CN108268976B - A planning method for minimizing the maximum completion time of multi-imaging satellite area coverage tasks - Google Patents

Abstract

The invention discloses a multi-imaging satellite area coverage task maximum completion time minimum planning method, and belongs to the technical field of satellite communication. The method comprises two stages, namely, a coverage mode generation stage and a coverage mode selection stage are separated, so that the method is reasonable in structure and clear in hierarchy; the method can provide at least one coverage plan such that the imaging satellite spends as little time as possible completing the coverage. The method also evaluates the quality of the selected coverage scheme by calculating an optimality parameter for the coverage scheme.

Description

A planning method for minimizing the maximum completion time of multi-imaging satellite area coverage tasks

technical field

The invention relates to the technical field of satellite communications, and in particular to a planning method for minimizing the maximum completion time of a multi-imaging satellite area coverage task.

Background technique

Take the search for Malaysia Airlines MH370 as an example. On March 20, 2014, Australia claimed to have found the suspected wreckage of MH370 in the southern Indian Ocean. The location is: latitude -43.58, longitude 90.57. In order to search the area near the point, the range can be expanded to a square area centered on the point.

China has used multiple imaging satellites to search for MH370, and the imaging area of each imaging satellite is a strip-shaped area. Figure 1 shows a schematic diagram of a strip-shaped area imaged by an imaging satellite. As shown in Figure 1, by controlling the on-off time of the sensor (such as a camera) on the imaging satellite, the position of the strip-shaped area imaged by the sensor can vary along the imaging scan direction, as can the length of the strip-shaped region.

Since imaging satellite imaging takes time, it is very important to reasonably arrange the positions of the strip-shaped areas imaged by each imaging satellite, so that the time consumed by multiple imaging satellites is as little as possible on the premise of completely covering the entire area. significance.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a planning method for minimizing the maximum completion time of the multi-imaging satellite area coverage task. Possibly few coverage options.

In order to achieve the above object, embodiments of the present invention provide a planning method for minimizing the maximum completion time of a multi-imaging satellite area coverage task, including generating a coverage pattern and selecting a coverage pattern, wherein generating a coverage pattern specifically includes the following steps: determining a plurality of imaging satellites Divide the rectangular area to be covered into a plurality of grids to generate a first grid list G; for each imaging satellite in the plurality of imaging satellites: determine that the imaging scanning direction of the imaging satellite is the first inclination The direction is still the second inclination direction; when it is determined that the imaging scanning direction of the imaging satellite is the first inclination direction, the upper left corner vertex of any grid in the first grid list G is used as the base point, according to the imaging scanning direction of the imaging satellite. Reordering the divided multiple meshes to generate a second mesh list LG, taking the upper left corner vertex and the lower right corner vertex of the meshes in the second mesh list LG as base points, according to the strip-shaped area covered by the imaging satellite The width of the four vertices of the coverage pattern of the imaging satellite is determined to form a coverage pattern of the imaging satellite, and the grids in the second grid list LG are traversed to form the coverage pattern list of the imaging satellite; When the direction is the second oblique direction, take the top right vertex of any grid in the first grid list G as the base point, and reorder the divided grids according to the imaging scanning direction of the imaging satellite to generate a third grid. the grid list LG, and taking the upper right corner vertex and the lower left corner vertex of the grid in the third grid list LG as base points, and determining the four vertices of the coverage pattern of the imaging satellite according to the width of the strip-shaped area covered by the imaging satellite, to form a coverage pattern of imaging satellites, and traverse the grids in the third grid list LG to form a coverage pattern list of imaging satellites; traverse a plurality of imaging satellites to obtain a set of coverage patterns, the set of coverage patterns including each List of coverage modes of imaging satellites; selecting a coverage mode specifically includes the following steps: for each imaging satellite in multiple imaging satellites: setting the initial value of the lower bound of time, the initial value of time consumption, the upper limit of the number of iterations, the lager The initial value of the Rangian multiplier sequence and the initial value of the time coefficient sequence; according to the startup time and shutdown time of the sensor carried on the imaging satellite, the time required for the imaging satellite to execute the coverage mode is calculated; the Lagrangian relaxation technique is used to establish The objective function that minimizes the time required for the imaging satellite to execute the coverage mode to obtain the target value of the time consumed by the imaging satellite to execute the coverage mode; In the mode list, select a coverage mode with the smallest time consumption target value; traverse multiple imaging satellites to select a coverage mode with the smallest time consumption target value of each imaging satellite to form a coverage plan; modify the coverage plan to Obtain the revised coverage scheme; update the initial value of the lower bound of time and the initial value of time consumption; calculate the optimality parameters of the revised coverage scheme according to the initial value of the updated lower bound of time and the initial value of the updated time consumption. value; by updating the Lagrangian multiplication to update the objective function based on the updated objective function, and re-select a coverage mode with the smallest time target value of each imaging satellite to form a coverage scheme, and recalculate the optimality parameters for the newly formed coverage scheme. value; update the value of the Lagrangian multiplier multiple times, when the update times of the value of the Lagrangian multiplier reaches the upper limit of the number of iterations, select the most selected and reselected coverage scheme from the multiple coverage schemes. The covering scheme with the smallest value of the optimality parameter is used as the covering scheme for covering the rectangular area.

Through the above technical solution, the planning method for minimizing the maximum completion time of the multi-imaging satellite area coverage task is divided into two stages, and the generation coverage mode and the selection coverage mode are separated, so that the method has a reasonable structure and a clear hierarchy; the method can provide at least one A coverage scheme that takes as little time as possible for imaging satellites to complete coverage.

Other features and advantages of embodiments of the present invention will be described in detail in the detailed description section that follows.

Description of drawings

The accompanying drawings are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the specification, and are used to explain the embodiments of the present invention together with the following specific embodiments, but do not constitute limitations to the embodiments of the present invention. In the attached image:

FIG. 1 shows a schematic diagram of a strip-shaped area imaged by an imaging satellite;

2 is a flow chart of generating a coverage pattern of a method for minimizing the maximum completion time of a multi-imaging satellite area coverage task according to an embodiment of the present invention;

FIG. 3 is a flow chart of selecting a coverage mode of a planning method for minimizing the maximum completion time of a multi-imaging satellite area coverage task according to an embodiment of the present invention.

Detailed ways

The specific implementations of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific implementation manners described herein are only used to illustrate and explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention.

