Graph Laplacian Based Distributed Formation Control And Distributed Localization

With the rapid development of communication technology,sensor technology and artificial in-telligence,multi-agent systems have shown active vitality in the fields of multi-robot cooperation and wireless sensor network,which has received wide attention from domestic and overseas re-searchers.Multi-agent systems are complex systems that consist of a large number of autonomous or semi-autonomous individuals which can communicate and interact with each other.In nature,some animals move in clusters,such as birds,fish,and ant colony.They carry out collective motions through inter-individual interaction and collaboration.Researchers are inspired by these intelligent characteristics,hoping that the agent(including but not limited to mobile robots,sensor nodes,unmanned aerial vehicles,ships)can cooperate to complete certain tasks.Distributed for-mation control and distributed localization are two key issues of multi-agent systems,which have become hot topics in recent years.For distributed formation control problem and distributed localization problem in 2D,the main contents of this paper are summarized as follows:For leader-follower networks,this paper studies the formation control problem under the di-rected and switching topology.As a first step towards the general problem,we assume that in the target configuration the followers lie in the convex hull spanned by the leaders.First,we suppose that the followers can obtain the speed of the leaders.Then we propose a distributed controller and obtain the necessary and sufficient condition to ensure the global convergence.Second,we release this hypothesis and consider that followers cannot obtain the speed of the leaders.A speed synchronization control based on the internal model principle is proposed and the same necessary and sufficient condition to ensure global convergence is obtained.For leader-follower networks under directed and switching topologies.We aim to release the assumption that in the target configuration the followers lie in the convex hull spanned by the lead-ers.According to the actual needs for the formation,we study the two formation control problems,that is,formation marching control and formation rotating control.For the above two formation problems,we consider directed and switching sensing topology,and address the communication topology which is undirected and switching.We propose an approach based on the barycentric coordinates to cope with the above two problems.Distributed controllers are developed and we obtain sufficient graphical conditions ensuring global convergence.For distributed localization with bearing-only measurements,we consider undirected and switching topologies.Each node has its own local coordinate system and has no knowledge about the global orientation.Each node can only measure the bearing of neighboring nodes in its local coordinate system.We propose a distributed localization algorithm based on complex Laplacian,which can overcome the challenge of lacking global coordinate system and switching topology.Sufficient graphical conditions are obtained such that the proposed distributed localization algo-rithm is globally convergent.For distributed localization with mixed measurements,we consider undirected and switching topologies.Each node has its own local coordinate system and has no knowledge about the global orientation.The key idea is to utilize the barycentric coordinate to transform the measurements in local coordinate systems to the linear equation constraints concerning the nodes' absolute co-ordinates in the global coordinate system.Thus the distributed localization problem with mixed measurements can be treated in a unified framework.Based on this unified framework,a distributed algorithm is proposed for each node to iteratively solve its absolute coordinate.A necessary and sufficient graphical condition is obtained to ensure global convergence.