Inverse Dynamische Spiele in der Regelungstechnik
Zusammenfassung der Projektergebnisse
Already today, highly automated systems are increasingly interacting with each other and with humans. For example, autonomous robot platforms transport goods in warehouses, where humans and other vehicles controlled by humans are present as well. Further examples are mixed traffic scenarios with autonomous vehicles and vehicles with human drivers or physically coupled shared control systems for teleoperation. In such scenarios, conflicts between the partners arise naturally and the theory of Dynamic Games (DG) (coupled dynamic optimization problems) is promising to resolve such conflicts and realize equilibrium solutions between the partners. However, to find such solutions the cost functions, i.e. the optimization criteria, of all partners/players need to be known. Since this is typically not the case, e.g. the human cost function is usually unknown, so-called Inverse Dynamic Game (IDG) methods are needed that infer the cost functions from measurement data. This inverse problem to DGs was insufficiently researched before this project and the only existing methods showed high computation times. During the project, we first formulated a formal problem definition of IDGs and developed several computational efficient methods to solve it, which even enable identification of the cost functions in real-time. Additionally, we provided a theoretical analysis of all developed methods, which treats the non-uniqueness of the IDG problem by formulating a set of all possible cost function combinations that are able to explain the measurement data and thus, reflect the players’ behavior. Finally, we looked at the application of the newly developed methods to real-world data. Here, conditions were stated when the newly developed methods can be applied. As practical example, we investigated whether a DG is a general model for the multi-agent collision avoidance behavior of robot platforms controlled by either humans or autonomously. On one side, the practical example highlighted the necessity to consider the application conditions of our newly developed methods described before. On the other side, the example showed that in future a DG model can be promising to describe the collision avoidance behavior between humans, although it turned out to be not generally applicable. For example, situations where the robots are controlled by arbitrary automation algorithms could not be well described by a DG.
Projektbezogene Publikationen (Auswahl)
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Solution Sets for Inverse Non-Cooperative Linear-Quadratic Differential Games. IEEE Control Systems Letters, 3(4), 871-876.
Inga, Jairo; Bischoff, Esther; Molloy, Timothy L.; Flad, Michael & Hohmann, Soren
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Validation of a Human Cooperative Steering Behavior Model Based on Differential Games. 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), 3124-3129. IEEE.
Inga, Jairo; Flad, Michael & Hohmann, Soren
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Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control. IEEE Transactions on Automatic Control, 65(2), 897-904.
Molloy, Timothy L.; Inga, Jairo; Flad, Michael; Ford, Jason J.; Perez, Tristan & Hohmann, Soren
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“Inverse Dynamic Games Based on Maximum Entropy Inverse Reinforcement Learning”
J. Inga, E. Bischoff, F. Köpf & S. Hohmann
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“Online Inverse Linear-Quadratic Differential Games Applied to Human Behavior Identification in Shared Control”, Proceedings of the European Control Conference, 2021.
J. Inga, A. Creutz & S. Hohmann
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Inverse Noncooperative Dynamic Games. Communications and Control Engineering, 143-187. Springer International Publishing.
Molloy, Timothy L.; Inga, Charaja Jairo; Hohmann, Sören & Perez, Tristan
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Inverse Stochastic Optimal Control for Linear-Quadratic Gaussian and Linear-Quadratic Sensorimotor Control Models. 2022 IEEE 61st Conference on Decision and Control (CDC), 2801-2808. IEEE.
Karg, Philipp; Stoll, Simon; Rothfus, Simon & Hohmann, Soren
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Excitation for Adaptive Optimal Control of Nonlinear Systems in Differential Games. IEEE Transactions on Automatic Control, 68(1), 596-603.
Karg, Philipp; Kopf, Florian; Braun, Christian A. & Hohmann, Soren
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“Inverse Dynamic Optimization and its Application to Human-Machine Systems”, Workshop of the VDI/VDE-GMA FA 2.15, 2023.
P. Karg & S. Hohmann
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Trustworthiness of Optimality Condition Violation in Inverse Dynamic Game Methods Based on the Minimum Principle. 2024 IEEE Conference on Control Technology and Applications (CCTA), 824-831. IEEE.
Karg, Philipp; Kienzle, Adrian; Kaub, Jonas; Varga, Balint & Hohmann, Sören
