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.