used by the agents and for assigning thermodynamic costs to control decisions taken by the agents. The first case study of this thesis is an air handling unit. In a real-life experiment and a simulation experiment, decentralized control approaches, system identification methods and various distributed model-based approaches are applied. In a simulation, both algorithms are applied and the results are compared. The second case study deals with a building energy system, with both simulated and real-life versions, whose set points are calculated using the sequential algorithm. The algorithm is compared to a state-of-the-art DMPC algorithm and to a rule-based benchmark control approach. Among the main advantages of the investigated DMPC agents is the reduction of complexity by exploiting the weak coupling of subsystems. Compared to fully decentralized controllers, e.g. separated feedback control loops, a higher energy efficiency can be achieved as the system as a whole can transition into the most efficient operation. Moreover, compared to state-of-the-art control systems, the DMPC agents could potentially reduce the effort for tailoring a new control strategy to a building as they support a highly automated data-driven model development
A transformerless H-bridge inverter as a bidirectional power flow controller in a microgrid based P/V droop control
No full textIn modern power distribution grids, the evolution of new power control methodologies in microgrid applications is growing increasingly due to the large demand for DG sources integration. However, with the rising level of the DG sources penetration in the distribution network and for maintaining a reliable operation of the main grid, the power flow exchange at the point of common coupling between the microgrid and the utility grid should be controlled. A few research studies in academia and industry has concentrated on the decentralized bidirectional power flow control, especially in low-voltage distribution networks. Therefore, in this thesis, a series transformerless H-bridge inverter which plays the role of a series power flow controller is placed at PCC between the microgrid and the main utility grid to satisfy this target.
This dissertation focuses on developing suitable power control strategies and algorithms of the system components to satisfy a desired real power flow reference at PCC. The proposed work is realized by power flow calculations and time-domain simulations, respectively. In power flow calculations, the series power flow controller is modeled as a voltage source inverter, where an overall power flow algorithm and an optimization function are designed to control the real power transfer between both networks. The limits of the proposed approach have been investigated by adjustment of different droop settings and various network conditions. However, in time-domain simulations, the proposed series controller is modeled as a transformerless H-bridge inverter, where two novel power control strategies are implemented to control the bidirectional real power transfer at PCC. Furthermore, the power control loop of the DG units in the microgrid is supported by P/V droop characteristic which is varied depending on the PCC voltage changes. The bidirectional real power flow is controlled by injecting the needed voltage magnitude and phase angle depending on the desired and measured real power at PCC. The series injected voltage changes the microgrid side voltage and thus, the P/V droop controllers respond automatically to satisfy the assigned power reference. Several case scenarios have been investigated using SimPowerSystems and PLECS tool boxes of Matlab/Simulink. The proposed methods and methodologies show promising results, in which they confirm the feasibility and applicability of the proposed series power flow controller concept and its associated methodologies.
A verification task has been fulfilled by investigating the disconnection and reconnection process of the microgrid and the proposed series power flow controller under short circuit events. The microgrid is represented by a single DG unit and the series power flow controller is represented by the transformerless H-bridge inverter. The islanding and resynchronization process of the microgrid is redeemed by activating a synchronization controller within the island control mode of the microgrid. However, the disconnection and reinsertion process of the transformerless H-bridge inverter is realized based on two different approaches which are selected depending on the fault location. After fault clearance, the simulation results of the test validation model depict smooth transition and soft reinsertion of the microgrid and the transformerless H-bridge inverter, respectively
MPC-basierte Bewegungsplanung für Fahrsimulatoren mit echtzeitfähiger Fahrerprädiktion
Full text linkThe usage of human-centered motion simulation systems has been a significant component of the research and development process in various fields for many years. The predominant areas of application are in flight and driving simulation, where such systems are used for the testing of new components or setups as well as for pilot and driver training. The reasons for using a simulator rather than performing an experiment in the real world are safety, time and cost efficiency, as well as the perfectly controllable and reproducible experiment conditions.
Independent of the particular application, the level of immersion for a test person in the simulator is crucial in order to be able to transfer the results from simulator experiments to the real world. Thus, modern motion simulation systems are equipped with various immersion systems including a visual system for environment representation, an audio system for noise simulations as well as a motion system to reproduce the real world forces.
