Scalability Analysis of Algebraic Graph-Based Multi-UAVs Formation Control

In multiple unmanned aerial vehicle (UAV) formation control systems, high scalability can guarantee the formation stability when UAVs join in or leave the system, and thus improves the robustness of the formation flight. This paper investigates the scalability problem for multi-UAV formation control with double-integrator dynamics. To be more specific, we focus how to build communication links with fixed control parameters such that the formation can always keep stable when adding/removing arbitrary number of UAVs. A bio-inspired method - Veteran Rule is proposed to solve this problem. Compared to the existing methods, our proposed method does not require to re-design or adaptively adjust the control parameters/gains for the changed Laplacian matrix. Furthermore, the convergence rate of the system under the Veteran Rule is analyzed. Surprisingly, the convergence rate of the system reaches the maximum value when all the in-degrees equal a particular value, rather than goes to infinity. Moreover, to guarantee the robustness of the formation system, we study the tolerance on undesired communication links (which break our proposed Veteran Rule). An upper bound for the coupling strength of the undesired communication links is provided by using Gershgorin circle theorem. Finally, simulation results corroborate the effectiveness of our results.