Abstract
In this paper, a new approach for the optimal synchronization of homogeneous multi-agent systems is presented. In contrast to existing approaches, we offer an intuitive cost for the transition of each agent to a common synchronization trajectory, which facilitates tuning of the cost weights. The introduced LQ optimal tracking problem is solved by reducing it to a LQ regulator problem. By choosing a linear parameterization of the synchronization trajectory, we enable the distributed implementation of the optimal synchronization controller. We give examples how such a parameterization can be chosen and how it influences the required communication between the agents. Furthermore, we derive an optimal communication topology that minimizes the weighted sum of all agents’ transition costs. Finally, we demonstrate our results in a simulation example.
Zusammenfassung
Im vorliegenden Beitrag wird ein neuer Ansatz zur optimalen Synchronisierung homogener Multi-Agenten-Systeme vorgestellt. Ein intuitives Gütemaß für die Transition der Agenten auf die Synchronisationstrajektorie erleichtert dabei die Wahl der Kostengewichte gegenüber bekannten Ansätzen. Das eingeführte LQ optimale Folgeregelungsproblem wird gelöst, indem es auf ein LQ Reglerproblem reduziert wird. Die Wahl einer linearen Parametrierung für die Synchronisierungstrajektorie ermöglicht die verteilte Implementierung des optimalen Regelgesetzes. Es werden Beispiele angegeben, wie eine solche Parametrierung gewählt werden kann und wie diese Wahl die erforderliche Kommunikation zwischen den Agenten beeinflusst. Schließlich wird eine optimale Kommunikationstopologie hergeleitet, welche die gewichtete Summe der Transitionskosten aller Agenten minimiert. Die Ergebnisse werden an einem Simulationsbeispiel demonstriert.
Dedicated to the 60th birthday of Prof. Dr.-Ing. Jürgen Adamy.
About the authors
Dr.-Ing. Sebastian Bernhard was with the Control Methods and Robotics Lab, headed by Prof. Dr.-Ing. Jürgen Adamy, at the Technical University of Darmstadt from 2014 to 2019. In his research, he derived methods to design explicit controllers for optimal tracking over infinite horizons and optimal output regulation of square, over-actuated and under-actuated systems. The article at hand originates from collaborative work on applying these methods to the synchronization of multi-agent systems at that time. Currently, he focuses on the intelligent navigation of autonomous mobile robots. He was a technical consultant for algorithms for autonomous systems at IAV GmbH and has recently joined the department he[a]t of Continental Automotive at their AI Lab in Berlin.
Dr.-Ing. Jonathan Hermann was a research associate at the Control Systems and Mechatronics Lab at the Institute of Automatic Control and Mechatronics in the Department of Electrical Engineering and Information Technology at the Technical University of Darmstadt. He is currently an employee of CARIAD SE working in the field of driver assistance systems. The presented contribution originates from his time as a research associate, where he focused on the design of communication topologies and synchronization control laws for multi-agent systems.
Prof. Dr.-Ing. Ulrich Konigorski is Head of the Control Systems and Mechatronics Lab at the Institute of Automatic Control and Mechatronics in the Department of Electrical Engineering and Information Technology at the Technical University of Darmstadt. His method-oriented main areas of research are the modeling and design of linear and non-linear MIMO-Systems while the application-oriented research focuses in particular on modeling, simulation and digital control of mechatronic systems as well as the analysis and design of chassis and vehicle dynamics control.
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