Trajectory Tracking for Quadrotors with Attitude Control on $\mathcal{S}^2 \times \mathcal{S}^1$

The control of a quadrotor is typically split into two subsequent problems: finding desired accelerations to control its position, and controlling its attitude and the total thrust to track these accelerations and to track a yaw angle reference. While the thrust vector, generating accelerations, and the angle of rotation about the thrust vector, determining the yaw angle, can be controlled independently, most attitude control strategies in the literature, relying on representations in terms of quaternions, rotation matrices or Euler angles, result in an unnecessary coupling between the control of the thrust vector and of the angle about this vector. This leads, for instance, to undesired position tracking errors due to yaw tracking errors. In this paper we propose to tackle the attitude control problem using an attitude representation in the Cartesian product of the 2-sphere and the 1-sphere, denoted by $\mathcal{S}^2\times \mathcal{S}^1$. We propose a non-linear tracking control law on $\mathcal{S}^2\times \mathcal{S}^1$ that decouples the control of the thrust vector and of the angle of rotation about the thrust vector, and guarantees almost global asymptotic stability. Simulation results highlight the advantages of the proposed approach over previous approaches.

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.