Launch vehicle ascent trajectory optimization based on modified Gauss Pseudospectral method

A direct method is discussed for multistage launch vehicle ascent trajectory optimization. First the optimal control problem is modeled with the performance index as maximum terminal mass. A modified Gauss Pseudospectral method is used to design a rapid optimal algorithm for multistage launch vehicle ascent trajectory. The nonlinear terminal state constraints are converted into linear terminal state constraints through state equation matrix and Gauss weight coefficient. Based on linear gravity assumption, the analytical vacuum solution is obtained and used as initial guess. The simulation shows that the proposed algorithm can achieve the trajectory optimal goal with high precision and rapid convergence when all the terminal and path constraints are satisfied.