Projektdaten

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

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In this proposal, we deal with the data-driven modeling and predictive control of non-holonomic vehicles in the Koopman framework. Both indiviual 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. However, the considered system class is not only of practical importance, but also interesting from a system-theoretic perspective. Even the simplest representative, i.e., the differential-drive mobile robot, exhibits the typical characteristics that render this system class challenging for controller design. For example, Brockett’s condition is violated such that there does not exist a continuous, static state-feedback law solving the set-point stabilization problem. This is linked to the fact that arguments based on linearization are of limited use even locally, unlike for many other nonlinear systems. The reason is that key properties like controllability are not preserved when linearizing. These facts are the reason why feedback control of such systems remains a topic of current interest [12], in particular for predictive control, see, e.g., [9] and the references therein. Furthermore, non-holonomic vehicles are also interesting from a modeling perspective. To automate their behavior, accurate models are key for tasks such as motion planning and modelbased closed-loop control. To that end, in robotics, often simple nominal kinematic models based on first principles are employed because it can be arduous to derive first-principles models that take into account higher-order effects. In particular, if such a model is derived, it anyway needs to be calibrated with measurement data to identify its parameters hard to determine a priori, e.g., those pertaining to friction. However, while coarse, kinematic first-principles models are often easy to obtain, their accuracy is usually limited, especially for high-fidelity tasks, e.g., since inertia as well as wheel-floor contacts, wear, and manufacturing imperfections are not taken into account. Wear and imperfections can make even seemingly identical robots behave characteristically differently, giving indispensable value to data-driven methods. Indeed, effects like wear even induce timevarying dynamics such that even the very same robot may behave differently over time. Hence, an adaptation of a basic model to the particular data at hand is often required. Even more so, in robotics, increasingly, fleets of robots are employed for large-scale automation and cooperating teams or swarms of robots are considered for flexible, efficient, and resilient task solution. This means that many tailored models may need to be learned, making a time and data-efficient learning process paramount. In that regard, this project will show how physical a-priori knowledge can be incorporated into data-inferred models to increase efficiency and accuracy. Morever, this project will make use of transfer learning to jump-start the learning process for a further robot when given a baseline model. The same techniques can be used to adapt robot models to changes of the dynamics, e.g., due to wear. Predictive controllers tailored to the properties of the learned models will allow reliable performance both when operating individual robots and when operating cooperating robots in a distributed manner. The developed methods are not only analyzed theoretically and tested in simulations but also validated with real-world hardware experiments and data.