In recent years, convex optimization has been widely applied in aircraft trajectory optimization and guidance. For rocket vertical landing, the dynamics are highly nonlinear, which easily causes convergence issues in convex optimization. Moreover, for the existing convex optimization methods, it is difficult to implement landing guidance with a performance-limited engine in which the thrust cannot be continuously and instantly regulated. To address these two issues, a novel rocket vertical landing guidance method is developed, in which the guidance in the normal and tangential planes with respect to the rocket velocity is separated to enhance the convergence property of convex optimization. Normal guidance adopts biased proportional navigation to easily satisfy the pinpoint landing with the required attitude angles. For tangential guidance, convex optimization and model predictive control are employed to optimize the thrust command that satisfies the landing velocity limit. Based on this, an impulse equivalent transformation method is designed to derive thrust commands that satisfy the engine limits. Simulation results indicate that the proposed guidance method can achieve precise landing and satisfy various constraints while being highly robust to uncertainties. Moreover, the efficiency, convergence property, and control smoothness are significantly improved.

近年来，凸优化在飞机轨迹优化和制导中得到了广泛的应用。对于火箭垂直着陆，动力学是高度非线性的，这容易导致凸优化中的收敛问题。此外，现有的凸优化方法难以在推力无法连续瞬间调节的性能受限的发动机上实现着陆引导。针对这两个问题，提出了一种新的火箭垂直着陆引导方法，该方法将火箭速度的法向平面和切向平面上的引导分离，以增强凸优化的收敛性。正常制导采用偏置比例导航，轻松满足所需姿态角的精确着陆。对于切向引导，采用凸优化和模型预测控制来优化满足着陆速度限制的推力指令。在此基础上，设计了一种脉冲当量变换方法来推导满足发动机限制的推力指令。仿真结果表明，所提出的制导方法可以实现精确着陆，满足各种约束条件，同时对不确定性具有很强的鲁棒性。此外，显着提高了效率、收敛性和控制平滑度。仿真结果表明，所提出的制导方法可以实现精确着陆，满足各种约束条件，同时对不确定性具有很强的鲁棒性。此外，显着提高了效率、收敛性和控制平滑度。仿真结果表明，所提出的制导方法可以实现精确着陆，满足各种约束条件，同时对不确定性具有很强的鲁棒性。此外，显着提高了效率、收敛性和控制平滑度。