编队飞行最优相对轨迹生成与跟踪控制

燃料消耗和对参考轨迹的跟踪误差是编队任务的主要关注因素，为尽量节省燃料且减小跟踪误差，需要设计合理的参考轨迹与跟踪控制算法。为此，首先推导描述星间相对运动的完整动力学方程以及对参考轨迹的跟踪误差方程，基于完整相对动力学模型的无摄动形式，利用LGR(Legendre Gauss Radau)法将最优轨迹规划问题转化为非线性规划问题，使其可以数值求解;进而设计了带极点配置的H∞控制器，通过将系统闭环极点配置到左半复平面的合适区域，可以得到满意的跟踪误差同时维持合理的燃料消耗，在存在地球引力摄动、空间环境扰动以及主星轨道机动的情况下，能够完成对期望轨迹的跟踪。仿真结果显示了结果的有效性。

Optimal relative trajectory generation and tracking control of formation flying

The fuel consumption and tracking errors are two major concerns in the formation flying. Reasonably designed reference trajectories and control algorithms can help to save fuel and minimize tracking errors. The full relative dynamics of the follower with respect to the leader and the tracking error dynamics are derived. Based on the unperturbed form of the full relative dynamics, the optimal trajectory generation problem is transformed into a nonlinear programming problem using LGR(Legendre Gauss Radau) method and thus can be solved numerically. An H∞ control law with pole placement is developed to achieve reasonable tracking errors and fuel consumption. The controller can track the reference trajectories under Earth gravity perturbation, environmental disturbances and leader maneuver. Simulation results show the efficiency of the main results.