In this application, unless otherwise stated, the directional words used such as "top left vertex", "bottom left vertex", "top right vertex" and "bottom right vertex" generally refer to those shown with reference to the accompanying drawings. "Top Left Vertex", "Bottom Left Vertex", "Top Right Vertex", "Bottom Right Vertex". "Inside and outside" means inside and outside relative to the contours of each component itself.

In the embodiment of the present application, the imaging scan line is the center line along the scan direction of the imaging scan area of the corresponding imaging satellite.

In the embodiments of the present application, the coverage mode may refer to an imaging coverage area (or an imaging scan area) of an imaging satellite.

Override schema generation

For example, using N _T imaging satellites to cover the rectangular area A that you want to cover may include two stages: generating a coverage pattern and selecting a coverage pattern, where the _NT imaging satellites form an imaging satellite list S, and S can be denoted as

2 is a flow chart of generating a coverage pattern of a method for minimizing the maximum completion time of a multi-imaging satellite area coverage task according to an embodiment of the present invention; as shown in FIG. 2 , in an embodiment of the present invention, a coverage pattern is generated Can include:

In step S101, the imaging scanning directions of multiple imaging satellites are determined;

定义第i个网格g_i的左上角顶点、右上角顶点、左下角顶点和右下角顶点的坐标分别为p₁(i)＝＜x₁(i),y₁(i)＞、p₂(i)＝＜x₂(i),y₂(i)＞、p₃(i)＝＜x₃(i),y₃(i)＞、p₄(i)＝＜x₄(i),y₄(i)＞；In step S102, the rectangular area A to be covered is divided into a plurality of grids to generate a first grid list G, and the grids in the first grid list G are sequentially numbered, wherein the first grid list G can be recorded as

Define the coordinates of the top-left vertex, top-right vertex, bottom-left vertex, and bottom-right vertex of the i-th mesh g _i as p ₁ (i)=<x ₁ (i), y ₁ (i)>, p ₂ (i)=<x ₂ (i), y ₂ (i)>, p ₃ (i)=<x ₃ (i), y ₃ (i)>, p ₄ (i)=<x ₄ (i) ,y ₄ (i)>;

For each imaging satellite in list S of imaging satellites:

In step S103, it is determined whether the imaging scanning direction of the imaging satellite is the first oblique direction or the second oblique direction. The first inclination direction may include, for example, the direction of "from the upper left vertex to the lower right vertex" or the direction of "from the lower right vertex to the upper left vertex", or a general tendency along the direction of "from the upper left vertex to the lower right vertex". Orientation or direction "from the lower right vertex to the upper left vertex" (eg, slanted to the left relative to vertical in the figure). The second inclination direction may include, for example, the direction of "from the lower left vertex to the upper right vertex" or the direction of "from the upper right vertex to the lower left vertex", or generally along the direction of "from the lower left vertex to the upper right vertex" Orientation or direction "from the top right vertex to the bottom left vertex" (eg, slanted to the right relative to vertical in the figure).

In step S104, when it is determined that the imaging scanning direction of the imaging satellite is the first inclined direction, the upper left corner vertex of any grid in the first grid list G is used as the base point, and the imaging scanning direction of the imaging satellite is divided into Reordering the plurality of grids (ie, renumbering the grids in the first grid list G) to generate a second grid list LG;

In step S105, taking the upper left corner vertex and the lower right corner vertex of the grid in the second grid list LG as base points, the four vertices of the coverage pattern of the imaging satellite are determined according to the width of the strip-shaped area covered by the imaging satellite, to form a coverage pattern of imaging satellites, and traverse all grids in the second grid list LG to form a coverage pattern list of imaging satellites;

In step S106, when it is determined that the imaging scanning direction of the imaging satellite is the second inclined direction, the upper right corner vertex of any grid in the first grid list G is used as the base point, and the imaging scanning direction of the imaging satellite is divided into The plurality of grids of are reordered (that is, the grids in the first grid list G are renumbered) to generate a third grid list LG;

In step S107, the upper right corner vertex and the lower left corner vertex of the grid in the third grid list LG are used as base points, and the four vertices of the coverage pattern of the imaging satellite are determined according to the width of the strip-shaped area covered by the imaging satellite. forming a coverage pattern of imaging satellites, and traversing all grids in the third grid list LG to form a coverage pattern list of imaging satellites;

In step S108, each imaging satellite in the imaging satellite list S is traversed to obtain a coverage pattern set, where the coverage pattern set includes a coverage pattern list of each imaging satellite.

In an embodiment of the present invention, with the upper left vertex of any grid in the first grid list G as the base point, the divided grids are reordered (numbered) according to the imaging scanning direction of the imaging satellite to generate The second grid list LG may specifically include:

A grid g _z is arbitrarily selected from the first grid list G, and the upper left corner vertex p ₁ of the selected grid g _z is determined on a line parallel to the imaging scanning direction of the imaging satellite (hereinafter referred to as the imaging scanning line) (z) are two points P _l (x _l , y _l ) and P _r (x _r , y _r ) whose distance is R, where R may be, for example, a value greater than the length of the diagonal vertex line of the rectangular area A , x _l and y _l are the longitude and latitude values of the point P _l (x _l , y _l ), respectively, x _r and y _r are the longitude and latitude values of the point P _r (x _r , y _r ), respectively, and x _l <x _r .

Two points on the imaging scan line of the imaging satellite at a distance R from the upper left corner vertex p ₁ (z) of the selected grid g _z can be expressed by equation (1):

Among them, x represents longitude, y represents latitude, x _l <x ₁ (z)<x _r , x ₁ (z) and y ₁ (z) are respectively the upper left corner vertex p ₁ (z) of the selected grid g _z The longitude and latitude values of , x _l and x _r are the longitude values of point P _l (x _l , y _l ) and point P _r (x _r , y _r ) respectively, R is the set value, A, B, C The parameters of the scanning line for the imaging of the imaging satellite;

Take the point P _r (x _r , y _r ) as the starting point, take the point P _l (x _l , y _l ) as the end point to determine the reference vector, take the point P _r (x _r , y _r ) as the starting point, take the first grid The upper left corner vertex p ₁ (i) of any grid g _i in the list G determines a vector as the end point, and calculates the projection of the vector on the reference vector;

Traverse the grids in the first grid list G to obtain a vector projection list;

The projections in the vector projection list are arranged in descending order to reorder (number) the corresponding grids in the first grid list G to construct a second grid list LG.

