高超声速滑翔飞行器再入轨迹快速、高精度优化

针对高超声速滑翔飞行器再入轨迹优化问题，提出一种基于稀疏差分法和网格细化技术的快速、高精度求解方法。该方法应用局部配点法将再入轨迹优化问题转化为非线性规划(NLP)问题，从两方面提高轨迹优化的效率和精度。一方面，引入一种高效的稀疏差分法计算NLP的一阶偏导数，提高NLP的求解效率；另一方面，提出一种基于新型广义二分网格的网格细化算法调整离散节点的数量和分布，使得方法能够采用较少的节点数目取得较高的优化精度，从而减小NLP的规模和计算量。应用该方法求解了高超声速滑翔再入轨迹优化问题，仿真结果表明所述方法能够快速生成一条严格满足各种约束的最优三维再入轨迹。在此基础上，研究了滑翔飞行器的再入落点区范围，进一步检验了该方法的有效性。

Rapid and High Accuracy Approach for Hypersonic Glide Vehicle Reentry Trajectory Optimization

 A method based on sparse difference and mesh refinement is proposed for hypersonic glide reentry trajectory optimization. The method converts the trajectory optimization into the nonlinear programming (NLP) using the local collocation method and the efficiency and accuracy are improved in two aspects. On the one hand, an efficient sparse difference method is introduced to calculate the first-order partial derivatives of the NLP functions so that the NLP can be solved efficiently. On the other hand, an adaptive mesh refinement method is proposed to refine the mesh so that the high accuracy can be achieved with a smaller mesh size, thereby reducing the NLP size and the computational load. The proposed method is applied to the maximum cross range optimization of a hypersonic glide reentry vehicle. The numerical results show that the method can generate an optimal three-dimensional reentry trajectory satisfying all constraints rapidly. Furthermore, the landing footprint of the hypersonic glide reentry vehicle is studied using the method, which further demonstrates the effectiveness of the method.