Distributed Topology Fault-Tolerant Formation Control Based on Rigid Topology Optimization and Reconstruction

This paper mainly studies three-dimensional (3D) distributed topology fault-tolerance among multi-agent systems (MASs). Considering the link quality and energy consumption factors, the weight function is designed. Combined with rigid graph theory, by studying the transitivity of rigid graph, the relationship between local optimal rigidity and global optimal rigidity, and the substitutability of local rigidity, the edge deletion operation is proposed and its feasibility is proved. Through the above theory and operation, a 3D distributed optimal rigid topology generation algorithm is designed, which ensures 3-degree of MAS. Furthermore, after analyzing the interaction topology problem of formation, a fault-tolerant control algorithm of distributed optimal rigid topology is designed. Finally, combined with the problem of formation control with switching topology, the effectiveness of the proposed algorithm is verified by simulation.