Three-Dimensional Trajectory Optimization for Lunar Ascent Using Gauss Pseudospectral Method

In this paper, the problem of fuel-optimal lunar ascent trajectory optimization using constant-thrust propulsion is considered. The whole lunar ascent process is divided into two phases: vertical-rise phase and orbit-insertion phase, respectively. Considering the influence of rotation of the moon, a three-dimensional kinematics and dynamics model for lunar ascent is established. The fuel-optimal lunar ascent trajectory optimization problem is posed as a two-phase constrained nonlinear trajectory optimization problem solved by using Gauss pseudospectral method. Initial guesses for this trajectory optimization problem are obtained by solving a subproblem where the angular rate of pitch angle and yaw angel is not constrained. Four scenarios of the two-phase lunar ascent trajectory optimization problem are designed. The simulation results show that all state and control variables satisfy the related constraints and practical engineering condition in each scenario. The developed direct trajectory optimization framework has the adaptability to address various scenarios of the two-phase lunar ascent mission.