# A Distributed Autonomous Mission Planning Method for the Low-Orbit Imaging Constellation
## 2 Problem Description
### MSOOSP Task Planning Process
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Mathematical Symbols**} \\ \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\({}_{\text{j}}\)} & the end time of the execution of task t\({}_{\text{j}}\) & 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 \\  & & the highest bid 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 \\  & & 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 \(s_{i}\) \\  & & 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 3: Description list of mathematical symbols. is inefficient and unnecessary. Considering the efficiency and effectiveness of the algorithm, the task broadcast range can be predetermined based on the characteristics of the constellation, and then the task planning algorithm can be carried out within this range. In order to ensure the normal operation and long-term control of satellites, ground stations routinely obtain information such as satellite flight orbits and operational status through measurement, control and tracking. Therefore, when the user puts forward the demand, the ground station is able to directly calculate the information such as the visible time window of each satellite for each task using tools such as Satellite Ephemeris.