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doi: 10.3934/jimo.2021092
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Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

Qian Zhao , Bitao Jiang , , Xiaogang Yu and  Yue Zhang

Beijing Institute of Remote Sensing Information, Beijing 100089, China

* Corresponding author: Bitao Jiang

Received  February 2021 Revised  March 2021 Early access April 2021

Fund Project: This paper is supported by the National Natural Science Foundation of China (Grant Nos: 91638301)

Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.

Keywords: Collaborative mission planning, remote sensing, geostationary orbit, multiple heterogeneous satellite, metaheuristic algorithm.
Mathematics Subject Classification: Primary: 90B50, 90C30; Secondary: 37N05.
Citation: Qian Zhao, Bitao Jiang, Xiaogang Yu, Yue Zhang. Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021092
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show all references

References:
[1]

N. Bianchessi, J.-F. Cordeau, J. Desrosiers, G. Laporte and V. Raymond, A heuristic for the multi-satellite, multi-orbit and multi-user management of Earth observation satellites, European Journal of Operational Research, 177 (2007), 750-762.  doi: 10.1016/j.ejor.2005.12.026.  Google Scholar

[2]

R. Deutsch, Orbital Dynamics of Space Vehicles, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963.  Google Scholar

[3]

M. Dorigo and C. Blum, Ant colony optimization theory: A survey, Theoret. Comput. Sci., 344 (2005), 243-278.  doi: 10.1016/j.tcs.2005.05.020.  Google Scholar

[4]

M. Dorigo and G. Di Caro, Ant colony optimization: A new meta-heuristic, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 2 (1999), 1470-1477.  doi: 10.1109/CEC.1999.782657.  Google Scholar

[5]

M. Dorigo, M. Birattari and T. Stutzle, Ant colony optimization, IEEE Computational Intelligence Magazine, 1 (2006), 28-39.   Google Scholar

[6]

J. Dungan, J. Frank, A. Jónsson, R. Morris and D. Smith, Advances in planning and scheduling of remote sensing instruments for fleets of earth orbiting satellites, In Earth Science Technology Conference, 2002. Google Scholar

[7]

S. D. Florio, T. Zehetbauer and T. Neff, Optimal operations planning for SAR satellite constellations [C], In Low Earth Orbit. 6th International Symposium on Reducing the Costs of Spacecraft Ground Systems and Operations, 2005. Google Scholar

[8]

F. T. Hwang, Y. Y. Yeh and S. Y. Li, Multi-objective optimization for multi-satellite scheduling system, In Proceedings of 31st Asian Conference on Remote Sensing, 2010. Google Scholar

[9]

J. Li, S. Zhang, X. Liu and R. He, Multi-objective evolutionary optimization for geostationary orbit satellite mission planning, Journal of Systems Engineering and Electronics, 28 (2017), 934-945.  doi: 10.21629/JSEE.2017.05.11.  Google Scholar

[10]

K. T. Malladi, S. M. Minic, D. Karapetyan and A. P. Punnen, Satellite constellation image acquisition problem: A case study, In Space Engineering, Springer, Cham, (2016), 177–197. doi: 10.1007/978-3-319-41508-6_7.  Google Scholar

[11]

K. T. Malladi, S. Mitrovic-Minic and A. P. Punnen, Clustered maximum weight clique problem: Algorithms and empirical analysis, Comput. Oper. Res., 85 (2017), 113-128.  doi: 10.1016/j.cor.2017.04.002.  Google Scholar

[12] M. Mitchell, An Introduction to Genetic Algorithms, MIT press, 1998.  doi: 10.7551/mitpress/3927.001.0001.  Google Scholar
[13]

S. Mitrovic-Minic, D. Thomson, J. Berger and J. Secker, Collection planning and scheduling for multiple heterogeneous satellite missions: Survey, optimization problem, and mathematical programming formulation, Modeling and Optimization in Space Engineering, 144 (2019), 271-305.   Google Scholar

[14]

M. D. Shuster, A survey of attitude representations, J. Astronaut. Sci., 41 (1993), 439-517.   Google Scholar

[15]

S. N. Sivanandam and S. N. Deepa, Genetic algorithms, In Introduction to Genetic Algorithms, Springer, Berlin, Heidelberg, (2008), 15–37  Google Scholar

[16]

M. Vasquez and J.-K. Hao, A "logic-constrained" knapsack formulation and a tabu algorithm for the daily photograph scheduling of an Earth observation satellite, Comput. Optim. Appl., 20 (2001), 137-157.  doi: 10.1023/A:1011203002719.  Google Scholar

[17]

X. Liu, B. Bai, Y. Chen and F. Yao, Multi satellites scheduling algorithm based on task merging mechanism, Appl. Math. Comput., 230 (2014), 687-700.  doi: 10.1016/j.amc.2013.12.109.  Google Scholar

[18]

Y. Zhang, J. Wang, B. Yuan, C. Wang and L. Shi, Research on multi-satellite observation multi-region task planning based on genetic algorithm, In IOP Conference Series: Materials Science and Engineering, 685 (2019), 012002. doi: 10.1088/1757-899X/685/1/012002.  Google Scholar