Taking the upper right corner vertex of any grid in the first grid list G as the base point, reordering (numbering) the divided grids according to the imaging scanning direction of the imaging satellite to generate the third grid list LG may specifically include: :

A grid g _z is arbitrarily selected from the first grid list G, and two points P with a distance R from the upper right corner vertex p ₂ (z) of the selected grid g _z are determined on the imaging scanning line of the imaging satellite _l (x _l , y _l ) and P _r (x _r , y _r ), where R can be, for example, a value greater than the length of the diagonal vertex line of the rectangular area A, and x _l and y _l are points P _l ( x _l , y _l ) longitude and latitude values, x _r and y _r are the longitude and latitude values of the point P _r (x _r , y _r ), respectively, and x _l <x _r .

Two points on the imaging scan line of the imaging satellite at a distance R from the upper-right vertex p ₂ (z) of the selected grid g _z can be expressed by equation (2):

Among them, x represents longitude, y represents latitude, x _l <x ₂ (z)<x _r , x ₂ (z) and y ₂ (z) are respectively the upper right corner vertex p ₂ (z) of the selected grid g _z The longitude and latitude values of , x _l and x _r are the longitude values of point P _l (x _l , y _l ) and point P _r (x _r , y _r ) respectively, R is the set value, A, B, C are the parameters of the imaging scanning line of the imaging satellite;

Take the point P _l (x _l , y _l ) as the starting point, take the point P _r (x _r , y _r ) as the end point to determine the reference vector, take the point P _l (x _l , y _l ) as the starting point, the first grid list The upper right corner vertex p ₂ (i) of any grid g _i in G determines a vector as the end point, and calculates the projection of this vector on the reference vector;

Traverse the grids in the first grid list G to obtain a vector projection list;

Arrange the projections in the vector projection list in descending order, reorder (number) the corresponding grids in the first grid list G, and construct a third grid list LG.

In an embodiment of the present invention, the upper left corner vertex and the lower right corner vertex of the grid in the second grid list LG are used as base points, and the four factors of the coverage mode of the imaging satellite are determined according to the width of the strip-shaped area covered by the imaging satellite. vertices to form a coverage pattern of the imaging satellite, and traverse all the grids in the second grid list LG to form the coverage pattern list of the imaging satellite, which may specifically include:

A first grid g _i is arbitrarily selected from the second grid list LG, and is determined on a straight line passing through the upper left corner vertex p ₁ (i) of the first grid g _i and perpendicular to the imaging scanning direction of the imaging satellite s _j The first vertex U ₁ (x _1,i ,y _1,i ) and the second vertex U ₂ whose distance from the imaging scanning line Ax+By+C=0 is equal to half the width of the strip-shaped area covered by the imaging satellite (x _2,i ,y _2,i ),

The distance from the imaging scanning line Ax+By+C=0 on the straight line passing through the upper left corner vertex p ₁ (i) of the first grid g _i and perpendicular to the imaging scanning direction of the imaging satellite s _j is equal to the distance covered by the imaging satellite The first vertex U ₁ (x _1,i ,y _1,i ) and the second vertex U ₂ (x _2,i ,y _2,i ) that are half the width of the strip-shaped region can be obtained using the system of equations (3) to express:

Among them, x represents longitude, y represents latitude, C ₁ (i)=A·y ₁ (i)-B·x ₁ (i), x ₁ (i) and y ₁ (i) are the first grid g respectively The longitude and latitude values of the top-left vertex p ₁ ( _i ) of i, w _j is the width of the strip-shaped area imaged (covered) by the j-th imaging satellite s _j , A, B, and C are the imaging satellites The parameters of the sweep line, the first vertex and the second vertex are denoted as U ₁ (x _1,i ,y _1,i ) and U ₂ (x _2,i ,y _2,i ), x _1,i and y ₁ respectively _{, i} are the longitude and latitude values of the first vertex, respectively, x _2,i and y _2,i are the longitude and latitude values of the second vertex, respectively;

A second grid g _k is selected in the second grid list LG. The number of the second grid g _k in the second grid list LG is greater than or equal to the number of the first grid, that is, k≥i. A straight line perpendicular to the imaging scanning direction of the imaging satellite s _j on the lower right corner vertex p ₄ (z) of the second grid g _k and the distance from the imaging scanning straight line is determined to be equal to half the width of the strip-shaped area covered by the imaging satellite. The third vertex U ₃ (x _3,i ,y _3,i ) and the fourth vertex U ₄ (x _4,i ,y _4,i ),

The distance from the imaging scan line determined on the line passing through the lower right corner vertex p ₄ (k) of the second grid g _k and perpendicular to the imaging scan direction of the imaging satellite s _j is equal to the width of the strip-shaped area covered by the imaging satellite Half of the third vertex U ₃ (x _3,i ,y _3,i ) and the fourth vertex U ₄ (x _4,i ,y _4,i ) can be expressed by equation (4):

where x represents longitude, y represents latitude, C ₄ (k)=A·y ₄ (k)-B·x ₄ (k), x ₄ (k) and y ₄ (k) are respectively the second grid g The longitude and latitude values of the lower right corner vertex p ₄ ( _k ) of k, w _j is the width of the strip-shaped area imaged with the jth imaging satellite, A, B, and C are the parameters of the imaging scanning line of the imaging satellite , the third vertex and the fourth vertex are respectively represented as U ₃ (x _3,i ,y _3,i )U ₄ (x _4,i ,y _4,i ), where x _3,i and y _3,i are the first The longitude and latitude values of the three vertices, x _4,i and y _4,i are the longitude and latitude values of the fourth vertex, respectively;

Take the first vertex U ₁ (x _1,i ,y _1,i ), the second vertex U ₂ (x _2,i ,y _2,i ), the third vertex U ₃ (x _3,i ,y _{3,i )} ) and the fourth vertex U ₄ (x _4,i ,y _4,i ) are the vertexes of the coverage area, forming a coverage pattern C _s of the imaging satellite s _j ;

For the first grid g _i and the second grid g _k satisfying k≥i, traverse the grids in the second grid list LG in turn to obtain the basic coverage pattern list of the imaging satellite s _j ;

Add a dummy coverage pattern C ₀ to the base coverage pattern list of the imaging satellite s _j to obtain the coverage pattern list Q _j of the imaging satellites, the dummy cover pattern C ₀ is defined as not covering any grid, energy consumption or Override mode with time zero;

Traverse all imaging satellites in the imaging satellite list to obtain the total coverage mode list CoverList.

