# Toward Low Time Fragmentation of Equipment: A Double-DQN Based TT&C Task Planning Approach
## 2 Scenario and Problem Description  
The TT&C scenario shown in Figure 1 is composed of satellites and ground stations. The set of satellites is \(S=\left\{s_{1},s_{2},s_{3},\ldots,s_{i},\ldots,s_{N}\right\}\), and \(s_{i}\) represents the \(i\)-th satellite. The set of ground stations is \(G=\left\{g_{1},g_{2},g_{3},\ldots,g_{h},\ldots,g_{M}\right\}\), and \(g_{h}\) represents the \(h\)-th ground station. Each ground station has \(L\) TT&C equipment. The set of all the TT&C equipment is \(A=\left\{a_{1},a_{2},a_{3},\ldots,a_{j},\ldots,a_{L},a_{L+1},\ldots,a_{2L}, \ldots,a_{ML}\right\}\), and \(a_{j}\) represents the \(j\)-th TT&C equipment. There are \(wn_{ij}\) visible windows between satellite \(s_{i}\) and TT&C equipment \(a_{j}\) in the planning horizon, and the set is \(W_{i,j}=\left\{w_{i,j}^{k}|k=0,1,2,\ldots,wn_{ij}\right\}\). \(w_{i,j}^{k}\) represents the \(k\)-\(th\) visible window between satellite \(s_{i}\) and TT&C equipment \(a_{j}\) in the planning horizon. For each visible window \(w_{i,j}^{k}\in W_{i,j}\), it can be expressed as \(w_{i,j}^{k}=\left[w_{i,j}^{k},w_{i,j}^{k},ud_{i,j}^{k}\right]\), where \(w_{i,j}^{k}\) and \(w_{i,j}^{k}\) are the start time and end time of the visible window. \(ud_{i,j}^{k}\) is the sign of orbit ascending or descending. \(W_{i}=\left(\cup_{1\leq j\leq ML}W_{i,j}\right)\) is the set of all the visible windows of satellite \(s_{i}\) between all the TT&C equipment. The set of all visible windows in the planning horizon is expressed as \(W=\cup_{1\leq i\leq N,1\leq j\leq ML}W_{i,j}\). During the planning horizon, all the \(N\) satellites in the space network need to be tracked, telemetered and commanded as required. \(om_{i}\) represents the TT&C requirements of the \(i\)-th satellite. Therefore, the space network has \(N\) TT&C tasks, and their set is denoted as \(OM=\left\{om_{i}|1\leq i\leq N\right\}\). For each \(om_{i}\in OM\), it is represented by a four-dimensional tuple \(om_{i}=\left\{id_{i},wr_{i},gr_{i},\omega_{i}\right\}\), where \(id_{i}\) represents the ID of the satellite to be TT&C in task \(om_{i}\). \(wr_{i}\) represents the requirement of the TT&C window, i.e., the number of TT&C windows required and the request of the orbit ascending or descending for task \(om_{i}\). \(gr_{i}\) indicates the type of TT&C equipment, that is, the function of the TT&C equipment required by task \(om_{i}\). \(\omega_{i}\) represents the revenue bought by completing task \(om_{i}\). As shown in Figure 2, \(w_{1,1}^{1}\), \(w_{3,1}^{2}\), and \(w_{2,1}^{3}\) are three scheduled windows of different tasks performed by the same equipment. A relatively short time interval, i.e., a time fragment, is easily formed between adjacent scheduled time windows of the same TT&C equipment. Specifically, two time intervals with lengths \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are, respectively, formed between the three consecutive time windows \(w_{1,1}^{1}\), \(w_{3,1}^{2}\), and \(w_{2,1}^{3}\) of the TT&C equipment \(a_{1}\). The length of \(\varepsilon_{1}\) is shorter than the threshold \(Th\), and the length of \(\varepsilon_{2}\) is longer than the threshold \(Th\). Therefore, \(\varepsilon_{1}\) forms a time fragment of equipment \(a_{1}\). In the planning horizon, if the interval between two adjacent time windows executing tasks in the same TT&C equipment is less than the threshold Th, a time fragment \(\Delta t_{l}\) is formed, and the set of time fragments is \(\Delta T=\left\{\Delta t_{1},\Delta t_{2},\Delta t_{3},\ldots,\Delta t_{l}, \ldots\right\}\). Figure 1: TT&C scenario. The essence of the TT&C task-planning problem of the space network is to allocate suitable visible windows of the suitable equipment to each satellite need to be tracked, telemetered and commanded. In this way, the TT&C equipment can track, telemetry, monitor, and control the satellite flight orbit, attitude, and operational status of the onboard subsystems.