A three-dimensional predictor-corrector entry guidance based on reduced-order motion equations

A three-dimensional predictor-corrector entry guidance algorithm is proposed in this paper. More accurate solutions of flight path angle and velocity are obtained with the guidance algorithm to reduce the order of motion equations, which greatly lower the amount of calculation for generating on-board three-dimensional trajectories. By planning two bank angle reversals, the burden on attitude control system is significantly reduced and the reliability of the lateral guidance is well guaranteed. Using the developed solutions and integrating the reduced-order motion equations numerically, the three-dimensional trajectory planning problem is transformed into two one-parameter searching problems: one is for the right guidance parameter and the other one is for the bank angle reversal points. Given the guidance parameter and bank angle reversal points, a feasible three-dimensional trajectory can be generated quickly and the guiding commands for the vehicle heading towards the landing site can be directly obtained. By comparing with the actual guided entry trajectory, the feasibility of the planned three-dimensional entry trajectory is evaluated. Though there are some differences between them, the actual trajectory is well approximated with the present method. Additionally, extensive numerical simulations have been carried out to test the validity and robustness of the proposed entry guidance algorithm. The simulation results demonstrate that the entry guidance works well and has a good flexibility.