Taking the upper right corner vertex and the lower left corner vertex of the grid in the third grid list LG as base points, four vertices of the coverage pattern of the imaging satellite are determined according to the width of the strip-shaped area covered by the imaging satellite to form one of the imaging satellites The coverage mode, and traversing the grids in the third grid list LG to form the coverage mode list of the imaging satellite may specifically include:

A first grid g _i is arbitrarily selected from the third grid list LG, and a straight line passing through the upper right corner vertex p ₂ (i) of the first grid g _i and perpendicular to the imaging scanning straight line is determined. a first vertex U ₁ (x _1,i ,y _1,i ) and a second vertex U ₂ (x _2,i ,y _2,i ) at a distance equal to half the width of the strip-shaped area covered by the imaging satellite;

The distance from the imaging scan line on the line passing through the upper right corner vertex p ₂ (i) of the first grid g _i and perpendicular to the imaging scan direction of the imaging satellite s _j is equal to the width of the strip-shaped area covered by the imaging satellite s j Half of the first vertex U ₁ (x _1,i ,y _1,i ) and the second vertex U ₂ (x _2,i ,y _2,i ) can be expressed by equation system (5):

Among them, x represents longitude, y represents latitude, C ₂ (i)=A·y ₂ (i)-B·x ₂ (i), x ₂ (i) and y ₂ (i) are the first grid g respectively The longitude and latitude values of the upper right corner vertex p ₂ (k) of _i , w _j is the width of the strip-shaped area imaged with the jth imaging satellite, A, B, and C are the parameters of the imaging scanning line of the imaging satellite , the first vertex and the second vertex are denoted as U ₁ (x _1,i ,y _1,i ) and U ₂ (x _2,i ,y _2,i ), respectively, and x _1,i and y _1,i are respectively The longitude and latitude values of the first vertex, x _2,i and y _2,i are the longitude and latitude values of the second vertex, respectively;

A second grid g _k is selected in the third grid list LG. The number of the second grid g _k in the second grid list LG is greater than or equal to the number of the first grid, that is, k≥i. On the lower left corner vertex p ₃ (k) of the second grid g _k and perpendicular to the imaging scanning direction of the imaging satellite s _j , determine the distance from the imaging scanning line equal to half the width of the strip-shaped area covered by the imaging satellite. The third vertex U ₃ (x _3,i ,y _3,i ) and the fourth vertex U ₄ (x _4,i ,y _4,i );

The distance from the imaging scan line on the line passing through the lower left corner vertex p ₃ (k) of the second grid g _z and perpendicular to the imaging scan direction of the imaging satellite s _j is equal to the width of the strip-shaped area covered by the imaging satellite s j Half of the third vertex U ₃ (x _3,i ,y _3,i ) and the fourth vertex U ₄ (x _4,i ,y _4,i ) can be expressed by equation (6):

where x represents longitude, y represents latitude, C ₃ (k)=A·y ₃ (k)-B·x ₃ (k), x ₃ (k) and y ₃ (k) are respectively the second grid g The longitude and latitude values of the lower left corner vertex p ₃ ( _k ) of k, w _j is the width of the strip-shaped area imaged with the jth imaging satellite, A, B, and C are the parameters of the imaging scanning line of the imaging satellite , the third vertex and the fourth vertex are respectively represented as U ₃ (x _3,i ,y _3,i )U ₄ (x _4,i ,y _4,i ), where x _3,i and y _3,i are the first The longitude and latitude values of the three vertices, x _4,i and y _4,i are the longitude and latitude values of the fourth vertex, respectively;

Take the first vertex U ₁ (x _1,i ,y _1,i ), the second vertex U ₂ (x _2,i ,y _2,i ), the third vertex U ₃ (x _3,i ,y _{3,i )} ) and the fourth vertex U ₄ (x _4,i ,y _4,i ) are the vertexes of the coverage area, forming a coverage pattern C _s of the imaging satellite s _j ;

For the first grid g _i and the second grid g _k satisfying k≥i, traverse the grids in the third grid list LG in turn to obtain the basic coverage pattern list of the imaging satellite s _j ;

Add a dummy cover pattern C ₀ to the base cover pattern list of each imaging satellite s _j to obtain the cover pattern list Q _j of the imaging satellites, the dummy cover pattern C ₀ is defined as not covering any grid, consuming Coverage mode with zero energy or time;

Traverse all imaging satellites in the imaging satellite list to obtain the total coverage mode list CoverList.

For example, the first inclination direction may refer to the direction of the straight line whose parameters A and B of the imaging scanning line satisfy A·B>0, and the second inclination direction may refer to, for example, the direction of the line in which the parameters A and B of the imaging scanning line satisfy A·B<0. direction.

Override mode selection

FIG. 3 is a flow chart of selecting a coverage mode of a planning method for minimizing the maximum completion time of a multi-imaging satellite area coverage task according to an embodiment of the present invention. As shown in Figure 3, in an embodiment of the present invention, in the case of sufficient imaging satellite resources, it is expected to complete the coverage of the rectangular area A in the shortest time, and selecting a coverage mode may include the following steps:

For each of the plurality of imaging satellites:

In step S201, the initial value BestLB' of the time lower bound, the initial value BestSolu' of the time consumption, and the Lagrange multiplier sequence λ={λ(1),λ(2)...,λ(i),... , the initial value of λ(N _G )}, the upper limit value T of the number of iterations, the time coefficient sequence ϕ={ϕ(1),ϕ(2)…,ϕ(s),…,ϕ(N _T )} of initial value, where λ(i) is the Lagrangian multiplier corresponding to the ith grid, where φ(s) is the time coefficient corresponding to the sth coverage pattern;

In step S202, according to the startup time and shutdown time of the sensor carried on the imaging satellite _sj , calculate the time ds required by the imaging satellite _sj to execute the coverage mode _{Cs ;}

In step S203, the Lagrangian relaxation technique is used to establish an objective function that minimizes the time required for the imaging satellite to execute the coverage mode, so as to obtain the time target value consumed by the imaging satellite to execute the coverage mode. The objective function can use formula (2') To represent;

Among them, u'(s) is the time target value of the time spent by the imaging satellite S _j to execute the coverage mode C _s , d _s is the time required for the imaging satellite s _j to execute the coverage mode C _s , and φ(s) is the same as the s-th coverage mode. The time coefficient corresponding to the mode, G′ is the grid set composed of the second grid list LG and the third grid list LG, λ(i) is the Lagrange multiplier corresponding to the ith grid, WC[ s,i] is defined as WC[s,i]=1 when judging that the s-th covering pattern C _s completely covers the _i -th grid gi, and judging that the s-th covering pattern C _s is not complete In the case of covering the _i -th grid gi, WC[s,i]=0;

In step S204, calculate the time consumption target value u' of each coverage mode C _s in the coverage mode list Q _j of the imaging satellite s _j according to formula (2'), and select the consumed time from the coverage mode list Q _j A coverage pattern C _s' with the smallest time target value u', all the imaging satellites s _j corresponding to the coverage pattern C _{s' with the smallest consumed time target value u'} form a coverage scheme SoluList.

