Three-dimensional event-triggered fixed-time cooperative guidance law against maneuvering target with the constraint of relative impact angles

In order to improve the flexibility and reduce the energy consumption of cooperative guidance laws considering the impact angle constraint, this paper proposes a three-dimensional event-triggered fixed-time cooperative guidance law with the constraint of relative impact angles. First, for the purpose of avoiding the precision degradation due to the estimation error of time-to-go especially facing a maneuvering target, the range-to-go and velocity along the line-of-sight (LOS) are taken as the coordination variables for achieving time-cooperative guidance. Secondly, instead of assigning specific desired impact angles for each missile, only the consensus errors of relative impact angles are utilized as the coordination variables for achieving space-cooperative guidance, which can avoid continually maneuvering for maintaining the constant desired impact angles, thus reducing the fuel consumption. Next, the guidance laws along the LOS and perpendicular to the LOS are developed, and the event-triggering mechanisms are designed to reduce the update frequency of cooperative guidance commands, thus further reducing the energy consumption. To guarantee the convergence rate, the fixed-time control theory is adopted and the stability of proposed event-triggered cooperative guidance laws are rigorously proved. In addition, it is also proved that there is no Zeno behavior when implementing the proposed event-triggered cooperative guidance laws. Finally, numerical simulations indicate that the strictly simultaneous attack is achieved and the constraint of relative impact angles is satisfied. Comparative studies demonstrate that the computation burden of cooperative guidance commands is relaxed and the fuel consumption is reduced by the proposed event-triggered cooperative guidance laws with the constraint of relative impact angles.