Three-Dimensional Dynamic Formation of Second-Order Multi-Agent System Based on Rigid Graphs

This paper studies the dynamic formation control of second-order multi-agent systems (MASs) in three-dimensional space based on the distance control approach. A rigid graph represents the communication topology between agents to improve the system’s robustness and stability and avoid collisions and deformations during formation operation. A distributed control strategy based on the relative states among neighbors is designed for each agent to achieve formation and formation maintenance under arbitrary initial conditions. The Lyapunov function, an error function of potential and kinetic energy, is constructed by rigid graph theory and a second-order integrator model. The decreasing of the Lyapunov function is proven by Barbalat’s theory, further indicating that the system is asymptotically stable. A second-order MAS composed of nine agents is constructed, and the dynamic scaling of rigid formations in 3D space is achieved through simulation to verify the effectiveness of the controller and the correctness of the theory.