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 dis-tances 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 for-mation. Firstly, by integrating the properties of the affine trans-formation and the stress matrix, the design of the target forma-tion 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 atti-tude are extracted. In the attitude loop, the desired attitude rep-resented 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 Lya-punov theory, it is prooved that the overall closed-loop error sys-tem is asymptotically stable. Finally, two illustrative examples are simulated to validate the effectiveness of the proposed theoreti-cal results.