In step S205, revise the coverage scheme SoluList, and obtain the revised coverage scheme SoluList';

In step S206, update the initial value BestLB' of the time lower bound, and the initial value BestSolu' of time consumption;

In step S207, formula (6') is used to calculate the optimality parameter of the revised feasible coverage mode according to the updated initial value of the lower bound of time BestLB' and the updated initial value of time consumption BestSolu';

Among them, BestLB' is the initial value of the updated time lower bound, BestSolu' is the initial value of the updated time consumption, and Gap' is the value of the optimality parameter of the revised coverage scheme;

In step S208, update the value of the Lagrange multiplier;

The objective function is updated by updating the value of the Lagrangian multiplier, and based on the updated objective function, a coverage mode with the smallest time-consuming target value of each imaging satellite is reselected to form a coverage scheme, and for the newly formed coverage scheme Recalculate the value of the optimality parameter;

In step S209, it is determined that the number of updates of the value of the Lagrange multiplier reaches the upper limit value T of the number of iterations;

In step S210, when it is judged that the number of updates of the value of the Lagrangian multiplier reaches the upper limit of the number of iterations, the coverage with the smallest value of the optimality parameter is selected from the selected and reselected multiple coverage schemes Scheme, as an overlay scheme for covering a rectangular area.

In a preferred embodiment of the present invention, the initial value BestLB' of the time lower bound can be set to a value of 0, for example, the initial value of the energy consumption BestSolu' can be set to a sufficiently large positive integer, for example, the upper limit value T of the number of iterations can be, for example, Set to a value of 100, the initial value of λ(i) can be set to a value of 10, for example, and the initial value of φ(s) can be set to a value of 10, for example.

In an embodiment of the present invention, modifying the coverage scheme SoluList, and obtaining the modified coverage scheme SoluList' may specifically include the following steps:

Determine whether the grid g _i in the rectangular area A is completely covered for the coverage scheme SoluList;

In the case of judging that the grid _gi in the rectangular area A is not completely covered, mark the grid gi as "uncovered", and find out the grid _gi that is marked as "uncovered" in the coverage scheme SoluList. The grid is closest to the coverage mode in position, select the coverage mode that is closest to the coverage mode in the coverage mode list of the imaging satellite corresponding to the coverage mode, and replace the coverage mode to obtain the corrected coverage mode. The coverage scheme SoluList'.

Updating the initial value of the time lower bound BestLB', the initial value of the time consumption BestSolu', and the initial value of the time coefficient sequence may specifically include the following steps:

The value LB'(t) of the lower bound of time consumed by the coverage scheme is calculated by formula (3'):

LB′(t)=LB′ ₁ (t)+LB′ ₂ (t)+LB′ ₃ (t) Equation (3′)

SoluList′为修正后的覆盖方案，C_s为第s个覆盖模式，u′(s)为成像卫星S_j执行覆盖模式C_s消耗的时间目标值，λ(i)为与第i个网格对应的拉格朗日乘子，max{d_s}为执行修正后的覆盖方案SoluList′中的一个覆盖模式所需要的最大时间，d_s为成像卫星s_j执行覆盖模式C_s所需要的时间，φ(s)为与第s个覆盖模式对应的时间系数；in,

SoluList' is the revised coverage scheme, C _s is the s-th coverage pattern, u'(s) is the time target value consumed by the imaging satellite S _j to execute the coverage pattern C _s , λ(i) is the same as the ith grid The corresponding Lagrangian multiplier, max{d _s } is the maximum time required to execute a coverage pattern in the revised coverage scheme SoluList′, d _s is the time required for the imaging satellite s _j to execute the coverage pattern C _s , φ(s) is the time coefficient corresponding to the sth coverage pattern;

Equation (4') is used to calculate the time solu'(t) consumed by the imaging satellite to execute the revised coverage scheme:

solu′(t)=max′{d _s } Equation (4′)

Among them, solu'(t) is the time consumed by the revised coverage scheme, max'{d _s } is the maximum time required to execute a coverage pattern in the revised coverage scheme SoluList', and d _s is the imaging satellite s _j The time required to execute the overlay mode C _s ;

Determine whether the value LB'(t) of the time lower bound is greater than the initial value BestLB' of the time lower bound. 'Update to the value LB'(t) of the lower bound of time;

Determine whether the value of the time solu'(t) consumed by the imaging satellite to execute the revised coverage scheme is less than the initial value of the time consumption BestSolu', when judging that the value of the time solu'(t) consumed by the imaging satellite to execute the revised coverage scheme is less than In the case of the initial value of time consumption BestSolu', update the initial value of energy consumption BestSolu' to the value of time solu'(t) consumed by the imaging satellite to execute the revised coverage scheme;

Use formula (5′) to update the value of the Lagrange multiplier:

λ′(i)=λ(i)+θ′·h(i) Equation (5′)

Among them, λ′(i) is the value of the updated Lagrangian multiplier, λ(i) is the Lagrangian multiplier corresponding to the ith grid, θ′=ρ·θ, ρ and θ are initialization coefficients, h(i)=1-v(i), v(i) is the number of coverage patterns that can completely cover grid g _i in the revised coverage scheme SoluList';

Use formula (8) to update the value of the time coefficient:

φ′(s)=φ(s)+θ· _ls Formula (8)

l_s是与覆盖模式C_s对应的条带形区域的长度，

max{d_s}为执行修正后的覆盖方案SoluList′中的一个覆盖模式所需要的最大时间，d_s为成像卫星s_j执行覆盖模式C_s所需要的时间。Among them, φ′(s) is the updated time coefficient corresponding to the sth coverage pattern, φ(s) is the time coefficient corresponding to the sth coverage pattern, θ is the initialization coefficient,

l _s is the length of the strip-shaped region corresponding to the coverage pattern C _s ,

max{d _s } is the maximum time required to execute one coverage pattern in the revised coverage scheme SoluList', and d _s is the time required for the imaging satellite s _j to execute the coverage pattern C _s .

In an embodiment of the present invention, selecting an overlay mode may further include the following steps:

Set the set value of the optimality parameter;

Determine whether the value of the optimality parameter Gap is less than the set value of the optimality parameter;

When it is judged that the value of the optimality parameter Gap is smaller than the set value of the optimality parameter, a modified coverage scheme corresponding to the optimality parameter Gap is selected as the coverage scheme for covering the rectangular area A.

