Distributed iterative learning control for multi-agent systems Theoretic developments and application to formation flying

摘要

The goal of this work is to enable a team of quadrotors to learn how to accurately track a desired trajectory while holding a given formation. We solve this problem in a distributed manner, where each vehicle has only access to the information of its neighbors. The desired trajectory is only available to one (or few) vehicle(s). We present a distributed iterative learning control (ILC) approach where each vehicle learns from the experience of its own and its neighbors' previous task repetitions and adapts its feedforward input to improve performance. Existing algorithms are extended in theory to make them more applicable to real-world experiments. In particular, we prove convergence of the learning scheme for any linear, causal learning function with gains chosen according to a simple scalar condition. Previous proofs were restricted to a specific learning function, which only depends on the tracking error derivative (D-type ILC). This extension provides more degrees of freedom in the ILC design and, as a result, better performance can be achieved. We also show that stability is not affected by a linear dynamic coupling between neighbors. This allows the use of an additional consensus feedback controller to compensate for non-repetitive disturbances. Possible robustness extensions for the ILC algorithm are discussed, the so-called Q-filter and a Kalman filter for disturbance estimation. Finally, this is the first work to show distributed ILC in experiment. With a team of two quadrotors, the practical applicability of the proposed distributed multi-agent ILC approach is attested and the benefits of the theoretic extension are analyzed. In a second experimental setup with a team of four quadrotors, we evaluate the impact of different communication graph structures on the learning performance. The results indicate, that there is a trade-off between fast learning convergence and formation synchronicity, especially during the first iterations.