凸优化由于求解效率高在飞行器轨迹规划和制导中得到广泛研究应用。但是，由于火箭垂直返回制导需要考虑气动力带来的非线性，现有的凸优化求解方法或简单地采取逐次线性化近似凸化最优控制问题，经常出现收敛性问题；或需针对具体问题进行相应的系列凸化剪裁，虽然改善了收敛性，但不同模型的凸化剪裁方法差别很大，通用性较差。为此，将偏置比例导引与凸优化相结合，用以求解存在落角、落速和推力范围约束的火箭垂直返回定点软着陆制导问题。提出的制导方法将该制导问题分解为法向满足落角与落点约束的偏置比例导引，以及切向满足速度与推力约束的凸优化和滚动时域控制制导。在切向制导中，提出利用三次多项式近似飞行轨迹以方便凸优化求解，并建立剩余飞行时间的估算方法以提供给比例导引。仿真结果表明，提出的制导方法能有效满足各种约束，实现火箭精确着陆。与现有的直接采取逐次线性化近似的凸优化方法相比，提出的方法由于将制导进行切向和法向分解，大为简化了凸优化模型，显著提高了求解效率和收敛性。此外，提出的方法无需复杂繁琐的凸化处理，对于一般的推力可控且对末速存在约束的固定终端位置的制导问题皆适用。
The landing-phase guidance of launch vehicle is a typical nonlinear optimal control problem. With the convex optimization method, the landing-phase guidance can be effectively realized by being converted into a convex programming problem, while satisfying constraints. However, due to the nonlinearity of the landing-phase guidance, the optimal solution by convex optimization would oscillate and could not converge if only successive linearization is used. On the other hand, if variable substitution and relaxation convexification techniques are employed, the optimal solution can be clearly improved. However, different convexification techniques should be used for different convex optimization problems, lacking versatility. To address this issue, the bias proportional guidance and convex optimization are integrated to solve the landing-phase guidance of launch vehicle with the terminal track angle, velocity and thrust constraints. With the proposed method, normal guidance and tangential guidance are separated. The former adopts bias proportional guidance to satisfy the constraints on the terminal track angle and the landing point. For the latter, convex optimization and receding horizon control are employed to satisfy the constraints on the terminal velocity and the thrust constraint, and the method to estimate time-to-go and approximate trajectory parameters based on cubic curves, which could provide the necessary approximate state, is presented. The simulation results indicate that the convex optimization guidance method combined with the proposed guidance can effectively satisfy the constraints, and compared with the existing guidance method that directly adopts convex optimization and receding horizon control, the proposed method clearly improves the solution efficiency and smoothness of the control quantity. Therefore, it is more applicable to practical engineering.
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