Data-driven modeling and predictive control of non-holonomic systems in the Koopman framework

• Applicants: Professor Dr.-Ing. Peter Eberhard, since 11/2024; Professor Dr. Karl Worthmann
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545246093

In this proposal, we deal with the data-driven modeling and predictive control of non-holonomic vehicles using extended dynamic mode decomposition (eDMD) in the Koopman framework. Both individual vehicles as well as cooperative teams of vehicles, alongside distributed predictive control, are considered. Non-holonomic vehicles are the archetype of mechanical systems with non-holonomic constraints and are of high practical relevance, e.g., in transportation and robotics. In particular, the considered system class is interesting from a system-theoretic perspective, e.g., since the underlying sub-Riemannian geometry makes measuring distances more intricate and thwarts control approaches building upon local arguments made on the basis of linearization. At the same time, building highly accurate models of such systems a priori can be difficult due to effects such as wheel slip, manufacturing inaccuracies, and time-varying effects such as wear. This is exacerbated when fleets of robots are used for cooperative task solution, where each system may behave perceptibly differently. To face these theoretical and practical challenges, the project will contribute to four key areas. Firstly, methods and guidelines for learning data-based surrogate models for prediction are developed following a training/validation/test paradigm, where in each step, different hardware manifestations of non-holonomic systems are considered. Key considerations include whether the non-holonomic constraints will be properly reflected in the learned models and how data can be appropriately sampled to also learn second-order effects. Secondly, a framework for predictive control based on the inferred models is developed. Since the learned system will not be controllable in the full lifted space, preventing the direct application of recent theory for the control of non-holonomic systems, the existing theoretic framework will be extended to deal with control on controllable manifolds with positive semi-definite cost. Thirdly, for sampling efficacy in applications such as robot fleets, transfer learning will be considered, tackling issues such as the exploration-exploitation trade off and data management at runtime. This enables the applicant to properly deal with time-varying effects like wear, where it is crucial that key characteristics like the non-holonomy, controllability properties, and symmetries are preserved in the data-driven surrogate model. The devised models will finally be used for distributed predictive control to achieve cooperative behavior where, potentially, each system may be considered through a different data-based model, going far beyond the start of the art, in which at best the simplest kinds of non-holonomic systems are considered for distributed predictive control.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr.-Ing. Henrik Ebel, until 11/2024