Multi-Agent Formation Control with Size Scaling for Polyhedral Structures Based on Local Angular and Distance Information

This paper investigates the group control problem of multi-agent systems in three-dimensional space, aiming to achieve the formation task of polyhedral shapes through local angular and distance constraints, and to navigate around obstacles and through narrow spaces using scale scaling control. The configuration method of using the first three agents to form a triangular basic framework and then applying vertex addition to complete the formation of the remaining agents is discussed. In this approach, the measured angular information of the agents maintains the angular rigidity of the entire formation, ensuring the uniqueness of the formation shape. By measuring distance information through only one agent, the size of the entire formation is also uniquely determined. Additionally, a configuration method is proposed in which the first four agents form a rectangular basic framework, followed by vertex addition to complete the formation of the remaining agents. This method also ensures angular rigidity, and the inclusion of distance measurements uniquely determines the size of the entire formation. Finally, using a simplified model of Quadrotor Unmanned Aerial Vehicles (QUAVs), simulation experiments demonstrate the formation’s ability to flexibly change its size when encountering obstacles and to pass through narrow spaces, verifying the effectiveness of the proposed formation scheme.