This thesis focuses on the motion planning for dynamic driving simulators, i.e. the reproduction of the physical accelerations and angular velocities acting on a driver in a real vehicle with the motion system of the simulator. The key challenges in this regard are the constrained motion space of technical simulation systems when compared to the practically unlimited motion space of a vehicle in the real world as well as the hard real-time constraint in combination with small sampling times of typically 1-10 ms for the online driver-in-the-loop application of the motion controller. Traditionally, the algorithms used for the motion planning of dynamic driving simulators, the so-called motion cueing algorithms (MCA), are based on a combination of linear, time-invariant high- and lowpass filters. These state-of-the-art approaches have some clear disadvantages such as the inability to directly incorporate the simulation system limitations into the motion planning or the incapability of dynamically prepositioning the simulator in order to increase the motion space for oncoming maneuvers.
With the goal to resolve the key motion cueing challenges and to overcome the main disadvantages of the state-of-the-art filter-based approaches, a motion cueing algorithm based on nonlinear model predictive control (MPC) is developed in the context of this thesis. The key idea is to formulate the motion cueing problem as a dynamical optimization problem over a moving time horizon, which is iteratively solved at every sampling step. The underlying problem formulation includes a suitable cost function to reach the motion cueing control objective and is constraint by the system dynamics as well as the actuator limitations of the used simulator geometry. The derived control scheme is applicable to various simulator geometries and is especially suited to exploit redundant degrees of freedom in simulation systems.
In order to fully exploit the predictive potential of the derived control approach in the online driver-in-the-loop application, an algorithm to predict the future driver behavior and consequently the future desired values for the MPC-based motion cueing algorithm is developed. The approach models the human driver as an optimal controller with the goal to follow a predefined reference route. Through this prediction approach, the controller is able to dynamically preposition the the simulator based on future maneuvers in order to increase the available motion space for their reproduction.
Since different human drivers in general perform similar control actions when confronted with the same driving situation or task, learning-based methods are employed in order to further increase the accuracy of the predicted future driving actions. In this thesis, learning-based approaches are used for an automated tuning of the control-based prediction method as well as for the development of a purely data-driven prediction method based on neural networks.
In order to be able to use the overall control scheme in the actual online driver-in-the-loop context, an efficient method for the numerical solution of the motion cueing as well as the driver prediction optimal control problems has to be used. In this thesis, an augmented Lagrangian approach to incorporate the nonlinear, state-dependent constraints in combination with a real-time capable projected gradient algorithm is employed.
Objective evaluations as well as the subjective comparison of the newly developed overall control scheme to a filter-based approach by means of an online simulator experiment show the huge potential of the newly developed method when compared to the state-of-the-art MCA.
Furthermore, the results show the broad applicability of the developed control scheme for various different use cases, including standard driving, driving dynamics applications as well as racetrack simulations. Finally, a run-time analysis demonstrates the efficiency of the employed numerical solution method and shows the real-time feasibility of the overall control scheme consisting of driver prediction and MPC-based motion cueing algorithm.Der Einsatz von Bewegungssimulationssystemen für Experimente mit menschlichen Probanden ist seit vielen Jahren ein wichtiger Bestandteil des Forschungs- und Entwicklungsprozesses in vielen Bereichen. Die vorherrschenden Anwendungsgebiete sind dabei die Flug- und Fahrsimulation, wo derartige Systeme für die Erprobung neuer Komponenten oder Einstellungen sowie für das Piloten- und Fahrertraining eingesetzt werden. Die Hauptgründe, ein Experiment in einem Simulator statt in der realen Welt durchzuführen, sind Sicherheit, Zeit- und Kosteneffizienz sowie die perfekt kontrollierbaren und reproduzierbaren Versuchsbedingungen. Unabhängig von der jeweiligen Anwendung ist es entscheidend, bei einer Testperson im Simulator einen möglichst realitätsnahen Gesamteindruck zu erzeugen, um die Ergebnisse aus Simulator-Experimenten in die reale Welt übertragen zu können. Moderne Bewegungssimulationssysteme sind daher mit verschiedenen Immersionssystemen ausgestattet, darunter ein visuelles System zur Umgebungsdarstellung, ein Audiosystem für Geräuschsimulationen sowie ein Bewegungssystem zur Reproduktion der in der Realität wirkenden physikalischen Kräfte.
