Published February 18, 2022 | Version v1
Journal article Open

Quaternion-based state-dependent differential Riccati equation for quadrotor drones: Regulation control problem in aerobatic flight

  • 1. Universidad de Sevilla


The quaternion is a powerful and common tool to avoid singularity in rotational dynamics in three-dimensional (3D) space. Here it has been particularly used as an alternative to Euler angles and rotation matrix. The application of the quaternion is exercised in quadrotor modeling and control. It changes the dynamics and represents a singularity-free attitude model. Here for the first time (for the best knowledge of authors), the state-dependent differential Riccati equation (SDDRE) control has been implemented on the quaternion-based model of a quadcopter. The proposed control structure is capable of aerobatic flight, and the Pugachev’s Cobra maneuver is chosen to assess the capability of the quaternion-based SDDRE approach. The introduced control simulator is validated by comparison with conventional dynamics based on Euler angles, controlled using a proportional-derivative (PD) controller on a normal regulation flight. The simulator successfully performed the Cobra maneuver and also validated the proposed structure. The more precision in regulation along with lower energy consumption demonstrated the superiority of the introduced approach.


This work is supported by the HYFLIERS project (HYbrid FLying-rolling with-snakE-aRm robot for contact inspection) funded by the European Commission H2020 Programme under grant agreement ID: 779411 ( The work has also been partially funded by the European Commission H2020 Programme under AERIAL-CORE project 871479.


Preprint quaternion.pdf

Files (1.9 MB)

Name Size Download all
1.9 MB Preview Download

Additional details


HYFLIERS – HYbrid FLying-rollIng with-snakE-aRm robot for contact inSpection 779411
European Commission
AERIAL-CORE – AERIAL COgnitive integrated multi-task Robotic system with Extended operation range and safety 871479
European Commission