Formation Of Multi-agent Systems Based On Complex Laplacian

With the continuous progress and development of science and technology,the tasks that people need to complete are becoming more and more complex,and it is difficult for a single agent with limited capabilities to deal with complex tasks.Multi-agent systems have received a lot of attention from scholars as they can not only improve efficiency but also accomplish tasks that cannot be accomplished by a single agent through inter-agent collaboration.The research of multi-agent systems includes formation control,flocking problems,rendezvous problems and so on,formation means that the agent can move to a specific target or direction in a preset geometric shape.At present,there are many methods to study formation control,once the preset formation of most formation control methods is completed,switching to another formation often requires changing the control protocol of many agents or even all agents.The method of studying the formation of multi-agent systems based on the complex Laplacian matrix only needs to change the control protocol of the two agents to switch to any formation after the combination of translation,rotation and scaling of the desired formation.However,in most of the literature,the two leaders are fixed and the collision between agents and obstacles is not considered.To solve this problem,this thesis studies the obstacle avoidance and formation problems of the optional dual-leaders multi-agent systems based on the approach of the complex Laplacian matrix,the main research work and results are as follows:(1)The explicit expression that each agent converges to its final state when only using the complex Laplacian matrix to complete the formation is derived,which is jointly determined by the initial values of the agents and the left eigenvector corresponding to the two zero eigenvalues of the system matrix.An algorithm for solving the left eigenvector corresponding to the two zero eigenvalues of the system matrix is proposed,and the validity of the displayed expression is verified by simulation on MATLAB.In addition,the influence of the communication topology of the multi-agent system on the final state of convergence of each agent is analyzed.(2)Based on the formation of complex Laplacian matrix,a method of controlling two leaders to achieve static formation is proposed.Two agents named leaders at the position of the 2-rooted of the system matrix is selected and the control protocol is designed for these two leaders to make them move to the preset two fixed points.The remaining agents are constantly affected by the two leaders in the communication process to realize the preset fixed-point formation,the final formation position is only determined by the two leaders.In addition,the artificial potential field method is used to prevent collisions between agents and obstacles,and obstacle avoidance control protocols are designed for each agent.The simulation results verify that the agent avoids collisions with obstacles while completing the static formation.(3)On the basis of using complex Laplace matrix to realize static formation,a method of controlling two leaders to realize dynamic formation is proposed.The two agents at the locations of 2-rooted are selected as the leaders,a control protocol is designed for them that the two leaders can track linear motions or curved motions that do not change drastically.The rest of the agents are constantly affected by the two leaders during the communication process,and all agents can maintain the preset formation of motion when they move in a straight line or a curve that does not change drastically.After the corresponding obstacle avoidance strategy is designed for each agent,even if there are obstacles during the movement,the original formation will not change drastically and the formation can immediately resume and continue to move after agents complete the obstacle avoidance operation.