Simultaneous trajectory optimization framework for lunar ascent with terrain

This paper proposes a simultaneous trajectory optimization framework to determine the optimal trajectory of lunar ascent with terrain. By considering the influence of the rotation of the moon, a three-dimensional kinematics and dynamics model for the lunar ascent process is given. To ensure flight safety, the terrain model is considered the collision-free path constraints of this trajectory optimization problem. Moreover, the terminal position and velocity are transformed into orbit elements as terminal insertion constraints. The maximum angular rate of the pitch and yaw angle is also constrained. Given that lunar ascent is subject to the tradeoff between fuel and payload, as well as to conserve fuel for possible contingencies, minimum fuel use is used as the performance index. The formulated trajectory optimization problem is discretized into a nonlinear programming (NLP) problem by the hp-adaptive pseudospectral method, which is used to deal with the complex terrain constraints. The initial values for solving the NLP problem are generated by the homotopy-based backtracking strategy. Four scenarios are designed to test the capability of the proposed simultaneous trajectory optimization framework for lunar ascent with terrain. Simulation results indicate that the proposed simultaneous trajectory optimization framework has enough adaptability to efficiently address the lunar ascent trajectory optimization problem with complex terrain constraints. The results of this study will benefit future autonomous lunar ascent missions.