Modeling and Simulation of Mission Planning Problem for Remote Sensing Satellite Imaging

Mission planning problem for remote sensing satellite imaging is studied. Firstly, the time constraint satisfaction problem model is presented after analyzing the characteristic of time constraint. Then, An optimal path searching algorithm based on the discrete time window is proposed according to the non-uniqueness for satellite to mission in the visible time window. Simulation results verify the efficiency of the model and algorithm.


Introduction
Remote sensing satellite can receive the information from the Earth sent by satellite borne senor in space, which have advantages of no constraint on any country, wide coverage, etc.They are widely applied in military reconnaissance, resources exploration, weather forecast and so forth.How to fulfill maximum imaging missions cooperatively through the effective strategy is the current problem of mission planning for remote sensing satellite [1].
The manoeuvrability of rolling and pitching can extend the visible time window for satellite to target compared with the satellite just rolling [2], and the imaging time window becomes a continuous selectivity variable.To tackle the problem of mission planning for remote sensing satellite , the characteristic of time constraint is analyzed.The time constraint satisfaction problem model is presented, and an optimal path searching algorithm is proposed.

Analysis of time constraint
Basic concepts in connection with time constraint are defined as follows:  Definition 1 Visible time window means the time window visible for satellite to target all the time.The Euler Angle for satellite to target is bijective with time in visible time window. Definition 2 Imaging time window means the time window imaging for satellite to target.
The Euler Angle for satellite to target is invariant in imaging time window.Figure 1 shows the visible time window and imaging time window for satellite to target.There are many similar constraints between satellite rolling and pitching and satellite just rolling, such as rolling angle constraint, pitching angle constraint, visible time window constraint and so forth [3][4].No more details here.In this paper, time constraint is the main constraint to be discussed [5].
The characteristics of time constraint for remote sensing satellite mission planning problem are as follows:  The non-uniqueness of imaging time window for satellite to target.The imaging time window can be confirmed by imaging start time and imaging duration, and the imaging start time for satellite to target can be selected from the visible time window randomly. The non-uniqueness of imaging Euler Angle for satellite to target.The Euler Angle for satellite to target is changed with time in the visible time window, while it is invariant in the imaging time window.All illustrated in figure 1.
 The non-uniqueness of satellite attitude transition time between neighbouring targets.The attitude transition time between neighbouring targets can be confirmed by the imaging Euler Angles.To confirm the imaging time window and imaging Euler Angle is the key problem in this article, and the imaging time window can be determined by imaging duration, while the imaging Euler Angle can be determined by imaging start time.So the problem is transformed into determining the imaging duration and imaging start time.

Time constraint satisfaction problem model
Time constraint satisfaction problem can be indicated by , , V D C triples [6], where V is the set of imaging time windows for targets, D is the set of visible time windows for targets, and C is the set of constraint conditions, including time window constraint, drift angle adjusting time constraint, maximum imaging time constraint in single orbit, and attitude transition time constraint.
In the remote sensing satellite mission planning problem, the variables are involved as follows:  The constraint conditions consisting of equation ( 2)-( 5): where i  and j  are the rolling angles of mission i and j, i q and j q are the pitching angles of mission i and j, s t is the attitude stabilization time.
Equation ( 2) means the imaging time window for satellite to mission should be contained in the visible time window; Equation (3) shows the drift angle adjusting time is set to a constant [7]; Equation ( 4) is to ensure that the total imaging time of the satellite in single orbit could not exceed the upper limit; Equation (5) shows the required attitude transition time between neighbouring targets [8][9] (see figure 2).

Optimal path searching algorithm
An optimal path searching algorithm based on the discrete time window is designed in this paper.Firstly, the visible time windows for planning missions need to be discrete according to certain fraction, generating a plurality of time points.Then, each time point is taken as the imaging start time.Lastly, the mature Hopfield neural network algorithm is used to search for the optimal path through continuous updating [10], and get the minimum energy consumption path.

Assumed that
is the set of mission need to be planned, and Step 1: Sorting the planning missions according to the visible time order for satellite to missions.
Step 2: Parting the visible time windows of the planning missions by discrete fraction a , and the visible time window is divided into a parts, getting a time points, and taking each time point as imaging start time for satellite to the mission (see figure 3).( , ) ( ,  ( 1), , , )

Sub-satellite track
where i is the mission ID, j is the time point number, q and ij Tcon are the rolling angle, pitching angle and imaging duration for satellite to mission.
Step 4: Starting from each time point of the first mission according to the time point number, it is extended to the feasible time point of the following mission satisfied the constraint conditions.
Step 5: Using Hopfield neural network algorithm update the time point path from first mission to the last one according to the minimum energy principle, and getting the optimal path minimized energy and consumed constraint conditions.Figure 4 shows flow of the optimal path searching algorithm.

