Study of Real-Time Online Closed-Loop Guidance Method Based on Adaptive Pseudo-spectral Method

At present, there are many methods for trajectory optimization problems in dealing with finite thrust orbit maneuvers, including indirect, direct, and hybrid methods. In this paper, a real-time optimal guidance method based on self-adaptive hp-Radau pseudo-spectral method which is sampled at free frequency is proposed. The detailed design method is given in the paper. We analyzed the objects and conditions applicable to the guidance method and the stability of the algorithm is proved by mathematical derivation. In this paper, the optimal analysis of the coplanar orbital lifting time is taken as an example. The simulation results show that the introduction of the guidance law ensures the stability and guidance accuracy of the system after the introduction of interference. It is proved that the adaptive real-time on-line closed-loop guidance law based on the hp-Radau pseudo-spectral method has higher computational efficiency and better convergence when dealing with the optimization problems with small number or range of orbital elements.