Der Fokus dieser Arbeit liegt auf der Bewegungsplanung für dynamische Fahrsimulatoren, d.h. der Nachbildung der physikalischen Beschleunigungen und Winkelgeschwindigkeiten, die auf einen Fahrer in einem realen Fahrzeug wirken, mit dem Bewegungssystem des Simulators. Die zentralen Herausforderungen sind dabei der stark eingeschränkte Bewegungsraum technischer Simulationssysteme im Vergleich zum praktisch unbegrenzten Bewegungsraum eines Fahrzeugs in der realen Welt sowie die harte Echtzeitanforderung in Kombination mit kleinen Abtastzeiten von typischerweise 1-10 ms für die Online-Anwendung. Traditionell bestehen die für die Bewegungsplanung von dynamischen Fahrsimulatoren verwendeten Algorithmen, die sogenannten Motion Cueing-Algorithmen (MCA), aus einer Kombination von linearen, zeitinvarianten Hoch- und Tiefpassfiltern. Diese Ansätze haben einige klare Nachteile. Beispielsweise können die Beschränkungen des Simulationssystems nicht direkt in der Bewegungsplanung berücksichtigt werden. Ebenso ist es nicht möglich, den Simulator dynamisch vorzupositionieren, um so den Bewegungsraum für bevorstehende Manöver zu vergrößern.
Mit dem Ziel, die wichtigsten Herausforderungen des Motion Cueings anzugehen und die Hauptnachteile der filterbasierten Ansätze zu überwinden, wird im Rahmen dieser Arbeit ein Motion Cueing-Algorithmus basierend auf der nichtlinearen modellprädiktiven Regelung (MPC) entwickelt. Die Grundidee dabei besteht darin, das Motion Cueing-Problem als ein dynamisches Optimierungsproblem über einen bewegten Zeithorizont zu formulieren, das in jedem Abtastschritt iterativ gelöst wird. Die zugrundeliegende Problemformulierung beinhaltet eine geeignete Kostenfunktion zur Erreichung des Motion Cueing-Kontrollziels unter Berücksichtigung der Systemdynamik und der Aktorbeschränkungen der verwendeten Simulatorgeometrie. Der entwickelte Bewegungsplanungsansatz ist in Kombination mit verschiedenen Simulatorgeometrien anwendbar und eignet sich insbesondere zur Ausnutzung redundanter Freiheitsgrade in Simulationssystemen.
Um das prädiktive Potenzial des entwickelten Bewegungsplanungsverfahrens in der Online-Anwendung voll ausnutzen zu können, wird ein Algorithmus zur Prädiktion des zukünftigen menschlichen Fahrerverhaltens und folglich der zukünftigen Sollwerte für den MPC-basierten Motion Cueing-Algorithmus entwickelt. Der Ansatz modelliert den menschlichen Fahrer als einen optimierungsbasierten Regler mit dem Ziel, einer vordefinierten Referenzroute zu folgen. Durch diesen Prädiktionsalgorithmus ist der entwickelte MCA in der Lage, den Simulator auf der Grundlage zukünftiger Manöver dynamisch vorzupositionieren, um so den verfügbaren Bewegungsraum für deren Reproduktion zu vergrößern. Da verschiedene menschliche Fahrer in der Regel ähnlich agieren, wenn sie mit der gleichen Fahrsituation konfrontiert sind, ist es möglich, lernbasierte Methoden zu verwenden, um die Genauigkeit der vorhergesagten zukünftigen Fahraktionen weiter zu erhöhen. In dieser Arbeit werden die lernbasierten Ansätze sowohl für eine automatisierte Parametrierung der reglerbasierten Prädiktionsmethode als auch für die Entwicklung einer rein datengetriebenen Vorhersagemethode auf der Basis neuronaler Netze verwendet.
Um den Gesamtalgorithmus in der Online-Anwendung nutzen zu können, muss eine effiziente Methode zur numerischen Lösung der dynamischen Optimierungsprobleme für das Motion Cueing sowie für die Fahrerprädiktion gewählt werden. In dieser Arbeit wird ein erweiterter Lagrange-Ansatz zur Einbeziehung der nichtlinearen, zustandsabhängigen Beschränkungen in Kombination mit einem echtzeitfähigen projizierten Gradientenverfahren verwendet.
