CN108334979B - A multi-imaging satellite mission planning method for area coverage - Google Patents

A multi-imaging satellite mission planning method for area coverage Download PDF

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CN108334979B
CN108334979B CN201810010372.0A CN201810010372A CN108334979B CN 108334979 B CN108334979 B CN 108334979B CN 201810010372 A CN201810010372 A CN 201810010372A CN 108334979 B CN108334979 B CN 108334979B
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胡笑旋
朱外明
杨善林
靳鹏
夏维
罗贺
马华伟
王国强
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Hefei University of Technology
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Abstract

The invention discloses a multi-imaging satellite task planning method facing area coverage, and belongs to the technical field of satellite communication. The multi-imaging satellite task planning method comprises two stages, wherein 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 multi-imaging satellite mission planning method can provide at least one coverage scheme, so that the total energy consumed by a plurality of imaging satellites is as small as possible. The method also evaluates the quality of the selected coverage scheme by calculating an optimality parameter for the coverage scheme.

Description

Multi-imaging satellite task planning method facing area coverage
Technical Field
The invention relates to the technical field of satellite communication, in particular to a multi-imaging satellite task planning method facing area coverage.
Background
Taking the search of horse navigation MH370 as an example, 3 months and 20 days 2014, australia claims to find suspected MH370 debris in the south indian ocean at the location: latitude-43.58, longitude 90.57. To search for the area near the point, the range may be expanded to a square area centered on the point.
China has invoked multiple imaging satellites to conduct a search of the MH370, each imaging satellite having an imaging region that is a strip-shaped region. Fig. 1 is a schematic diagram showing a strip-shaped region imaged by one imaging satellite, and as shown in fig. 1, by controlling the on-off time of a sensor (such as a camera) on the imaging satellite, the position of the strip-shaped region imaged by the sensor can be changed along the imaging scanning direction, and the length of the strip-shaped region can also be changed.
Because the imaging of the imaging satellites needs to consume energy, the positions of the strip-shaped areas imaged by the imaging satellites are reasonably arranged, so that the total energy consumed by the imaging satellites is as small as possible on the premise that the whole area is completely covered, and the method has a vital significance.
Disclosure of Invention
The invention aims to provide a region coverage-oriented multi-imaging satellite task planning method, which obtains a coverage scheme with the lowest consumed total energy by adjusting the length of a strip-shaped region imaged by an imaging satellite and the position along the imaging scanning direction of the imaging satellite.
In order to achieve the above object, an embodiment of the present invention provides a method for planning a multi-imaging satellite mission facing area coverage, including generating a coverage mode and selecting the coverage mode, where the generating the coverage mode specifically includes 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 a plurality of imaging satellites: judging whether the imaging scanning direction of the imaging satellite is a first inclined direction or a second inclined direction; under the condition that the imaging scanning direction of the imaging satellite is judged to be a first inclined direction, the upper left vertex of any grid in the first grid list G is taken as a base point, the divided grids are reordered according to the imaging scanning direction of the imaging satellite to generate a second grid list LG, the upper left vertex and the lower right vertex of the grid in the second grid list LG are taken as base points, four vertices of a coverage mode of the imaging satellite are determined according to the width of a strip-shaped area covered by the imaging satellite to form one coverage mode of the imaging satellite, and the grids in the second grid list LG are traversed to form a coverage mode list of the imaging satellite; under the condition that the imaging direction of the imaging satellite is judged to be the second inclination direction, the divided grids are reordered according to the imaging scanning direction of the imaging satellite by taking the top right vertex of any grid in the first grid list G as a base point to generate a third grid list LG, the top right vertex and the bottom left vertex of the grid in the third grid list LG are taken as base points, four vertices of the coverage mode of the imaging satellite are determined according to the width of the strip-shaped area covered by the imaging satellite to form one coverage mode of the imaging satellite, and the grids in the third grid list LG are traversed to form the 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 a plurality of imaging satellites: setting an initial value of an energy lower bound, an initial value of energy consumption, an upper limit value of iteration times and an initial value of a Lagrange multiplier sequence; calculating the length of a strip-shaped area of a coverage mode of the imaging satellite; calculating the energy consumed by the imaging satellite to execute the coverage mode according to the length of the strip-shaped area of the coverage mode of the imaging satellite; establishing an objective function for minimizing energy consumed by the imaging satellite by adopting a Lagrange relaxation technology so as to obtain an energy target value consumed by the imaging satellite in a coverage mode; calculating an energy target value consumed by each coverage mode in the coverage mode list executed by the imaging satellite, and selecting one coverage mode with the minimum consumed energy target value from the coverage mode list; traversing the plurality of imaging satellites to select a coverage mode with a minimum energy target value consumed by each imaging satellite to form a coverage scheme; modifying the coverage scheme to obtain a modified coverage scheme; updating the initial value of the lower energy bound and the initial value of energy consumption; calculating the value of the optimality parameter of the modified coverage scheme according to the initial value of the updated lower energy bound and the initial value of the updated energy consumption; updating an objective function by updating the values of the Lagrange multipliers, reselecting a coverage mode with the minimum consumed energy target value of each imaging satellite based on the updated objective function to form a coverage scheme, and recalculating the value of the optimality parameter 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 mode 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.
