间接Legendre伪谱法的欠驱动航天器姿态运动轨迹跟踪

针对仅带有两组喷气推力器的非轴对称欠驱动刚性航天器，提出一种基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法。首先采用Legendre伪谱法(LPM)离线规划出系统的最短时间姿态机动参考轨迹。接着将实际运行轨迹与参考轨迹之间的偏差作为变量，根据Pontryagin极小值原理必要条件把系统姿态运动跟踪问题转化为一个两点边值问题(TPBVP)。最后采用 Legendre-Gauss-Lobatto(LGL)点将此两点边值问题离散转化为一个线性方程组来求解，避免了对传统Riccati微分方程的积分运算。数值仿真校验了本文基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法的有效性。

Attitude Motion Trajectory Tracking for Underactuated Spacecraft Based on Indirect Legendre Pesudospectral Method

An attitude motion tracking control algorithm is studied via the indirect Legendre pseudospectral method for the asymmetric underactuated rigid spacecraft equipped with only two pairs of jet thrusters. Firstly, the Legendre pseudospectral method (LPM) is employed to plan a reference trajectory of the min-time attitude maneuver for the system. Secondly, defining the deviation between the actual and reference trajectories as the variable, and then the attitude motion tracking problem can be transformed into a two-point boundary value problem (TPBVP) according to the necessary condition of the Pontryagin minimal value theory. At last, the Legendre-Gauss-Lobatto (LGL) points are utilized to transfer the TPBVP into a system of linear equations to be solved. It avoids the integral operating for the traditional Riccati differential equations. The effectiveness of the attitude motion tracking control algorithm based on indirect LPM for an initial disturbance in the underactuated spacecraft is verified through the numerical simulation.