单推力航天器交会对接轨迹规划及跟踪控制

针对单推力航天器交会对接问题，提出一种轨迹规划及跟踪算法。首先，考虑到追踪航天器只沿本体X轴安装推力器，且推力方向固定，为了实现从起始位置转移至期望位置并满足姿态要求，基于三维螺旋线设计两阶段转移轨迹，根据初末位置以及末端速度方向要求，求解螺旋线参数。该螺旋线可以保证在初末速度方向固定情况下，曲率积分最小。其次，为了降低轨迹跟踪难度并减小初始时刻的位置跟踪控制力，需要将转移轨迹初始速度与追踪星X轴重合。传统螺旋线无法满足该约束条件。本文对传统螺旋线进行改进，提出一种旋转螺旋线轨迹设计方法。通过引入姿态旋转矩阵，将螺旋线在三维空间旋转，在不改变曲线形状的前提下满足初末位置及速度方向要求。然后，为了跟踪转移轨迹以及跟踪期望推力方向，提出基于CLF（Control Lyapunov Function）的滑模控制策略，当追踪星X轴与期望推力方向夹角较大时，采用CLF，保证最优性；当姿态误差收敛至滑模面附近时，切换为滑模控制，以提升系统鲁棒性。最后，通过仿真验证旋转螺旋线相比于传统螺旋线的优势。

Rendezvous and docking of spacecraft with single thruster: Path planning and tracking control

A novel path planning and tracking control approach is proposed for rendezvous and docking of spacecraft with a single thruster. Firstly, since the thruster is fixed along the X axis of the spacecraft, the transfer trajectory of the spacecraft from the initial position to the desired position is designed as a helix whose parameters are calculated to ensure that the initial point and final velocity of the trajectory are in accordance with those of the spacecraft. The curvature of the trajectory can be minimized by the proposed helical motion. Secondly, to reduce the difficulty in trajectory tracking and decrease the amplitude of the control torque, this paper proposes an improved helical motion by rotating the traditional helical line with appropriate angles in 3-D space. In this way, the initial direction of the trajectory can be aligned with the X axis of the spacecraft, while the curvature integral of the curve is minimized. Furthermore, to track the planned trajectory and the desired force direction, a sliding mode based Control Lyapunov Function (CLF) method is presented. When the angle between the X axis and the desired control force direction is large, the standard CLF law is adopted. Then the control law switches to sliding mode control in the case that the states are near the sliding mode surface. Simulations are conducted to show the superiority of the proposed rotated helical motions to traditional approaches.