Simulation example
The parameters of satellite and other constraints in simulation are shown in table 1  The set of planning missions was presented with trips segmented by circular Areatarget [11] and missions clustered by point targets from 1 18 t t [12].All shown in table 3    The searching capability of the proposed optimal path searching algorithm is related to the degree of discretization for visible time window.For the traditional mission planning methods, the greater the degree of discretization, the better the astringency of the optimal solution, and the computing resources on the ground can also meet the requirements.As for the autonomous mission planning, computing resources is limited for satellite, and if the degree of discretization is set too high, it will increase the amount of computation.On the contrary, if the degree of discretization is set too small, it will not guarantee the astringency of the optimal solution.This is also the difference between the autonomous mission planning on the satellite and the traditional mission planning on the ground.
Therefore, in this paper, the simulation was analyzed through setting different numbers to find a relatively suitable number of discrete fraction.And then, the suitable number was taken as the degree of discretization to get the relatively optimal solution, which can reduce the amount of computation, but also can guarantee the astringency of the solution.
Different numbers of discrete fraction were 5, 10, 20, 50, and the 5 fraction was taken as an example to introduce the solving process of the algorithm.
Firstly, the visible time windows of the planning missions were parted by 5 discrete fractions, and then the imaging pitch angle and imaging duration for each time point were calculated by using STK.Table 5 shows the information of each time point.According to the information of each time point in table 5, the optimal path consumed minimum energy was calculated by using Hopfield neural network algorithm.That is, Assumed that the initial Euler Angle for satellite starts from zero, and the Euler Angle for satellite along the direction of sub-satellite track is positive when rolling to left or pitching forward, and negative when rolling to right or pitching backward.Table 6 is the command sequence of attitude maneuver for satellite in the optimal path.As in table 6, when the discrete fraction is 5, the total imaging time for satellite is 544.2 seconds satisfied the maximum imaging time in single orbit that the total imaging time of the satellite in single orbit could not exceed 600 seconds.The total attitude maneuver time is 217.45 seconds, and the total energy consumed by optimal path is 674.66 kJ.
According to the above process, the total imaging time, total attitude maneuver time and total energy consumed in optimal path for 10, 20, and 50 fractions were calculated.All shown in It can be seen from table 8, with the increase of discrete fraction, the total imaging time for satellite to planning missions remained steady, the total attitude maneuver time dropped off, and the energy consumed reduced gradually too. Figure 5 shows the relationships between the total energy consumed by satellite in optimal path and the degree of discretization for time window.As in figure 5, with the increase of discrete fraction, the total energy consumed by is convergent, and when the fraction comes to 23, the total energy consumed has remained unchanged basically, the total energy keeps 644.40 kJ.Therefore, the best discrete fraction can be set to 23, and the corresponding optimal path is,  9 shows the command sequence of attitude maneuver for the best discrete fraction.According to the data in table 9, the total energy consumed for the best fraction 23 was calculated to be 664.27kJ, and there is little difference compared with the result as 664.40 kJ obtained by figure 5. Therefore, the result calculated for fraction 23 can be taken as the optimal solution of the mission planning problem.
Figure 6 shows the attitude maneuver strategy of satellite.Assumed that the attitude maneuver is carried out immediately after completing the imaging missions for satellite.

Conclusion and future work
The mission planning problem for remote sensing satellite imaging is studied from the time constraint.The time constraint satisfaction problem model is presented, and an optimal path searching algorithm based on the discrete time window is proposed.Simulation results show that the proposed algorithm can meet the requirement of minimum consumed energy, but also can reduce the computation and improve the speed of mission planning.
Considering that the best discrete fraction is variable even for the same satellite, and the future work is analysing the influence factors of the best discrete fraction from orbit altitude, orbit inclination, satellite mass, satellite inertia, etc, and establishing the relationship between the best fraction and influence factors.

Figure 1 .
Figure 1.The visible time window and imaging time window for satellite to target

Figure 2 .
Figure 2. The constraint of attitude transition time for satellite

3 MATEC
n Ts Te Ts Te Ts Te  TW is the set of visible time windows.The discrete fraction for visible time window is denoted as a .The steps of the algorithm are as follows: Web of Conferences 179, 03024 (2018) https://doi.org/10.1051/matecconf/2018179030242MAE 2018

Figure 3 .
Figure 3. Discrete of visible time windowStep 3: Calculating the Euler Angle and imaging duration for each time point, and defining it as,

Figure 4 .
Figure 4. Flow of the optimal path searching algorithm

Figure 5 .
Figure 5.The total energy consumed by satellite in optimal path for different fraction

Figure 6 .
Figure 6.Attitude maneuver strategy of satellite for mission planning problem


The maneuver rate of rolling and pitching are denoted as  and  separately.

Table 1 .
and table 2. Parameters of remote sensing satellite
and table 4.

Table 3 .
Position of targets

Table 4 .
Set of planning missionsAs in table 4, the imaging Euler Angles for segmenting trips are already confirmed, so its time window needn't to be discrete.

Table 5 .
Information of each time point

Table 6 .
Command sequence of attitude maneuver

Table 7 .
The optimal path for different fraction

Table 8 .
The calculating results for different fraction

Table 9 .
Command sequence of attitude maneuver for the best discrete fraction