Three-Dimensional Fixed-Time Cooperative Guidance Law with Impact Angle Constraint and Prespecified Impact Time

In this paper, by utilizing fixed-time control technique and a leader-follower control scheme, a three-dimensional (3-D) cooperative guidance law is developed to tackle impact angle constrained simultaneous arrival problem. Firstly, in the line-of-sight (LOS) direction, guidance command for the leader is put forward to make impact time error converge to zero in fixed time such that the leader is capable of reaching the target at prespecified impact time. Then, guidance command for each follower is designed based on information from adjacent interceptors to guarantee each follower's impact time achieves consensus with that of the leader. Secondly, in the azimuth direction and elevation direction of the LOS, guidance commands are put forward to nullify the LOS angular rates within fixed time. Then, the interceptors are able to reach the target with desired impact angles. Meanwhile, the cooperative guidance law's fixed-time convergence is rigorously proved by Lyapunov stability theory. Finally, simulations are given to illustrate the effectiveness of the theoretical results.