Propagated error correction of the gauss pseudospectral method for skip reentry trajectory planning

Gauss pseudospectral method (GPM) is one of the potential approaches to generate the optimal trajectory for skip reentry trajectory planning. However, there is an unacceptable propagated error between the trajectory results of the GPM and the propagated results via a separate Runge-Kutta propagator. In this paper, a strategy of error correction is proposed to solve this problem. Firstly, an augmented reentry model is established by transforming the load factor into an equality constraint. Then, two load relief methods are provided to restrain the load factor in the final phase. Finally, two different methods are used to reduce the propagated errors in two different phases of the trajectory based on the distribution of the propagated errors. Taking the skip reentry trajectory planning problem of Apollo, the results show that the peak value of the load factor is significantly reduced in the final phase, and the spherical distance between the trajectory results of the GPM and the propagated results reaches a smaller magnitude, which satisfies the practical requirement.