# A Distributed Autonomous Mission Planning Method for the Low-Orbit Imaging Constellation
## 2 Problem Description
### MSOOSP Task Planning Process  
Figure 1 shows the task planning process of MSOOSP, which is divided into the following three parts. (1) Phase 1. Task broadcast  
When the ground station receives a mission request from the user, it first uploads the mission information to the satellite that is able to establish a satellite-to-earth link at the current moment. The satellite then broadcasts the received information through the inter-satellite link so that all satellites in the constellation have access to the mission information. It should be noted that for smaller constellations, when the satellite receives information transmitted by the ground station, it can broadcast throughout the entire constellation range as described above. With the tremendous progress of small satellite technology, low-orbit large-scale small satellite constellations have become an important development direction, resulting in a large number of research and application plans [22; 23]. Adopting fully distributed algorithms for autonomous task planning in large-scale constellations \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Mathematical Indices**} \\ \hline s\({}_{\text{i}}\) & the satellite with index i & \(|\text{S}|\) & the number of satellites \\ \hline M\({}_{\text{i}}\) & the maximum storage capacity of satellite s\({}_{\text{i}}\) & t\({}_{\text{j}}\) & the mission with index j \\ \hline \(|\text{T}|\) & the number of missions & m\({}_{\text{j}}\) & the estimated consumption of storage for the execution of task t\({}_{\text{j}}\) \\ \hline d\({}_{\text{j}}\) & the required observing duration of task t\({}_{\text{j}}\) & ts\({}_{\text{j}}\) & the start time of the execution of task t\({}_{\text{j}}\) \\ \hline \multirow{2}{*}{te\({}_{\text{j}}\)} & \multirow{2}{*}{the end time of the execution of task t\({}_{\text{j}}\)} & \multirow{2}{*}{trj\({}_{\text{j,j}}\)} & the required attitude transition time for the satellite to perform two adjacent tasks between t\({}_{\text{j}}\) and t\({}_{\text{j}}\) \\ \hline p\({}_{\text{j}}\) & the priority of the task t\({}_{\text{j}}\) & r\({}_{\text{j}}\) & the benefit of task t\({}_{\text{j}}\) \\ \hline \(|\text{W}_{\text{j}}|\) & the total number of O-VTWs of satellite s\({}_{\text{i}}\) for task t\({}_{\text{j}}\) & w\({}_{\text{ijk}}\) & the kth O-VTW of satellite s\({}_{\text{i}}\) for task t\({}_{\text{j}}\) \\ \hline ws\({}_{\text{ijk}}\) & the start time of w\({}_{\text{ijk}}\) & we\({}_{\text{ijk}}\) & the end time of w\({}_{\text{ijk}}\) \\ \hline \multirow{2}{*}{\(x_{\text{ijk}}\)} & the decision variable that determines whether the task & \multirow{2}{*}{g\({}_{\text{ijk}}\)} & the bidding function for the time window w\({}_{\text{ijk}}\) \\  & t\({}_{\text{j}}\) is executed in w\({}_{\text{ijk}}\) & & \\ \hline \(\alpha\) & the parameter of TPS & b\({}_{\text{i}}\) & the task bundle constructed by satellite s\({}_{\text{i}}\) \\ \hline \multirow{2}{*}{\(z_{i}=\left\{z_{i1},\ z_{i2},\ldots,\ z_{i|T|}\right\}\)} & the highest bid satellite list of all tasks under the satellite s\({}_{i}\)’s cognition \\ \hline \multirow{2}{*}{\(y_{i}=\left\{y_{i1},\ y_{i2},\ldots,\ y_{i|T|}\right\}\)} & the highest bid list of all tasks under the satellite \(s_{i}\)’s cognition \\ \hline \multirow{2}{*}{\(h_{i}=\left\{h_{i1},\ h_{i2},\ldots,\ h_{i|T|}\right\}\)} & the timestamp list of other satellite’s information obtained by satellite \(s_{i}\) \\ \hline \multirow{2}{*}{\(u_{i}=\left\{u_{i1},\ u_{i2},\ldots,\ u_{i|T|}\right\}\)} & the list of task preemption markers under the cognition of satellite \(s_{i}\) \\ \hline \multirow{2}{*}{\(v_{i}=\left\{v_{i1},\ v_{i2},\ldots,\ v_{i|T|}\right\}\)} & the task preemption timestamp list under the cognition of satellite \(s_{i}\) \\ \hline \multirow{2}{*}{\(q_{i}=\left\{q_{i1},\ q_{i2},\ldots,\ q_{i|T|}\right\}\)} & the number of communications made by the satellite \(s_{i}\) that consistently considers itself to be the highest bidder \\ \hline \end{tabular}
\end{table} 
Table 2: Description list of mathematical indices.