序列凸优化的小天体附着轨迹优化

针对小天体附着多约束轨迹优化问题，提出一种基于序列凸优化的轨迹优化方法。首先采用内球谐引力场模型对目标小天体附近的不规则引力场进行精确建模，内球谐引力场模型是对经典球谐系数法的改进，形式简单，计算量小，并且克服了经典球谐系数模型在形状不规则的小天体附近不收敛的问题。对于小天体附着多约束轨迹优化问题，通过约束松弛、线性化、离散化过程，转化为一个可以迭代求解的二阶锥规划问题（SOCP），进而采用内点法进行解算。数学仿真结果显示，优化结果符合各项约束条件，以零速度到达了目标着陆点，且符合燃耗最优的优化目标。利用序列凸优化算法进行小天体附着燃耗最优轨迹设计，推导简便，计算速度快，精度高，具有应用价值。

Soft Landing Trajectory Optimization on Asteroids by Convex Programming

This paper presents a strategy for the soft landing trajectory optimization on an asteroid. The interior gravity field model, a counterpart of the classical spherical harmonic model, is used to estimate the gravity acceleration near the target asteroid. This model has an advantage in computational efficiency and its convergence properties can be guaranteed within the constructed interior Brillouin sphere. The soft-landing optimization problem on an asteroid is converted into a successive second-order convex programming (SOCP) through constraints slack, linearization of dynamics and discretization which can be solved by the primal-dual interior-point methods. The numerical simulations shows that the lander arrives at the target site with zero velocity and all the constraints are satisfied. The fuel consumption is also optimal. Solving soft-landing optimization problem on an asteroid with convex programming has an advantage in computational effectiveness and can potentially be implemented in the future asteroid mission.