Study on trajectory optimization for single-stage-to-orbit space planes using gauss pseudospectral method

A direct optimization algorithm, which satisfies multiple path and terminal constraints, is proposed to generate the optimal trajectories for the single-stage-to-orbit space planes. Minimum fuel cost is selected as the optimality criterion in this method, and a segment strategy of the ascent trajectory is proposed according to the characteristics of the combined engines. The optimal control problem is transformed into a multi-stage optimal control problem, and a Gauss pseudo-spectral method is used to solve the parameterized control variables. Both the numerical simulations and simplified calculation based on the Gauss pseudospectral method are carried out to test the effectiveness and robustness of the proposed algorithm. Results demonstrate that the algorithm can rapidly generate the optimal ascent trajectory for single-stage-to-orbit space planes and achieve complex flight missions.