Multi-Agent Consensus Theory for Formation Control

In multi-agent consensus theory, the adjacency matrix is defined according to the topological structure of multi-agent systems. This adjacency matrix serves as the fundamental component for controlling formation movement, where multiple agents achieve a predetermined formation configuration. The implementation typically involves defining neighborhood relationships through matrices, where each element a_ij indicates the connection strength between agent i and agent j. Agents start from dispersed initial positions and gradually converge through local interaction protocols, often implemented with consensus algorithms like: x_i(k+1) = x_i(k) + εΣa_ij(x_j(k) - x_i(k)) where x_i represents the state of agent i, and ε is the control gain. This cooperative process enables the entire system to achieve formation objectives through distributed coordination, without centralized control. Such formation movement finds extensive applications in military, industrial, and civilian domains, including UAV formations, automated warehouse systems, and intelligent transportation networks, where precise spatial coordination is critical. Key functions in implementation typically include topology representation, consensus computation, and formation error minimization through gradient-based control laws.