High-Precision Trajectory Tracking in Changing Environments Through $\mathcal{L}_1$ Adaptive Feedback and Iterative Learning

Abstract: As robots and other automated systems are introduced to unknown and dynamic environments, robust and adaptive control strategies are required to cope with disturbances, unmodeled dynamics and parametric uncertainties. In this paper, we propose and provide theoretical proofs of a combined $\mathcal{L}_1$ adaptive feedback and iterative learning control (ILC) framework to improve trajectory tracking of a system subject to unknown and changing disturbances. The $\mathcal{L}_1$ adaptive controller forces the system to behave in a repeatable, predefined way, even in the presence of unknown and changing disturbances; however, this does not imply that perfect trajectory tracking is achieved. ILC improves the tracking performance based on experience from previous executions. The performance of ILC is limited by the robustness and repeatability of the underlying system, which, in this approach, is handled by the $\mathcal{L}_1$ adaptive controller. In particular, we are able to generalize learned trajectories across different system configurations because the $\mathcal{L}_1$ adaptive controller handles the underlying changes in the system. We demonstrate the improved trajectory tracking performance and generalization capabilities of the combined method compared to pure ILC in experiments with a quadrotor subject to unknown, dynamic disturbances. This is the first work to show $\mathcal{L}_1$ adaptive control combined with ILC in experiment.