# Self-Organizing Control of Mega Constellations for Continuous Earth Observation
## 3 Results and Discussion
### Self-Organizing Control of Mega Constellation  
This paper focuses on self-organizing control to keep continuous coverage within the designed latitude zones, whereas collision avoidance control has not been considered so far. Since the proposed continuous coverage constraint relates to coplanar satellites only, the self-organizing control of different orbital planes is independent of each other. The initial simulation parameters are listed in Table 4. In order to demonstrate the effect of relative motion-bound control, the initial errors of \(\delta\Omega,\delta\omega,\delta f\) are set as \(\delta\Omega\in[-5,5]\deg\), \(\delta\omega\in[-1,1]\deg\), \(\delta f\in[-1,1]\deg\). The initial and final distributions of the mega constellation are shown in Figures 19 and 20, respectively. Satellites that satisfy the continuous coverage constraint are colored green, while others are colored red. It can be observed that unqualified satellites turn into qualified satellites under self-organizing control. The number of unqualified satellites is reduced from 248 to 0, shown in Figure 21. The control effects in the geocentric inertial system changing with time are shown in Figure 22, which reveals the convergence of the proposed self-organizing control. Figure 17: RAAN differences away from the target RAAN under \(I_{2}\) perturbation. Red lines represent \(\delta\Omega_{\text{min}}\) and \(\delta\Omega_{\text{max}}\) respectively. Blue lines represent RAAN differences. Figure 18: Control effects of coplanar satellites in the geocentric inertial system. The time histories of the maximum bound difference, minimum bound difference, semi-major axis difference, and RAAN difference are given in Figures 23-26. All the minimum relative motion bounds converge to expected constraints automatically under control. The semi-major axis differences are restricted within 98.02 m, and the maximum drift of RAAN at the final moment is 5.46\({}^{\circ}\), which is far away from the \(8\Omega\) drift constraint. \begin{table}
\begin{tabular}{l l} \hline
**Parameters** & **Values** \\ \hline Simulation Time & 60 days \\ \hline Step Length & 600 s \\ \hline \multirow{5}{*}{Designed Configuration} & \(a_{\mathrm{t}}=R_{\mathrm{e}}+1145\) km \\  & \(e_{\mathrm{t}}=0\) \\  & \(i_{\mathrm{t}}=60^{\circ}\) \\  & \(P=48\) \\  & \(S=36\) \\ \hline \multirow{5}{*}{Initial Orbit Errors} & \(\delta a=[-100,100]\) m, uniform \\  & \(\delta r=[0,0.1]\), uniform \\  & \(\delta i=[-0.1,0.1]\) deg, uniform \\  & \(\delta\Omega=[-5,5]\) deg, uniform \\  & \(\delta w\) \([-1,1]\) deg, uniform \\  & \(\delta f=[-1,1]\) deg, uniform \\ \hline Perturbations & \(J_{2}\), atmospheric drag, lunar gravity, solar gravity \\ \hline Control Coefficients & \(k_{\mathrm{bound}}=2\times 10^{-8},k_{a}=2\times 10^{-8}\) \\ \hline Ballistic Coefficient & \(C_{D}A/m=0.01\) \\ \hline Minimum Elevation Angle & \(E_{\mathrm{min}}=20^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters for the mega-constellation case. Figure 19: Initial distribution of the mega constellation. Red dots represent satellites that do not satisfy the continuous coverage constraint while green dots represent satellites that satisfy the continuous coverage constraint. Figure 21: Number of unqualified satellites in the mega constellation. Figure 22: Control effects of constellation satellites. Figure 23: Maximum bound differences of constellation satellites. Red line is zero-value standard. Blue lines are maximum bound differences. Figure 24: Minimum bound differences of constellation satellites. Red line is zero-value standard. Blue lines are minimum bound differences. Figure 25: Semi-major axis differences of constellation satellites. Figure 27 shows the coverage performance of the GW-2 sub-constellation at the final moment, where yellow dots represent virtual ground stations that can be single-covered, and red dots represent ground stations that cannot be single-covered.