By the technical scheme, the multi-imaging satellite task planning method facing the area coverage is divided into two stages, and the coverage mode generation and the coverage mode selection are separated, so that the method is reasonable in structure and clear in hierarchy; the multi-imaging satellite mission planning method can provide at least one coverage scheme which enables the total energy consumed by a plurality of imaging satellites to be as small as possible.
Additional features and advantages of embodiments of the invention will be set forth in the detailed description which follows.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention without limiting the embodiments of the invention. In the drawings:
FIG. 1 shows a schematic view of an imaged strip-shaped region of one imaging satellite;
FIG. 2 is a flow chart of coverage pattern generation for a method of multi-imaging satellite mission planning for area coverage according to an embodiment of the present invention;
fig. 3 is a flow chart of a coverage mode selection of a method for area coverage oriented multi-imaging satellite mission planning according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
In the present application, unless otherwise stated, the terms "upper left vertex", "lower left vertex", "upper right vertex", and "lower right vertex" used herein generally refer to the "upper left vertex", "lower left vertex", "upper right vertex", and "lower right vertex" shown in the drawings. "inner and outer" refer to the inner and outer contours of the respective component itself.
In an embodiment of the present application, the imaging scan line is a centerline of the imaging scan region of the corresponding imaging satellite in the scan direction.
In embodiments of the present application, coverage mode may refer to an imaging coverage area (or imaging scan area) of an imaging satellite.
Overlay mode generation
For example, using NTCovering a rectangular area A to be covered by the imaging satellites can comprise two stages of generating a covering mode and selecting the covering mode, wherein N isTThe imaging satellites form a list S, S of imaging satellites which can be recorded as
Figure BDA0001540081940000041
FIG. 2 is a flow chart of coverage pattern generation for a method of multi-imaging satellite mission planning for area coverage according to an embodiment of the present invention; as shown in fig. 2, in an embodiment of the present invention, generating the overlay mode may include:
in step S101, imaging scan directions of a plurality of imaging satellites are determined;
in step S102, a 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 numbered in sequence, where the first grid list G can be recorded as
Figure BDA0001540081940000042
Define the ith grid giThe coordinates of the top left corner vertex, the top right corner vertex, the bottom left corner vertex and the bottom right corner vertex are respectively p1(i)＝＜x1(i),y1(i)＞、p2(i)＝＜x2(i),y2(i)＞、p3(i)＝＜x3(i),y3(i)＞、p4(i)＝＜x4(i),y4(i)＞；
For each imaging satellite in the list S of imaging satellites:
in step S103, it is determined whether the imaging scan direction of the imaging satellite is the first inclination direction or the second inclination direction. The first tilt direction may include, for example, a direction "from an upper left corner vertex to a lower right corner vertex" or a direction "from a lower right corner vertex to an upper left corner vertex", or a direction that generally tends to follow a direction "from an upper left corner vertex to a lower right corner vertex" or "from a lower right corner vertex to an upper left corner vertex" (e.g., to tilt left in the figure relative to the vertical direction). The second tilt direction may include, for example, a direction "from a lower left corner vertex to an upper right corner vertex" or a direction "from an upper right corner vertex to a lower left corner vertex", or a general inclination in a direction "from a lower left corner vertex to an upper right corner vertex" or "from an upper right corner vertex to a lower left corner vertex" (e.g., tilted to the right in the figure with respect to the vertical direction).
