Side Laplacian Methods And Applications In Multiple Body Systems

With the progress of technological and development of scientific, multi-agents research is developing rapidly, consensus problems is one of the important research topics in multi-agent systems, In this paper, it studied a new method----edge Laplacian, of consistency in the formation control. The main content is as follows:1. The problem of state consistency and edge agreement are characterized. Edge Laplacian is introduced and summarized the nature of edge Laplacian. It get the similarity transformation between the graph and edge Laplacians through some theorems and proofs.2. It defined a reference formation of admissible, and described in detail the application of the edge Laplacian in the formation control by Measurement—restricted system and Control—restricted system, obtained the dynamic equations of the system of reduced—order system. Discussed the spanning tree and cycle of the topology of the system, observed that the formation error can be driven to the origin by utilizing the controls only on the tree edges, and neglecting the controls on the cycle edges.3. Cycles will improve the convergence rate of the edge agreement protocol, therefore, it provided the improved performance controllers and simulation.4. It pointing out how our analysis for formation consisting of agents with first order dynamics can be extended to those with double integrator dynamics.5. In the last, it discussed the edge Laplacian and nonlinear agreement. The actual physical model has many is nonlinear system, so the research of nonlinear system is very meaningful.