# Self-Organizing Control of Mega Constellations for Continuous Earth Observation
## 3 Results and Discussion
### Self-Organizing Control of Coplanar Satellites  
The coplanar satellites are selected as satellites of one orbit in GW-2 sub-constellation with an orbital altitude of 1145 km and inclination of 60\({}^{\circ}\). The designed configuration of the GW-2 constellation has been presented in Table 1. There are 48 orbital planes and 36 coplanar satellites in the GW-2 sub-constellation total. The simulation parameters are listed in Table 3. The initial errors of \(\delta\Omega,\delta\omega,\delta f\) are relatively large, which simulate the drift of \(\Omega,\omega,f\) under perturbations without control. The angular radius of the coverage range is calculated as \(\alpha_{\rm max}=17.19^{\circ}\). According to Equation (18), the RAAN drift should be within \(\delta\Omega_{\rm min}=-12.14^{\circ}\) and \(\delta\Omega_{\rm max}=12.14^{\circ}\). The drift range of the relative motion bound can be calculated using Equations (15) and (20) based on the extreme value of \(\delta\Omega\). Figure 10: Control effects changing with time. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Simulation Time & 60 days \\ \hline Step Length & 600 s \\ \hline \multirow{6}{*}{Designed Configuration} & \(a_{\rm t}=R_{\rm e}+1145\) km \\  & \(c_{\rm t}=0\) \\  & \(i_{\rm t}=60^{\circ}\) \\  & \(\Omega_{\rm t}=0^{\circ}\) \\  & \(\omega_{\rm t}=0^{\circ}\) \\ \hline \multirow{6}{*}{Initial Orbit Errors} & \(\delta a=[-100,100]\) m, uniform \\  & \(\delta e=[0,0.1]\), uniform \\ \cline{1-1}  & \(\delta i=[-0.1,0.1]\deg\), uniform \\ \cline{1-1}  & \(\delta\Omega=[-10,10]\deg\), uniform \\ \cline{1-1}  & \(\delta\omega=[-1,1]\deg\), uniform \\ \cline{1-1}  & \(\delta f=[-1,1]\deg\), uniform \\ \hline Perturbations & \(I_{2}\), atmospheric drag, lunar gravity, solar gravity \\ \hline Control Coefficients & \(k_{\rm bound}=2\times 10^{-8},k_{a}=2\times 10^{-8}\) \\ \hline Ballistic Coefficient & \(C_{D}A/m=0.01\) \\ \hline Minimum Elevation Angle & \(E_{\rm min}=20^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters for the coplanar satellites case. The initial distribution of the coplanar satellites in the geocentric inertial system is shown in Figure 11, while the final distribution is shown in Figure 12. The red dots represent satellites that do not satisfy the continuous coverage constraint, named unqualified satellites, whereas the green dots represent satellites that satisfy the continuous coverage constraint. The number of unqualified satellites changing with time is shown in Figure 13. The unqualified satellites are reduced from 11 to 0 due to the self-organizing control, which verifies the feasibility of the proposed control method. The differences in the maximum relative motion bounds away from their corresponding constraints are shown in Figure 14. The differences should be negative theoretically and they actually are. Hence the maximum bound control has not been performed during the simulation time. The differences in the minimum relative motion bounds away from their corresponding constraints are shown in Figure 15, from which it can be found that all minimum bounds are controlled to be larger than the constraints. The occurrence of the unqualified satellite at 40 days in Figure 13 can be understood by referring to Figure 15. The small drift in the minimum bound away from the constraint due to perturbations is identified as unqualified. Figure 14: The differences in maximum bounds away from the corresponding constraints. Red line is zero-value standard. Blue lines are maximum bound differences. Figure 13: Number of unqualified satellites in the coplanar satellites. The semi-major axis differences away from target value \(a_{\rm t}\) are shown in Figure 16. The maximum drift of the semi-major axis at the final moment is 54.27 m. The RAAN differences away from the target RAAN under \(J_{2}\) perturbation of the designed orbital plane are shown in Figure 17. The maximum drift of RAAN at the final moment is 9.73\({}^{\circ}\).