The set value of the optimality parameter can be set to 0.1, for example.

Embodiments of the present invention also provide a computer-readable storage medium, where instructions are stored on the storage medium, and the instructions are used to, when executed by the processor, cause the processor to execute any one of the above-mentioned maximum completion time of the multi-imaging satellite area coverage task Minimization planning method.

Through the above-mentioned embodiments, the planning method for minimizing the maximum completion time of the multi-imaging satellite area coverage task is divided into two stages, and the generation coverage mode and the selection coverage mode are separated, so that the structure of the method is reasonable and the hierarchy is clear; the method can provide at least one A coverage scheme that takes as little time as possible for imaging satellites to complete coverage.

The optional embodiments of the embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details of the above-mentioned embodiments. Within the scope of the technical idea of the embodiments of the present invention, the The technical solution undergoes a variety of simple modifications, and these simple modifications all belong to the protection scope of the embodiments of the present invention.

In addition, it should be noted that each specific technical feature described in the above-mentioned specific implementation manner may be combined in any suitable manner under the circumstance that there is no contradiction. To avoid unnecessary repetition, various possible combinations are not further described in this embodiment of the present invention.

Those skilled in the art can understand that all or part of the steps in the method of the above-mentioned embodiments can be completed by instructing the relevant hardware through a program. A chip, etc.) or a processor (processor) executes all or part of the steps of the methods in the various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, Read-Only Memory (ROM, Read-Only Memory), Random Access Memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes .

In addition, various implementations of the embodiments of the present invention may also be combined arbitrarily, as long as they do not violate the ideas of the embodiments of the present invention, they should also be regarded as the contents disclosed in the embodiments of the present invention.

Claims (9)

1. A method for planning minimization of maximum completion time of coverage tasks of multiple imaging satellite regions is characterized by comprising a coverage mode generation step and a coverage mode selection step, wherein the coverage mode generation step specifically comprises the following steps:

determining imaging scanning directions of a plurality of imaging satellites;

dividing a rectangular area to be covered into a plurality of grids to generate a first grid list G;

for each of the plurality of imaging satellites:

judging whether the imaging scanning direction of the imaging satellite is a first inclined direction or a second inclined direction;

reordering the divided meshes according to the imaging scanning direction of the imaging satellite with the top left corner vertex of any mesh in the first mesh list G as a base point to generate a second mesh list LG in case that the imaging scanning direction of the imaging satellite is judged to be the first tilt direction,

determining four vertexes of a coverage pattern of the imaging satellite according to the width of a strip-shaped region covered by the imaging satellite by taking the top left vertex and the bottom right vertex of the grid in the second grid list LG as base points to form one coverage pattern of the imaging satellite, and traversing the grids in the second grid list LG to form a coverage pattern list of the imaging satellite;

reordering the divided meshes according to the imaging scanning direction of the imaging satellite with the top right corner vertex of any mesh in the first mesh list G as a base point to generate a third mesh list LG in case that the imaging scanning direction of the imaging satellite is judged to be the second inclination direction,

determining four vertexes of a coverage mode of the imaging satellite according to the width of a strip-shaped area covered by the imaging satellite by taking the vertex at the upper right corner and the vertex at the lower left corner of the grids in the third grid list LG as base points to form one coverage mode of the imaging satellite, and traversing the grids in the third grid list LG to form a coverage mode list of the imaging satellite; traversing the plurality of imaging satellites to obtain a coverage pattern set, wherein the coverage pattern set comprises a coverage pattern list of each imaging satellite;

the selection of the overlay mode specifically comprises the following steps:

for each of the plurality of imaging satellites:

setting an initial value of a time lower bound, an initial value of time consumption, an upper limit value of iteration times, an initial value of a Lagrange multiplier sequence and an initial value of a time coefficient sequence;

calculating the time required by the imaging satellite to execute the coverage mode according to the startup time and the shutdown time of a sensor carried by the imaging satellite;

establishing an objective function with minimized time required by the imaging satellite to execute the coverage mode so as to obtain a target value of time consumed by the imaging satellite to execute the coverage mode;

calculating a time target value consumed by the imaging satellite to execute each coverage mode in the coverage mode list, and selecting one coverage mode with the minimum consumed time target value from the coverage mode list;

traversing the plurality of imaging satellites to select a coverage pattern for each imaging satellite that has a minimum elapsed time target value to form a coverage plan;

modifying the coverage scheme to obtain a modified coverage scheme;

updating an initial value of the lower time bound, an initial value of the time consumption;

calculating the value of the optimality parameter of the modified coverage scheme according to the initial value of the updated time lower bound and the initial value of the updated time consumption;

updating the objective function by updating the values of the lagrangian multipliers, reselecting one coverage mode with the smallest consumed time target value for each imaging satellite based on the updated objective function to form one coverage scheme, and recalculating the values of the optimality parameters for the newly formed coverage scheme;

and updating the value of the Lagrange multiplier for multiple times, and selecting the coverage scheme with the minimum value of the optimality parameter from the multiple selected and reselected coverage schemes as the coverage scheme for covering the rectangular area under the condition that the updating times of the value of the Lagrange multiplier reach the upper limit value of the iteration times.

2. The method for planning minimization of maximum completion time of a regional coverage task of a multi-imaging satellite according to claim 1, wherein reordering the divided grids according to the imaging scanning direction of the imaging satellite with the top left vertex of any grid in the first grid list G as a base point to generate the second grid list LG specifically comprises:

randomly selecting one grid from the first grid list G, and determining a first reference point and a second reference point which have set values of distances from the vertex at the upper left corner of the selected grid on an imaging scanning straight line of the imaging satellite, wherein the first reference point is positioned at the lower right of the second reference point;

determining a reference vector by taking the first reference point as a starting point and the second reference point as an end point, determining a vector by taking the first reference point as a starting point and the top left corner vertex of any grid in the first grid list G as an end point, and calculating the projection of the vector on the reference vector;

traversing grids in the first grid list G to obtain a vector projection list;

arranging the projections in the vector projection list in descending order to reorder the meshes in the first mesh list G, constructing the second mesh list LG;

with the vertex at the top right corner of any grid in the first grid list G as a base point, reordering the divided grids according to the imaging scanning direction of the imaging satellite to generate a third grid list LG specifically includes:

randomly selecting one grid from the first grid list G, and determining a first reference point and a second reference point which have set values of the distance from the vertex at the upper right corner of the selected grid on the imaging scanning straight line of the imaging satellite, wherein the first reference point is positioned at the lower left of the second reference point;

determining a reference vector by taking the first reference point as a starting point and the second reference point as an end point, determining a vector by taking the first reference point as a starting point and the top right corner vertex of any grid in the first grid list G as an end point, and calculating the projection of the vector on the reference vector;

traversing grids in the first grid list G to obtain a vector projection list;

arranging the projections in the vector projection list in descending order to reorder the corresponding meshes in the first mesh list G, constructing the third mesh list LG.

