考虑退绕问题的刚性航天器全局姿态稳定性控制

Global attitude stabilization of rigid spacecraft considering unwinding problem

针对刚性航天器姿态机动问题设计了能够有效减小能量损耗的非线性状态反馈控制器。由于修正罗德里格斯参数(modified rodrigues parameter,MRP)原始集在特征轴旋转角为±360°时存在奇异点,而相应的MRP映射集(shadow set)的奇异点处于特征轴旋转角为0°。将MRP原始集与映射集结合起来,实现全局非奇异姿态描述,解决了航天器姿态控制中的退绕(unwinding)问题。利用平方和(SOS)方法设计非线性状态反馈控制律,实现航天器全局姿态渐近稳定控制,同时实现更短控制路径,保证了控制过程中特征轴旋转角|Φ|≤180°。仿真结果表明了在干扰条件下该控制方法可有效控制航天器姿态稳定,且对能量损耗给出了定量分析结果。

A nonlinear state feedback controller which can designed for attitude maneuver of rigid spacecraft. Modified effectively decrease energy consumption was Rodrigues Parameter set possesses a singularity as the principal angle of rotation reaches ±360°,while the singularity of the corresponding shadow set occurs as the principal angle of rotation is 0°. MRP original set was combined with the shadow set for a global non-singularity description, which avoids the unwinding problem in spacecraft attitude control. The nonlinear state feedback control law, which is designed based on sum of squares （SOS） method, achieves both the global asymptotic stability and also the shorter control path, since the principle angle of rotation is bounded in 180°. Simulation results illustrate that the spacecraft attitude can be stabilized with the designed controller under perturbation and the energy consumption is also analyzed.