[19]

Y. Zhou, Y. Yan, X. Huang, Y. Yang and H. Zhang, Mission planning optimization for the visual inspection of multiple geosynchronous satellites, Engineering Optimization, 47 (2015), 1543-1563.  doi: 10.1080/0305215X.2014.979813.  Google Scholar

[20]

X. Zhu, J. Chen, C. hang and B. Qiao, Optimal fuel station arrangement for multiple GEO spacecraft refueling mission, Advances in Space Research, 66 (2020), 1924-1936.   Google Scholar

Figure 1.  LEO satellite observation
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Figure 2.  GEO satellite observation
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Figure 3.  The relationship between ship speed and coverage area
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Figure 4.  Mesh generation considering ship moving
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Figure 5.  General structure of solution method
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Figure 6.  Coverage ratio of task area over 17:29:08
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Figure 7.  Results of outer layer optimization
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Figure 8.  LEO Mission Selected
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Figure 9.  Results of inner layer optimization problems
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Figure 10.  GEO Satellite Optimal Path
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Table 1.  Satellite Orbit Parameters
$\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$
$\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0
$\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944
$\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888
$\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832
$\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944
$\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888
$\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832
$\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944
$\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888
$\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832
$\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944
$\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888
$\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832
$\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944
$\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888
$\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832
$\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944
$\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888
$\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832
$\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944
$\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888
$\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832
$\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944
$\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888
$\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
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$\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$
$\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0
$\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944
$\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888
$\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832
$\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944
$\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888
$\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832
$\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944
$\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888
$\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832
$\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944
$\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888
$\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832
$\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944
$\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888
$\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832
$\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944
$\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888
$\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832
$\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944
$\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888
$\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832
$\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944
$\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888
$\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
Table 2.  Constant Parameters
$\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$
Orbit perturbation constant J2 0.001082629989052 —
Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$
Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$
Radius of the earth Re 6.378137e3 km
Ship maximum speed $v_{max}$ 20 km/hour
Imaging width of LEO satellite $D_{LEO}$ 250km km
Imaging width of GEO satellite $D_{GEO}$ 250km km
Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour
Single imaging time of GEO satellite $t_{single}$ 20 s
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$\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$
Orbit perturbation constant J2 0.001082629989052 —
Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$
Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$
Radius of the earth Re 6.378137e3 km
Ship maximum speed $v_{max}$ 20 km/hour
Imaging width of LEO satellite $D_{LEO}$ 250km km
Imaging width of GEO satellite $D_{GEO}$ 250km km
Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour
Single imaging time of GEO satellite $t_{single}$ 20 s
Table 3.  Access calculation results
$\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$
$\boldsymbol{1}$ 4 1 0.119444
$\boldsymbol{2}$ 4 2 0.113889
$\boldsymbol{3}$ 4 3 0.108333
$\boldsymbol{4}$ 4 11 0.125
$\boldsymbol{5}$ 4 12 0.122222
$\boldsymbol{6}$ 4 21 0.133333
$\boldsymbol{7}$ 7 7 1.625
$\boldsymbol{8}$ 7 8 1.619444
$\boldsymbol{9}$ 7 16 1.636111
$\boldsymbol{10}$ 7 17 1.633333
$\boldsymbol{11}$ 7 18 1.627778
$\boldsymbol{12}$ 7 26 1.641667
$\boldsymbol{13}$ 7 27 1.641667
$\boldsymbol{14}$ 7 35 1.655556
$\boldsymbol{15}$ 7 36 1.652778
$\boldsymbol{16}$ 7 37 1.644444
$\boldsymbol{17}$ 7 45 1.663889
$\boldsymbol{18}$ 7 46 1.658333
$\boldsymbol{19}$ 7 54 1.675
$\boldsymbol{20}$ 7 55 1.669444
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$\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$
$\boldsymbol{1}$ 4 1 0.119444
$\boldsymbol{2}$ 4 2 0.113889
$\boldsymbol{3}$ 4 3 0.108333
$\boldsymbol{4}$ 4 11 0.125
$\boldsymbol{5}$ 4 12 0.122222
$\boldsymbol{6}$ 4 21 0.133333
$\boldsymbol{7}$ 7 7 1.625
$\boldsymbol{8}$ 7 8 1.619444
$\boldsymbol{9}$ 7 16 1.636111
$\boldsymbol{10}$ 7 17 1.633333
$\boldsymbol{11}$ 7 18 1.627778
$\boldsymbol{12}$ 7 26 1.641667
$\boldsymbol{13}$ 7 27 1.641667
$\boldsymbol{14}$ 7 35 1.655556
$\boldsymbol{15}$ 7 36 1.652778
$\boldsymbol{16}$ 7 37 1.644444
$\boldsymbol{17}$ 7 45 1.663889
$\boldsymbol{18}$ 7 46 1.658333
$\boldsymbol{19}$ 7 54 1.675
$\boldsymbol{20}$ 7 55 1.669444
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