In step S104, in a case where it is determined that the imaging scanning direction of the imaging satellite is the first inclination direction, with the top left corner vertex of any grid in the first grid list G as a base point, reordering the divided multiple grids according to the imaging scanning direction of the imaging satellite (i.e., renumbering the grids in the first grid list G) to generate a second grid list LG;
in step S105, with the top left corner vertex and the bottom right corner vertex of the grids in the second 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 all the grids in the second grid list LG to form a coverage pattern list of the imaging satellite;
in step S106, in a case where it is determined that the imaging scanning direction of the imaging satellite is the second inclination direction, with the top-right vertex of any grid in the first grid list G as a base point, reordering the divided multiple grids according to the imaging scanning direction of the imaging satellite (i.e., renumbering the grids in the first grid list G) to generate a third grid list LG;
in step S107, with the top-right corner vertex and the bottom-left corner vertex of the grids 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 all the grids in the third grid list LG to form a coverage pattern list of the imaging satellite;
in step S108, each imaging satellite in the list S of imaging satellites is traversed to obtain a set of coverage patterns including a list of coverage patterns for each imaging satellite.
In an embodiment of the present invention, the reordering (numbering) 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 may specifically include:
arbitrarily selecting a grid G from the first grid list GzThe grid g to be selected is determined on a line parallel to the imaging scan direction of the imaging satellite (hereinafter referred to as imaging scan line)zTop left corner vertex p of1(z) two points P at a distance Rl(xl,yl) And Pr(xr,yr) Where R may be, for example, a value greater than the length of the diagonal apex line of the rectangular area A, xlAnd ylAre respectively a point Pl(xl,yl) Warp and weft values of (2), xrAnd yrAre respectively a point Pr(xr,yr) Warp and weft values of, and xl＜xr。
Grid g selected on the imaging scanning line of the imaging satellitezTop left corner vertex p of1(z) two points at a distance R can be represented using equation set (1):
Figure BDA0001540081940000061
wherein x represents longitude, y represents latitude, xl＜x1(z)＜xr，x1(z) and y1(z) respectively, the selected grid gzTop left corner vertex p of1Longitude and latitude of (z)Value, xlAnd xrAre respectively a point Pl(xl,yl) And point Pr(xr,yr) R is a set value, A, B, C is a parameter of an imaging scan line of the imaging satellite;
at point Pr(xr,yr) As a starting point, with a point Pl(xl,yl) Determining a reference vector for the endpoint, at point Pr(xr,yr) Starting from an arbitrary grid G in the first grid list GiTop left corner vertex p of1(i) Determining a vector for the endpoint, calculating a projection of the vector on a reference vector;
traversing 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 meshes in the first mesh list G, constructing a second mesh list LG.
With the vertex at the upper right corner of any grid in the first grid list G as a 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:
arbitrarily selecting a grid G from the first grid list GzDetermining and selecting grid g on imaging scanning line of imaging satellitezTop right corner vertex p2(z) two points P at a distance Rl(xl,yl) And Pr(xr,yr) Where R may be, for example, a value greater than the length of the diagonal apex line of the rectangular area A, xlAnd ylAre respectively a point Pl(xl,yl) Warp and weft values of (2), xrAnd yrAre respectively a point Pr(xr,yr) Warp and weft values of, and xl＜xr。
Grid g selected on the imaging scanning line of the imaging satellitezTop right corner vertex p2(z) two points at a distance R can be represented using equation set (2):
Figure BDA0001540081940000071
wherein x represents longitude, y represents latitude, xl＜x2(z)＜xr，x2(z) and y2(z) respectively, the selected grid gzTop right corner vertex p2Longitude and latitude values of (z), xlAnd xrAre respectively a point Pl(xl,yl) And point Pr(xr,yr) The longitude value of (a), R is a set value, and A, B, C are parameters of an imaging scanning line of the imaging satellite;
at point Pl(xl,yl) As a starting point, with a point Pr(xr,yr) Determining a reference vector for the endpoint, at point Pl(xl,yl) As a starting point, an arbitrary grid G in the first grid list GiTop right corner vertex p2(i) Determining a vector for the endpoint, calculating a projection of the vector on a reference vector;
traversing 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, the corresponding meshes in the first mesh list G are reordered (numbered), and a third mesh list LG is constructed.
