基于自适应Radau伪谱法的再入段轨道设计算法

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

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.

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.