基于势场法的卫星编队保持及其稳定性分析

Satellite Formation Keeping and Its Stability Analysis Based on Artificial Potential Field Method

本文研究了基于人工势场法的卫星编队保持的控制方法。由于多体问题无法求其解析解,转而考虑领导-跟随结构的限制性多体问题。其惯性坐标系下的平衡结构对应了无穷多的坐标组合,使得误差动力学系统的平衡点处的雅可比矩阵无法求解。提出了一类由惯性坐标系到特殊参考坐标系的坐标变换,使对误差动力学系统的稳定性分析只取决于编队的构型。通过对参考坐标系下误差动力学系统的约化及其平衡点处雅克比矩阵的特征值的求解,证明了此类控制方法的稳定性。

In this paper,a control method of satellite formation keeping is investigated based on artificial potential field.Since the N-body problem doesn’t have analytical solutions,a leader-follower formation is proposed as a restricted N-body problem.The stable structure has infinite possible pairs of coordinates in the inertial frame,therefore the Jacobian matrix of the corresponding error dynamic system at the equilibrium point is unsolvable.By introducing a transformation of coordinates from inertial frame to a specific reference frame,the stability analysis of error dynamic system is only related to the structure of formation.By the reduction of error dynamic system in the reference frame and the solving of eigenvalues of Jacobian matrix at equilibrium point,the stability analysis of the novel control method is given.