In an embodiment of the present invention, taking the top left corner vertex and the bottom right corner vertex of the grids in the second 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 all the grids in the second grid list LG to form the coverage pattern list of the imaging satellite may specifically include:
arbitrarily selecting a first mesh g in the second mesh list LGiAfter passing through the first grid giTop left corner vertex p of1(i) And with imaging satellites sjIs determined to be equal to the imaging scanning line Ax + By + C By a distance of 0 on a line perpendicular to the imaging scanning directionFirst vertex U of half the width of the strip-shaped area covered by the satellite1(x1,i,y1,i) And a second vertex U2(x2,i,y2,i)，
Through the first grid giTop left corner vertex p of1(i) And with imaging satellites sjIs equal to a first vertex U of a half of the width of the strip-shaped area covered By the imaging satellite, the distance from the imaging scanning line Ax + By + C being 0 on a line perpendicular to the imaging scanning direction of (a)1(x1,i,y1,i) And a second vertex U2(x2,i,y2,i) Can be expressed using equation set (3):
Figure BDA0001540081940000081
wherein x represents longitude, y represents latitude, C1(i)＝A·y1(i)-B·x1(i)，x1(i) And y1(i) Are respectively a first grid giTop left corner vertex p of1(i) Warp and weft values of, wjFor the jth imaging satellite sjThe width of the imaged (covered) strip-shaped region, A, B, C, is a parameter of the imaging scan line of the imaging satellite, and the first vertex and the second vertex are respectively denoted as U1(x1,i,y1,i) And U2(x2,i,y2,i)，x1,iAnd y1,iRespectively the longitude and latitude values, x, of the first vertex2,iAnd y2,iRespectively the longitude value and the latitude value of the second vertex;
selecting a second grid g in the second grid list LGkSecond grid gkThe number in the second grid list LG is more than or equal to the number of the first grid, namely k is more than or equal to i, and the second grid g passes throughkTop point p of lower right corner4(z) and with imaging satellites sjIs determined to be a third vertex U at a distance from the imaging scanning line equal to half the width of the strip-shaped area covered by the imaging satellite on a line perpendicular to the imaging scanning direction of3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i)，
Through the second grid gkTop point p of lower right corner4(k) And with imaging satellites sjIs determined on a line perpendicular to the imaging scanning direction, and has a distance from the imaging scanning line equal to a third vertex U of half the width of the strip-shaped area covered by the imaging satellite3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i) Can be expressed using equation set (4):
Figure BDA0001540081940000091
wherein x represents longitude, y represents latitude, C4(k)＝A·y4(k)-B·x4(k)，x4(k) And y4(k) Are respectively a second grid gkTop point p of lower right corner4(k) Warp and weft values of, wjA, 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(x3,i,y3,i)U4(x4,i,y4,i)，x3,iAnd y3,iRespectively the longitude and latitude values, x, of the third vertex4,iAnd y4,iRespectively the longitude value and the latitude value of the fourth vertex;
with the first vertex U1(x1,i,y1,i) The second vertex U2(x2,i,y2,i) The third vertex U3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i) Forming an imaging satellite s for the vertex of the coverage areajAn overlay mode Cs；
For the first grid giAnd a second grid g satisfying that k is larger than or equal to ikSequentially traversing grids in the second grid list LG to obtain the imaging satellite sjA list of base overlay modes;
in imaging satellites sjBasic coverage mode ofAdding a virtual overlay mode C to the list0To obtain a list Q of coverage patterns of the imaging satellitesjVirtual overlay mode C0Coverage patterns defined as not covering any grid, with zero energy consumed or time;
and traversing all the imaging satellites in the imaging satellite list to obtain a total coverage mode list CoverList.
