Formation Control for a Group of Autonomous Underwater Vehicles Subject to Switching Topologies and Time Delay Factor

The presence of switchable communication topologies in a multi-agent system‏ causes the adjacency, degree, and Laplacian matrices of the group, and finally, its Fiedler eigenvalue, to constantly change, thereby affecting the group consensus. The key motivation of this study is to design an appropriate control law to achieve group consensus and create a hexagonal motion formation in a group of autonomous underwater vehicles by considering switching communication topologies between agents. For this purpose, first, the six degrees of freedom mathematical model of each AUV is presented and then the relationship between the agents of the group is modelled through the graph theory. The leader-follower consensus control algorithm is then designed to form a hexagonal arrangement between the leader and the follower robots. The proposed consensus control algorithm has been assessed in two different scenarios: 1- Switching communication topology between the follower robots, 2- Switching communication topology between the follower robots with time delay factor.