Re-understanding and improvement of the pseudo-spectral method for rapid footprint generation

A PS (pseudo-spectral) method with improved parameters is proposed for the rapid footprint generation of reusable vehicles. Three aspects of the method were explored, including the consistency of the discrete NLP (Nonlinear Programming) problem with the original problem, the impact of the NLP problems' convergence accuracy on the results, and the final convergence accuracy factors. The reasonable ranges of the IPOPT solver's convergence tolerance are redefined through these explorations. Furthermore, the solution process of the footprint is partially optimized. Finally, the results show that the method can fully improve the computational efficiency of solving the footprint using the PS method. The average time of each trajectory is minor than 0.9s, showing the parameter-improved PS method's superiority.