Fuel-optimal powered descent guidance with free final-time and path constraints
Fuel-optimal powered descent guidance with free final-time and path constraints
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DOI：
10.1016/j.actaastro.2020.03.025
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发表时间：
2020-07
影响因子：
3.5
通讯作者：
Runqiu Yang;Xinfu Liu
中科院分区：
文献类型：
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作者：
Runqiu Yang;Xinfu Liu
本文提出了一种基于凸优化的方法来有效地获得具有自由最终时间和路径约束的燃料最优动力下降问题的数值解。为了避免猜测最终时间，我们建议选择高度而不是时间作为系统动力学的自变量。这一选择还带来了极大的便利，包括滑行坡度和推力方向约束，其中边界可以依赖于高度。然后，通过适当的凸化技术，将所建立的最优控制问题转化为凸问题，如非线性保持线性化方法和松弛技术等。松弛技术是一种关键技术，但分析其有效性通常是非常具有挑战性的，特别是在存在路径约束的情况下。在本文中，我们可以证明所采用的松弛是有效的。接下来，我们对凸问题进行离散化，并应用逐次凸优化得到原问题的解。然而，为了获得高精度和低计算量的解，我们提出了一种新的选择非均匀离散点的策略加四阶龙格-库塔或梯形离散化方法。数值结果表明了该方法在求解动力下降问题上的有效性和高效性，并揭示了当路径约束被激活时最优推力幅值分布的有趣结构。
This paper presents a convex optimization-based approach to efficiently obtain the numerical solution of the fuel-optimal powered descent problem with free final-time and path constraints. To avoid guessing the final-time, we propose to choose altitude, instead of time, as the independent variable in the system dynamics. This selection also brings great convenience in incorporating the glide-slope and thrust direction constraints in which the bounds can be altitude-dependent. Then, the formulated optimal control problem is converted into a convex problem via appropriate convexification techniques, such as the nonlinearity-kept & linearization approach and relaxation, etc. Relaxation is a critical technique, but analyzing its validity is generally very challenging, especially when path constraints are present. In this paper we can prove that the relaxation used is valid. Next, we discretize the convex problem and apply successive convex optimization to get the solution of the original problem. Nevertheless, in order to obtain the solution with high accuracy and low computational cost, we propose a new strategy of selecting nonuniform discretized points plus the Runge-Kutta 4th order or trapezoidal discretization method. Numerical results are provided to show the effectiveness and high efficiency of the proposed method in solving the powered descent problem and reveal an interesting structure of the optimal thrust magnitude profile when path constraints become active.