基于自适应Radau伪谱法的再入段轨道设计算法

针对传统Radau伪谱法处理非光滑平面时精度不高和效率不足的缺点，提出了一种基于自适应Radau伪谱算法的再入段轨道设计算法。该算法可以根据状态方程的拟合精度对再入段轨道进行自适应调整。在轨道曲率较高的区域，通过增加区段数量提高计算精度；在轨道曲率较低的区域，通过提高插值多项式的阶次提高计算精度。仿真结果显示，该算法形成的配点分布更为合理，相对传统的Radau算法具有高精度、高效率等优点，求解效果优于传统的Radau伪谱法，可将其应用到再入段轨道优化的工程实际中。 

The Re-Entry Orbit Design Algorithm Based on an Adaptive Radau Pseudo-Spectral Method

To solve the problems of low accuracy and poor efficiency of the traditional Radau pseudo-spectral method in dealing with non-smooth surfaces, an adaptive Radau pseudo-spectral method was proposed to generate the optimal re-entry orbit. The algorithm could adjust the intervals adaptively according to the approximation precision of state equations. In regions of relatively high curvature, the accuracy was increased by dividing a segment into more mesh intervals, whereas in regions of relatively low curvature, accuracy was increased by increasing the degree of the approximating polynomial within a mesh interval. Simulation results show that the nodes distribution generated by the adaptive Radau pseudo-spectral re-entry orbit design algorithm is more reasonable and efficient than that of the traditional Radau pseudo-spectral method. The algorithm can be applied to re-entry orbit design in practical engineering due to its high efficiency and high precision.