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 paper 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.

A fixed-time nonlinear circular guidance law that satisfies the impact time constraint is proposed. By utilizing the geometric principle that the length of a circular arc connecting the missile and the target can be analytically calculated, the exact expression of time-to-go is obtained. Thus, the impact time error can be shaped to zero, and the missile can intercept the target at the desired time, which is crucial in a salvo attack. The settling time of the impact time error is proved to be bounded by a fixed time, which does not depend on initial conditions, but is only determined by two guidance parameters. Moreover, the criteria for choosing the guidance parameters values are established analytically, rather than by trial-and-error or empirically, which can provide valuable guidelines for guidance law designers. To address the look angle constraint, deviated pure pursuit (DPP) is employed, and switching logic between guidance laws is provided. Unlike many existing impact time control guidance laws, the formulation of the one proposed is based on nonlinear engagement kinematics, and the implementation does not execute numerical calculations, which can improve the guidance accuracy and reduce computation burdens on the guidance system. A series of nonlinear simulations are implemented to verify the effectiveness of the proposed guidance law.

To plan the path for unmanned aerial vehicles (UAVs) considering the impact angle and acceleration constraints, a novel geometric rule is proposed in this paper. Firstly, under the nonlinear engagement kinematics, the geometric rule is derived from the modified circular curve including two parameters, one for the convergence of the acceleration, the other for extending the flight envelope. Furthermore, the convergence of the nominal guidance law developed from the geometric rule is rigorously proved. Secondly, to eliminate the angle tracking error regardless of the initial error size, a fixed-time convergent controller is adopted to formulate the impact angle control guidance law. Moreover, the implementation of the proposed guidance law only requires angle information, which can be readily obtained by the on-board device. The proposed guidance law is also applicable for varying-speed UAVs and moving targets. The simulation results and the comparative studies demonstrate the validity and superiority of the proposed guidance law.