To solve the problem of communication topology switching for UAV formation,a method for UAV formation control based on the joint errors is proposed.This method is essentially an extension of the consensus control theory.Based on the position of the UAV,an elastic look-ahead point is set.Using the position and velocity errors of each UAV,the linear state equation with the joint errors is established.The error feedback between other UAVs in the formation is introduced and an elasticity extension consensus controller is designed.The classic consistency controller is a special case for the extended consensus control in the case of not knowing certain errors between the UAVs.Finally,the stability of the fixed communication topology system is verified by using the Hurwitz stability analysis method,and the sufficient conditions for its stability are given.The condition of exponential convergence of switching communication topology is obtained by using Lyapunov stability analysis method.The simulation results show that the method can keep the formation stable under fixed and switched topologies and the elasticity formation can adapt to the speed change of the leader UAV.