Objektive Auswertungen sowie der subjektive Vergleich des neu entwickelten Bewegungsplanungsalgorithmus mit einem filterbasierten Ansatz mittels eines online Simulator-Experiments zeigen das große Potenzial des neu entwickelten Verfahrens im Vergleich zu den filterbasierten Ansätzen. Darüber hinaus zeigen die Ergebnisse die breite Anwendbarkeit des entwickelten MCAs für verschiedene Anwendungsfälle, darunter Standardfahrten, Fahrdynamikanwendungen sowie Rennstreckensimulationen. Abschließend zeigt eine Laufzeitanalyse die Effizienz der verwendeten numerischen Lösungsmethode und demonstriert die Echtzeitfähigkeit des Gesamtverfahrens bestehend aus Fahrerprädiktion und MPC-basiertem Motion Cueing-Algorithmus
Optimal trajectory planning for multiphysics problems governed by electromagnetic and thermal phenomena
No full textMultiphysics problems include various physical phenomena such as fluid flow, heat transfer or electromagnetism, to mention just a few. The mathematical description of this type of problem therefore requires a system of nonlinearly coupled partial differential equations (PDE - Partial Differential Equation), usually defined on complex spatial domains. Electromagnetic heating systems are governed by electromagnetic and thermal phenomena and are a typical example of such problems.
This thesis discusses optimization-based approaches to determine an optimal excitation and spatial configuration of electromagnetic actuators. The objectives of the trajectory planning problems are tailored to several induction heating processes and hyperthermia therapy. The incorporation of state constraints for the trajectory planning such as constraints on the temperature of the object to be heated or on the temperature gradient is another focus. All three problems, i.e., the optimization of the excitation of the actuator, the optimization of the actuator configuration, and the incorporation of state constraints, are tackled by formulating and numerically solving suitable optimization problems.
The primary benefit of the presented solution strategy is its wide applicability to various problems of electromagnetic heating without the necessity to overcome the numerical challenges by developing numerical algorithms and solvers. Instead, an optimization framework is presented that uses state-of-the-art simulation software to numerically solve the optimization problems. The numerical level is extended by an algorithmic level to incorporate proper optimization methods.
The applicability and accuracy of the optimization framework is exemplified for simulation studies ranging from induction heating processes to hyperthermia therapy. The numerical results demonstrate the optimization of the excitation and spatial configuration of the actuator for selected problems and reveal the simple adaptation of the solution strategy to other electromagnetic heating problems.Multiphysikprobleme umfassen unterschiedliche und in einer wechselseitigen Beziehung stehende physikalische Effekte wie zum Beispiel fluiddynamische Vorgänge, Wärmeleitung oder elektromagnetische Felder. Eine hinreichend genaue mathematische Beschreibung derartiger Probleme erfordert daher partielle Differentialgleichungen, welche häufig auf komplexen Ortsgebieten definiert sind. Ein typisches Beispiel sind elektromagnetische Heizvorgänge, die durch elektromagnetische und thermische Wechselwirkungen gekennzeichnet sind.
In dieser Arbeit werden optimierungsbasierte Ansätze für die Auslegung einer optimalen Ansteuerung der Aktorik sowie einer optimalen Aktorkonfiguration untersucht. Die Zielstellung der Trajektorienplanung wird auf verschiedene induktive Heizvorgänge und Formen der Hyperthermiebehandlung angepasst. Ein weiterer Schwerpunkt ist die Berücksichtigung von Zustandsbeschränkungen, um beispielsweise die Temperatur oder den Gradienten der Temperatur im Rahmen der Trajektorienplanung begrenzen zu können. Der Lösungsansatz für die unterschiedlichen Problemstellungen einer optimalen Aktoransteuerung und optimalen Aktorkonfiguration sowie für die Berücksichtigung von Zustandsbeschränkungen beruht auf der geeigneten Formulierung und numerischen Lösung von Optimierungsproblemen.
Der Vorteil des vorgestellten Lösungsansatzes zur optimalen Trajektorienplanung beruht auf dessen breiter Anwendbarkeit. Verschiedenste Problemstellungen des elektromagnetischen Heizens können bewältigt werden ohne aufwendige Erweiterungen hinsichtlich der Numerik vornehmen zu müssen. Stattdessen wird eine Optimierungsumgebung vorgestellt, die auf Basis von FEM-Software die numerische Lösung der Optimierungsprobleme ermöglicht. Die numerische Ebene wird um eine algorithmische erweitert, in welcher geeignete Optimierungsroutinen implementiert werden.
Die Leistungsfähigkeit der Optimierungsumgebung wird mit Hilfe von Simulationsstudien von induktiven Heizvorgängen und Tumorbehandlungen aufgezeigt. Die Simulationsstudien führen letztendlich zu optimalen Ansteuerungen und Konfigurationen der Aktoren und verdeutlichen die breite Anwendbarkeit der Optimierungsumgebung auf verschiedene Problemstellungen des elektromagnetischen Heizens
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