OQTAL: Optimal quaternion tracking using attitude error linearization

The use of quaternions or quaternion error attitude control strategies for unmanned aerial vehicles (UAVs) is commonplace. Quaternion tracking error control is usually presented in rather theoretical works, where the control algorithm is almost exclusively chosen to be a suboptimal one. However, the application of optimal control techniques is usually associated to simplified attitude models frequently aimed at solving real-life problems. The work presented in this paper aims to formally merge the development of a complete theoretical quaternion error model with an optimal control strategy. Moreover, the application of optimal control algorithms to a fully defined quaternion error state-space model and the validation of the same in a real-time experimental setup is the focus of this research. The result is a novel controller named Optimal Quaternion Tracking of Attitude Error Linearization (OQTAL). The paper provides a comprehensive proof of stability, full simulation validation for a planetary landing gravity turn trajectory, and evidence of repeatable experimental work for a real-time quadrotor UAV on a motion capture testbed. OQTAL is compared with proven optimal forms of (PID) proportional-integral-derivative control and linear quadratic regulator control and is shown to have a 10%-20% reduction in error for the experimental setup trajectory tracking trials and an even larger tracking error reduction in the gravity turn simulation trials. Furthermore, for close tracking conditions, OQTAL behaves almost like a linear and time-invariant system, therefore requiring limited computation time for performing the trajectory tracking.