A Convex Optimization Framework for 6-DOF Lunar Powered Descent with a Normalized Finite Rotation Parameterization

There has been increasing interest in the Moon for deep space exploration missions in the last few decades. To accommodate fuel-optimal lunar landing missions, it is essential to develop a fast trajectory planning algorithm considering constrained six-degree-of-freedom (6-DOF) dynamics. On the one hand, the trajectory planning problem involves a coordination of the optimal fuel consumption and the vehicle’s position, velocity, and attitude, which requires computational efficiency. On the other hand, the initialization setup of the existing sequential convex optimization method provides the linear reference trajectory, which slows down the convergence of the iterative process. In this manuscript, an improved sequential convex programming algorithm is proposed to solve the minimum-fuel 6-DOF powered descent problem. Firstly, we suggest a trajectory planning method based on a normalized finite rotation formulation, which improves the efficiency of the computational processes. Secondly, we present an initial guess method that computes the projection-analogous gradient with respect to the terminal value, accelerating the convergence of the algorithm. The simulation results show that the proposed method improves computational efficiency, indicating the potential for future applications in autonomous landing missions.