Four-Stage Guidance Law for Impact Time and Angle Control Based on the Bezier Curve

The impact-time-angle-control guidance (ITACG) law can control the impact time and angle in a wide range of applications. The previous ITACG research generally suffer from the accuracy under the time-varying velocity condition, or the axial acceleration is required under 3-D conditions. This article develops a four-stage guidance technique based on the Bezier curve, and it is effective in both 2-D and 3-D scenarios. First, we proved a proposition that the length of the two-stage Bezier trajectory increases monotonically with the initial flight path angle. Based on this, the four-stage guidance strategy is studied. The first stage is to adjust the impact angle in the line-of-sight coordinate system. The second stage is to change the heading angle to match the Bezier trajectory with the distance-to-go. The third stage tracks the Bezier trajectory generated in the second stage. The fourth stage uses the proportional navigation guidance law to realize the end-game guidance. The proposed strategy was extended to 3-D scenarios, where the algorithm performed well even under the influence of gravity and aerodynamic drag, achieving accurate impact angle and time with high robustness. Finally, the effectiveness of the proposed algorithm is verified through four sets of simulation experiments.