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Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

  • * Corresponding author: Bitao Jiang

    * Corresponding author: Bitao Jiang 

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

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  • 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.

    Mathematics Subject Classification: Primary: 90B50, 90C30; Secondary: 37N05.

    Citation:

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  • Figure 1.  LEO satellite observation

    Figure 2.  GEO satellite observation

    Figure 3.  The relationship between ship speed and coverage area

    Figure 4.  Mesh generation considering ship moving

    Figure 5.  General structure of solution method

    Figure 6.  Coverage ratio of task area over 17:29:08

    Figure 7.  Results of outer layer optimization

    Figure 8.  LEO Mission Selected

    Figure 9.  Results of inner layer optimization problems

    Figure 10.  GEO Satellite Optimal Path

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV
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