Abstract:This paper studies the safety formation control of multi-agent systems in complex environments containing convex obstacles, non-convex obstacles and narrow gaps. Based on the Finite-time convergence Control Barrier Function(FCBF) and Iterative Regional Inflation by Semi-definite programming(IRIS), a safety formation control law is proposed to ensure the safety of the multi-agent systems while moving towards the target position. In particular, IRIS is used to abstract the obstacle-free space into elliptical safety regions, and the centers of the ellipse are set as a navigation point. FCBF is used to ensure that the multi-agent systems safely reach the target position while passing through the navigation point. FCBF is designed with geometric constraints and elliptical safety regions to achieve safety by ensuring forward invariance. This paper also incorporates the distributed control of multi-agent systems and designs a QP-based controller for each agent, that is, solves quadratic programming problems (QP) by using the designed CBFs as constraints. Finally, the feasibility of the algorithm in complex environments is verified by simulation.