Acta Astronautica ( IF 3.5 ) Pub Date : 2023-06-08 , DOI: 10.1016/j.actaastro.2023.06.003 Uliana Monakhova, Danil Ivanov, Yaroslav Mashtakov, Sergey Shestakov, Mikhail Ovchinnikov
The problem of relative drift elimination between the satellites in the swarm is considered in the paper. The proposed decentralized control takes into account a communication constraint such as limited size of communication area. Only the satellites within the communication area can be identified by relative motion determination system. The control aim is to eliminate the mean relative drift between all the satellites inside the communication area. The purpose of the work is to study the performance of the proposed decentralized control algorithm. It is shown that the system matrix of differential equations for the vector of relative drifts is related to the Laplacian matrix of the communication graph. In the case of the connected swarm, all but one eigenvalues of the system are negative, and the remaining one is equal to zero. It means that all the relative drifts converge to the same value under the proposed control. The speed of convergence is defined by the minimum absolute eigenvalue that depends on the graph topology. The initial drift and the convergence speed make it possible to estimate the communication distance that provides the connectivity of the graph. Considering normally distributed errors of the initial velocity after the launch, it is possible to estimate the distance between any two satellites after the convergence. It allows us to estimate the communication distance that ensures the relative drift elimination between all the satellites in the swarm. The obtained estimations are validated using Monte Carlo simulations. In numerical simulations the swarm of 3U CubeSats in low-Earth orbit is considered. The decentralized control is implemented by differential aerodynamic drag via the change of cross-sectional area using onboard reaction wheels.
中文翻译:
纳米卫星群分散控制的通信区域估计
文中考虑了群体中卫星之间的相对漂移消除问题。所提出的分散控制考虑了通信限制,例如通信区域的有限大小。相对运动确定系统只能识别通信区域内的卫星。控制目标是消除通信区域内所有卫星之间的平均相对漂移。这项工作的目的是研究所提出的分散控制算法的性能。结果表明,相对漂移向量的微分方程组矩阵与通信图的拉普拉斯矩阵相关。在连接群的情况下,系统的所有特征值只有一个是负的,其余的特征值等于零。这意味着所有相对漂移在建议的控制下收敛到相同的值。收敛速度由取决于图拓扑的最小绝对特征值定义。初始漂移和收敛速度可以估计提供图形连通性的通信距离。考虑正态分布的误差发射后的初速度,可以估计任意两颗卫星收敛后的距离。它使我们能够估计确保群中所有卫星之间的相对漂移消除的通信距离。使用蒙特卡罗模拟验证获得的估计。在数值模拟中,考虑了近地轨道上的 3U 立方体卫星群。分散控制是通过使用机载反作用轮改变横截面积的差分气动阻力来实现的。