Taking the vertex at the top right corner and the vertex at the bottom left corner of the grids 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 grids in the third grid list LG to form the coverage pattern list of the imaging satellite may specifically include:
arbitrarily selecting a first mesh g in the third mesh list LGiAfter passing through the first grid giTop right corner vertex p2(i) And a first vertex U which is positioned on a straight line vertical to the imaging scanning straight line and has a distance equal to half of the width of the strip-shaped area covered by the imaging satellite from the imaging scanning straight line is determined1(x1,i,y1,i) And a second vertex U2(x2,i,y2,i)；
Through the first grid giTop right corner vertex p2(i) And with imaging satellites sjIs equal to the first vertex U of the half of the width of the strip-shaped area covered by the imaging satellite1(x1,i,y1,i) And a second vertex U2(x2,i,y2,i) Can be expressed using equation set (5):
Figure BDA0001540081940000101
wherein x represents longitude, y represents latitude, C2(i)＝A·y2(i)-B·x2(i)，x2(i) And y2(i) Are respectively a first grid giTop right corner vertex p2(k) Longitude value ofAnd latitude value, wjA, 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(x1,i,y1,i) And U2(x2,i,y2,i)，x1,iAnd y1,iRespectively the longitude and latitude values, x, of the first vertex2,iAnd y2,iRespectively the longitude value and the latitude value of the second vertex;
selecting a second grid g in the third grid list LGkSecond grid gkThe number in the second grid list LG is more than or equal to the number of the first grid, namely k is more than or equal to i, and the second grid g passes throughkLower left corner vertex p3(k) And with imaging satellites sjIs determined to be a third vertex U at a distance from the imaging scanning line equal to half the width of the strip-shaped area covered by the imaging satellite on a line perpendicular to the imaging scanning direction of3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i)；
Through the second grid gzLower left corner vertex p3(k) And with imaging satellites sjIs located at a distance from the imaging scanning line equal to half the width of the strip-shaped area covered by the imaging satellite on a line perpendicular to the imaging scanning direction3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i) Can be expressed using equation set (6):
Figure BDA0001540081940000111
wherein x represents longitude, y represents latitude, C3(k)＝A·y3(k)-B·x3(k)，x3(k) And y3(k) Are respectively a second grid gkLower left corner vertex p3(k) Warp and weft values of, wjA, 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, third vertexThe point and the fourth vertex are respectively denoted as U3(x3,i,y3,i)U4(x4,i,y4,i)，x3,iAnd y3,iRespectively the longitude and latitude values, x, of the third vertex4,iAnd y4,iRespectively the longitude value and the latitude value of the fourth vertex;
with the first vertex U1(x1,i,y1,i) The second vertex U2(x2,i,y2,i) The third vertex U3(x3,i,y3,i) And a fourth vertex U4(x4,i,y4,i) Forming an imaging satellite s for the vertex of the coverage areajAn overlay mode Cs；
For the first grid giAnd a second grid g satisfying that k is larger than or equal to ikSequentially traversing grids in the third grid list LG to obtain the imaging satellite sjA list of base overlay modes;
at each imaging satellite sjAdds a virtual overlay mode C to the base overlay mode list0To obtain a list Q of coverage patterns of the imaging satellitesjVirtual overlay mode C0Coverage patterns defined as not covering any grid, with zero energy consumed or time;
and traversing all the imaging satellites in the imaging satellite list to obtain a total coverage mode list CoverList.
The first inclination direction may refer to, for example, a direction of a straight line in which parameters a and B of the imaging scan straight line satisfy a · B > 0, and the second inclination direction may refer to, for example, a direction of a straight line in which parameters a and B of the imaging scan straight line satisfy a · B < 0.