3. The method of claim 2, wherein two points on the imaging scan line of the imaging satellite with a set distance from the top left vertex of the selected grid are represented by equation (1):

wherein x represents longitude, y represents latitude, x_l<x₁(z)<x_r，x₁(z) and y₁(z) longitude and latitude values, x, respectively, of the top left vertex of the selected mesh_lAnd x_rThe longitude values of the two points are respectively, R is the set value, and A, B, C are parameters of an imaging scanning line of the imaging satellite;

two points on the imaging scanning straight line of the imaging satellite, the distance of which from the vertex at the upper right corner of the selected grid is a set value, are expressed by an equation set (2):

wherein x represents longitude, y represents latitude, x_l<x₂(z)<x_r，x₂(z) and y₂(z) warp and weft values, x, respectively, of the top right vertex of said selected mesh_lAnd x_rThe longitude values of the two points are respectively, R is the set value, and A, B, C is the parameter of the imaging scanning line of the imaging satellite.

4. The method as claimed in claim 3, wherein determining four vertices of the coverage pattern of the imaging satellite according to the width of the strip-shaped region covered by the imaging satellite with the top left vertex and the bottom right vertex of the grid in the second grid list LG as base points to form one coverage pattern of the imaging satellite, and traversing the grid in the second grid list LG to form the coverage pattern list of the imaging satellite specifically comprises:

arbitrarily selecting a first grid in the second grid list LG, and determining a first vertex and a second vertex which are at a distance equal to half of the width of a strip-shaped area covered by the imaging satellite from an imaging scanning line on a line which passes through the top left vertex of the first grid and is perpendicular to the imaging scanning direction of the imaging satellite;

selecting a second grid in a second grid list LG, wherein the number of the second grid in the second grid list LG is greater than or equal to that of the first grid, and determining a third vertex and a fourth vertex which are away from an imaging scanning straight line by a distance equal to half of the width of a strip-shaped area covered by the imaging satellite on a straight line which passes through the vertex at the lower right corner of the second grid and is vertical to the imaging scanning direction of the imaging satellite;

forming a coverage mode of the imaging satellite by taking the first vertex, the second vertex, the third vertex and the fourth vertex as vertexes;

sequentially traversing grids in the second grid list LG for the first grid and the second grid to obtain a basic coverage mode list of the imaging satellite;

adding a virtual coverage pattern to the base coverage pattern list to obtain a coverage pattern list of the imaging satellites, the virtual coverage pattern being defined as a coverage pattern that does not cover any grid, consumes zero energy or has zero time;

taking the vertex of the upper right corner and the vertex of the lower left corner of the grid in the third grid list LG as base points, determining four vertices of the coverage pattern of the imaging satellite according to the width of the strip-shaped region covered by the imaging satellite to form one coverage pattern of the imaging satellite, and traversing the grid in the third grid list LG to form the coverage pattern list of the imaging satellite specifically includes:

arbitrarily selecting a first grid in the third grid list LG, and determining a first vertex and a second vertex which have a distance from the imaging scanning line equal to half of the width of the strip-shaped area covered by the imaging satellite on a line which passes through the vertex at the upper right corner of the first grid and is perpendicular to the imaging scanning line equation;

selecting a second grid in the third grid list LG, wherein the number of the second grid in the second grid list LG is greater than or equal to that of the first grid, and determining a third vertex and a fourth vertex which are away from an imaging scanning line by a distance equal to half of the width of a strip-shaped area covered by the imaging satellite on a line which passes through the vertex at the lower left corner of the second grid and is vertical to the imaging scanning direction of the imaging satellite;

forming a coverage mode of the imaging satellite by taking the first vertex, the second vertex, the third vertex and the fourth vertex as vertexes;

sequentially traversing grids in the third grid list LG for the first grid and the second grid to obtain a basic coverage mode list of the imaging satellite;

adding a virtual coverage pattern to the base coverage pattern list to obtain a list of coverage patterns for the imaging satellite, the virtual coverage pattern being defined as a coverage pattern that does not cover any grid, consumes zero energy, or is zero in time.

5. The method of claim 4, wherein the first vertex and the second vertex on a straight line perpendicular to the imaging scanning direction of the imaging satellite and passing through the top left corner vertex of the first grid are expressed by equation (3), wherein the distance between the first vertex and the imaging scanning straight line is equal to half of the width of the strip-shaped region covered by the imaging satellite:

wherein x represents longitude, y represents latitude, C₁(i)＝A·y₁(i)-B·x₁(i)，x₁(i) And y₁(i) Respectively the longitude value and the latitude value of the top left corner vertex of the first grid, w_jA, B, C are parameters of the imaging scan line of the imaging satellite for the width of the strip-shaped region imaged with the jth imaging satellite, the first vertex and the second vertex being respectively denoted as U₁(x_1,i,y_1,i) And U₂(x_2,i,y_2,i)，x_1,iAnd y_1,iRespectively a longitude value and a latitude value, x, of the first vertex_2,iAnd y_2,iThe longitude value and the latitude value of the second vertex are respectively;

determining, on a straight line passing through a lower right corner vertex of the second grid and perpendicular to an imaging scanning direction of the imaging satellite, a third vertex and a fourth vertex that are at a distance from the imaging scanning straight line equal to half a width of a strip-shaped region covered by the imaging satellite, using equation set (4):

wherein x represents longitude, y represents latitude, C₄(k)＝A·y₄(k)-B·x₄(k)，x₄(k) And y₄(k) Warp and weft values, w, respectively, of the vertices of the lower right corner of the second grid_jA, B, C are parameters of the imaging scan lines of the imaging satellites for the width of the strip-shaped region imaged with the jth imaging satellite, the third and fourth vertices being denoted as U, respectively₃(x_3,i,y_3,i)U₄(x_4,i,y_4,i)，x_3,iAnd y_3,iRespectively the longitude value and the latitude value of the third vertex，x_4,iAnd y_4,iThe longitude value and the latitude value of the fourth vertex are respectively;

