Dynamic affine formation control of networked under-actuated quad-rotor UAVs with three-dimensional patterns

This paper focuses on the solution to the dynamic affine formation control problem for multiple networked under-actuated quad-rotor unmanned aerial vehicles (UAVs) to achieve a configuration that preserves collinearity and ratios of distances for a target configuration. In particular, it is investigated that the quad-rotor UAVs are steered to track a reference linear velocity while maintaining a desired three-dimensional target formation. Firstly, by integrating the properties of the affine transformation and the stress matrix, the design of the target formation is convenient and applicable for various three-dimensional geometric patterns. Secondly, a distributed control method is proposed under a hierarchical framework. By introducing an intermediary control input for each quad-rotor UAV in the position loop, the necessary thrust input and the desired attitude are extracted. In the attitude loop, the desired attitude represented by the unit quaternion is tracked by the designed torque input. Both conditions of linear velocity unavailability and mutual collision avoidance are also tackled. In terms of Lyapunov theory, it is prooved that the overall closed-loop error system is asymptotically stable. Finally, two illustrative examples are simulated to validate the effectiveness of the proposed theoretical results.