A new method of rapid trajectory optimization for Mars Pin-Point Landing

Aiming at planning the vehicle's entry trajectory for Mars Pin-Point Landing, a new method based on hp-Radau pseudospectral algorithm is proposed. The vehicle's dynamics, state constraints during Mars Entry phase and vehicle's mobility and safety constraints are taken into consideration synthetically. By combining the properties of collocation points of hp-Radau pseudospectral algorithm, the problem of trajectory optimization can be converted into a large-scale parameters optimization problem with multi-constraints, thus a solving framework of trajectory optimization is obtained. Also, the analytical form of Jacbian matrix of performance index and constraint equations is derived in order to improve the method's efficiency. The simulation result indicates that: (1) the hp-Radau pseudospectral algorithm can be used to solve the trajectory optimization problem during Mars Entry , and has more efficient performance compared with the radau pseudospectral algorithm; (2) Compared with the numeric difference method, the analytical form of Jacbian matrix could substantially increase the method's efficiency and time-consuming stability by 58.75% and 85.58% respectively.