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

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Abstract
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.

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