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

Abstract

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 S 2 × S 1 . We propose a non-linear tracking control law on S 2 ×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.

Geometric Reduced-Attitude Control of Fixed-Wing UAVs

“…In [64], the reduced attitude is steered along a geodesic path, while the full attitude is stabilized. In [65,66], the attitude control of a quadrotor is decoupled into thrust-vector control on S 2 , and control of the angle of rotation about the thrust vector. A similar approach is taken in [67] with a control allocation strategy that allows to prioritize reduced-attitude correction over yaw errors.…”

Constrained Control Allocation Approaches in Trajectory Control of a Quadrotor Under Actuator Saturation

“…This control law effectively decouples the reduced attitude error dynamics from the yaw. Decoupled attitude controllers have seen a rise in interest in recent years for this very purpose, with novel controllers being published in [5,20,21].…”