Control Barrier Functions for Formation Control of Leader-follower Multi-agent Systems

Abstract: This thesis studies formation control for a class of general leader-follower multi-agent systems with Control Barrier Functions (CBFs) such that connectivity maintenance is fulfilled for all the neighboring agents. In leader-follower multi-agent systems, only the leader agents are controlled by the externally designed input, while the followers are guided through their dynamic couplings with the neighboring agents. The main problem is how to keep all adjacent agents maintain within the communication distance during the formation process. In this thesis, Control Barrier Functions (CBFs) are utilized in order to maintain connectivity among the neighboring agents. This thesis firstly introduces a general first-order leader-follower multi-agent systems with proper connectivity constraints. All edges in the system are divided into three categories: follower-follower edges, leader-follower edges and leader-leader edges. Three different kinds of edges are discussed individually. For each category, the relevant topological conditions and control barrier functions are defined and proved for both tree graphs and general graphs. Several simulation examples are implemented to verify the developed results. Both theory and simulation results show that the developed results are a strong support for the formation control of leader-follower system in order to achieve connectivity maintenance.