State-Transformation-Based Recursive Design Strategy for Leader-Follower Safety Formation Control of Uncertain Multiple Quadrotors

This study is aimed at addressing the adaptive leader–follower safety formation control problem for multiple quadrotors with limited measurement range, unknown disturbances, and thrust saturation. We develop a novel state-transformation-based unified design strategy to solve the underactuation and nonlinear input coupling problems of quadrotors without dividing the outer and inner loop subsystems. First, the state transformation technique is introduced to extract virtual control variables from nonlinear coupled terms combined with the thrust input. Then, a unified formation error is designed to ensure safe formation tracking between the leader and followers with limited measurement range. In the design of a controller, compensating signals using radial basis function neural networks are introduced to compensate for unknown nonlinear terms and develop a modified command-filtered backstepping method. The proposed approach outperforms the existing hierarchical designs and can effectively avoid collisions between quadrotors, even in scenarios with thrust saturation and external disturbances. The Lyapunov stability theory is used to demonstrate that all the errors in the closed-loop system are bounded and can be arbitrarily reduced. Finally, comparative analyses are performed based on simulations to verify the effectiveness of the proposed theoretical approach.