基于凸优化和LQR的火箭返回轨迹跟踪制导

可重复使用运载火箭动力减速段制导, 面临各种苛刻的过程约束、终端约束及燃料最省的迫切需求, 给制导带来巨大挑战。因此, 提出一种基于分段凸优化和线性二次调节器(LQR)的轨迹跟踪制导律。采用分段凸优化方法对火箭基准速度进行跟踪, 大幅简化了优化模型从而降低凸优化求解的计算量, 同时确保火箭在各种初始误差和模型误差的情况下燃料最省。采用LQR方法实现对火箭飞行位置轨迹的高精度跟踪, 抵抗各种误差和干扰的影响。仿真结果表明:相对于传统的LQR跟踪制导方法, 所提方法能大幅减少燃料消耗, 且在各种误差和干扰下具有较高的轨迹跟踪精度和较强的抗干扰能力；相比于现有的滚动凸优化方法, 所提方法能显著降低求解计算量, 且方法可靠性更高。 

Rocket return trajectory tracking guidance based on convex optimization and LQR

For the powered descent phase of the reusable launch vehicle, various strict process constraints, terminal constraints and requirements on fuel saving exist, which bring great challenges to the guidance. This paper proposes a trajectory tracking guidance method based on convex optimization and linear quadratic regulator (LQR). The improved receding horizon convex optimization method is used to track the reference velocity of the rocket without requiring accurate thrust control input, which greatly simplifies the optimization model, and thus saves the computational cost of solving the optimal control problem. Meanwhile, the fuel is reduced as far as possible under various initial errors and model errors. On the other hand, the LQR technique is used to track the position of the rocket with high precision. The simulation results show that compared with the traditional LQR tracking guidance method, the proposed method can obtain comparable tracking accuracy, while greatly reducing fuel consumption. And compared to the existing receding horizon convex optimization, the proposed method can evidently reduce the computational cost and improve reliability.