a first vertex and a second vertex on a straight line which passes through the vertex at the upper right corner of the first grid and is perpendicular to the imaging scanning direction of the imaging satellite, and which has a distance from the imaging scanning straight line equal to half the width of the strip-shaped region covered by the imaging satellite, are expressed by equation system (5):

wherein x represents longitude, y represents latitude, C₂(i)＝A·y₂(i)-B·x₂(i)，x₂(i) And y₂(i) Respectively the longitude value and the latitude value of the top right vertex of the first grid, w_jA, B, C are parameters of the imaging scan line of the imaging satellite for the width of the strip-shaped region imaged with the jth imaging satellite, the first vertex and the second vertex being respectively denoted as U₁(x_1,i,y_1,i) And U₂(x_2,i,y_2,i)，x_1,iAnd y_1,iRespectively a longitude value and a latitude value, x, of the first vertex_2,iAnd y_2,iThe longitude value and the latitude value of the second vertex are respectively;

a third vertex and a fourth vertex on a straight line which passes through a vertex at the lower left corner of the second grid and is perpendicular to the imaging scanning direction of the imaging satellite, and which are at a distance from the imaging scanning straight line equal to half the width of the strip-shaped region covered by the imaging satellite, are expressed by equation set (6):

wherein x represents longitude, y represents latitude, C₃(k)＝A·y₃(k)-B·x₃(k)，x₃(k) And y₃(k) Respectively the longitude value and the latitude value of the vertex of the lower left corner of the second grid, w_jIs as followsThe widths, A, B, C, of the strip-shaped regions imaged by the j imaging satellites are all parameters of the imaging scanning lines of the imaging satellites, and the third vertex and the fourth vertex are respectively expressed as U₃(x_3,i,y_3,i)U₄(x_4,i,y_4,i)，x_3,iAnd y_3,iRespectively the longitude value and the latitude value, x, of the third vertex_4,iAnd y_4,iThe longitude value and the latitude value of the fourth vertex are respectively.

6. The method for minimizing the maximum completion time of the coverage tasks of the multiple imaging satellite regions according to claim 5, wherein the step of modifying the coverage scheme to obtain the modified coverage scheme specifically comprises the steps of:

judging whether the coverage scheme can completely cover the grids in the rectangular area;

in the case that the coverage scheme is judged not to be capable of completely covering the grids in the rectangular area, finding out a coverage pattern to be replaced, of which the strip-shaped area is closest to the uncovered grids, in the coverage scheme, and selecting a coverage pattern, of which the strip-shaped area is closest to the strip-shaped area of the coverage pattern to be replaced, from a coverage pattern list of the imaging satellite corresponding to the coverage pattern to be replaced to replace the coverage pattern to be replaced in the coverage scheme.

7. The method for planning minimization of maximum completion time of coverage tasks in multiple imaging satellite regions according to claim 6, wherein the objective function of minimization of time required for the imaging satellite to perform the coverage mode, which is established by Lagrangian relaxation technology, is expressed by equation (2'):

wherein u'(s) is a target value of time consumed by the imaging satellite to perform the s-th coverage mode, d_sTime required to perform an s-th coverage mode for the imaging satellitePhi(s) is a time coefficient corresponding to the s-th coverage mode, G' is a grid set formed by the second grid list LG and the third grid list LG, and lambda (i) is a Lagrangian multiplier corresponding to the i-th grid, WC [ s, i [ ]]Is defined as being in judging the s-th overlay mode C_sCompletely covers the ith grid g_iIn the case of (2), WC [ s, i ]]1, judging the s-th coverage mode C_sDoes not completely cover the ith grid g_iIn the case of (2), WC [ s, i ]]＝0。

8. The method according to claim 7, wherein the updating of the initial value of the lower time bound and the initial value of the time consumption comprises the following steps:

the lower bound LB '(t) of the time consumed by the coverage scheme is calculated using equation (3'):

LB′(t)＝LB′₁(t)+LB′₂(t)+LB′₃(t) formula (3')

Wherein,

LB′₂(t)＝∑λ(i)，

SoluList' is the revised coverage scheme, C_sFor the s-th coverage mode, u'(s) is a time target value consumed by the imaging satellite to perform the s-th coverage mode, λ (i) is a Lagrangian multiplier corresponding to the i-th grid, max { d }_sD is the maximum time required to perform a coverage mode in the revised coverage scheme_sFor the imaging satellite s_jThe time required for executing the s-th coverage mode, phi(s) being a time coefficient corresponding to the s-th coverage mode;

calculating the value of the time (t) consumed by the imaging satellite to perform the modified coverage scheme using equation (4'):

solu′(t)＝max′{d_sformula (4');

wherein solu '(t) is a value of time consumed by the imaging satellite to perform the modified coverage plan, max' { d_sD is the maximum time required to perform a coverage mode in the revised coverage scheme_sThe time required to perform an s-th coverage mode for the imaging satellite;

judging whether the value of the lower time bound is larger than the initial value of the lower time bound or not, and updating the initial value of the lower time bound to the value of the lower time bound under the condition that the value of the lower time bound is judged to be larger than the initial value of the lower time bound;

judging whether the value of the time consumed by the modified coverage scheme is smaller than the initial value of the time consumption, and updating the initial value of the time consumption to the value of the time consumed by the modified coverage scheme under the condition that the value of the time consumed by the modified coverage scheme is judged to be smaller than the initial value of the time consumption;

updating the value of the Lagrangian multiplier using equation (5'):

λ ' (i) ═ λ (i) + θ ' · h (i) formula (5 ')

Wherein λ '(i) is a value of an updated lagrangian multiplier, λ (i) is a lagrangian multiplier corresponding to an ith grid, θ' ═ ρ · θ, ρ and θ are initialization coefficients, h (i) ═ 1-v (i), and v (i) is the number of coverage modes that can completely cover the ith grid in the modified coverage scheme;

updating the value of the time coefficient using equation (8):

φ′(s)＝φ(s)+θ·l_sformula (8)

Where φ'(s) is the updated time coefficient corresponding to the s-th coverage mode, φ(s) is the time coefficient corresponding to the s-th coverage mode, θ is the initialization coefficient,

l_sis the length of the strip-shaped area corresponding to the s-th coverage pattern,

max{d_sd is the maximum time required to perform a coverage mode in the revised coverage scheme_sThe time required to perform the s-th coverage mode for the imaging satellite.

9. The method of claim 8, wherein the value of the optimality parameter of the modified coverage solution is calculated using equation (6'):

wherein BestLB ' is an initial value of the updated time lower bound, BestSolu ' is an initial value of the updated energy consumption, and Gap ' is a value of the optimality parameter of the modified coverage scheme.

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