Central Difference Convexification Method for Soft-Landing Trajectory Optimization in Planetary Powered Descending Phase

Aiming at the mission of real-time online guidance for fixed-point soft landing on planet, the paper designs an algorithm based on sequential convex optimization that is designed to solve the fuel-optimal trajectory. The pre-labeled central difference algorithm is used to linearize the dynamics equations and the termination condition based on the deviation of index is proposed to judge whether it converges, which can generate a fuel-optimal trajectory quickly. Besides, a fitting function is given to approximately estimate the optimal terminal time by analyzing the relationship between the terminal time of optimal trajectories and their remaining fuel, which can reduce the amount of unknown variables. The simulation results of this algorithm show the weak sensitivity to initial guess, good convergence and small terminal error compared to the traditional convexification method of linearizing the dynamics equations whose variables are substituted at first.