Transfer Learning for High-Precision Trajectory Tracking Through $\mathcal{L}_1$ Adaptive Feedback and Iterative Learning

Robust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined $\mathcal{L}_1$ adaptive control and iterative learning control (ILC) framework to achieve high-precision trajectory tracking in the presence of unknown and changing disturbances. The $\mathcal{L}_1$ adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses $\mathcal{L}_1$ adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high-level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined $\mathcal{L}_1$-ILC framework compared with approaches using ILC with an underlying proportional-derivative controller or proportional-integral-derivative controller. Results highlight that our $\mathcal{L}_1$-ILC framework can achieve high-precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller.

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

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.