Overlay mode selection
Fig. 3 is a flow chart of a coverage mode selection of a method for area coverage oriented multi-imaging satellite mission planning according to an embodiment of the present invention. As shown in fig. 3, in an embodiment of the present invention, for the problem that the sum of the energies consumed by a plurality of imaging satellites covering a rectangular area a is expected to be minimum under the condition that the imaging satellite resources are sufficient, selecting a coverage mode may include the following steps:
for each of a plurality of imaging satellites:
in step S201, an initial value BestLB of the lower energy bound, an initial value BestSolu of the energy consumption, and a lagrange multiplier sequence λ ═ λ (1), λ (2) …, λ (i), …, λ (N) are setG) An initial value of, an upper limit value of the number of iterations T, where λ (i) is the lagrangian multiplier corresponding to the ith grid;
in step S202, an imaging satellite S is computedjCover mode CsLength l of the strip-shaped regions；
In step S203, according to the imaging satellite SjCover mode CsLength l of the strip-shaped regionsComputing an imaging satellite S using the formula (1)jExecuting overlay mode CsEnergy consumed (energy(s):
energy(s)＝ls·djformula (1)
Wherein energy (S) is imaging satellite SjExecuting overlay mode CsEnergy consumed,/sFor imaging satellites SjCover mode CsLength of the strip-shaped region of (d)jFor imaging satellites SjConsumed energy and coverage mode CsAnd is a known value;
in step S204, an objective function for minimizing energy consumed by the imaging satellite is established by using a lagrangian relaxation technique to obtain an energy target value consumed by the imaging satellite in performing a coverage mode, where the objective function may be represented by equation (2);
Figure BDA0001540081940000121
wherein u (S) is an imaging satellite SjExecuting overlay mode CsThe target value of energy consumed is the imaging satellite SjExecuting overlay mode CsThe consumed energy, G' is the grid set formed by the second grid list LG and the third grid list LG, and λ (i) is the energy consumed by the ith grid list LGCorresponding Lagrange multiplier, WC [ s, i ]]Is defined as being in the judged coverage mode CsCompletely cover the grid giIn the case of (2), WC [ s, i ]]1, in the determination coverage mode CsDoes not completely cover the grid giIn the case of (2), WC [ s, i ]]＝0；
In step S205, an imaging satellite S is calculated according to equation (2)jExecution overlay mode list QjEach of the overlay modes CsAnd from the coverage pattern list QjIn which one coverage mode C is selected in which the target value u of the consumed energy is the smallests′All imaging satellites sjCorresponding to the minimum consumed energy target value us′Forming a coverage scheme SoluList.
In step S206, the coverage scheme SoluList is modified, and a modified coverage scheme SoluList' is obtained.
In step S207, the initial value BestLB of the lower energy bound and the initial value BestSolu of the energy consumption are updated;
in step S208, the optimality parameter of the modified coverage scheme is calculated from the initial value BestLB of the updated lower energy bound and the initial value BestSolu of the updated energy consumption using equation (6):
Figure BDA0001540081940000131
wherein, BestLB is the initial value of the updated lower energy bound, BestSolu is the initial value of the updated energy consumption, and Gap is the value of the optimality parameter of the corrected coverage scheme;
in step S209, the value of the lagrangian multiplier is updated;
updating an objective function by updating the values of the Lagrange multipliers, reselecting a coverage mode with the minimum consumed energy target value of each imaging satellite based on the updated objective function to form a coverage scheme, and recalculating the value of the optimality parameter for the newly formed coverage scheme;
in step S210, it is determined that the update time of the value of the lagrangian multiplier reaches the upper limit value T of the iteration time;
in step S211, in a case where it is judged that the number of updates of the value of the lagrangian multiplier reaches the upper limit value of the number of iterations, a coverage scheme having the smallest value of the optimality parameter is selected from the plurality of coverage schemes selected and reselected as a coverage scheme for covering the rectangular area.
In a preferred embodiment of the invention, the initial value of the lower energy bound BestLB may be set to a value of 0, for example, the initial value of the energy consumption BestSolu may be set to a sufficiently large positive integer, the upper limit value T of the number of iterations may be set to a value of 100, for example, and the initial value of λ (i) may be set to a value of 10, for example.
In an embodiment of the present invention, the modifying the coverage scheme SoluList to obtain a modified coverage scheme SoluList' may specifically include the following steps:
judging the grid g in the rectangular area A for the coverage scheme SoluListiWhether or not it is completely covered;
grid g in judgment rectangular area AiIn the case of a grid that is not completely covered, grid g is divided into two or more gridsiAnd marking as ' uncovered ', finding out a coverage mode which is closest to the position of the grid marked as ' uncovered ' in the coverage scheme SoluList, selecting one coverage mode which is closest to the position of the coverage mode from the coverage mode list of the imaging satellite corresponding to the coverage mode, and replacing the coverage mode to obtain the corrected coverage scheme SoluList '.
Updating an initial value BestLB of the lower energy bound and an initial value BestSolu of the energy consumption may specifically include the following steps:
the value lb (t) of the lower bound of energy consumed by the coverage scheme is calculated using equation (3):
LB(t)＝LB1(t)+LB2(t) formula (3)
Wherein LB (t) is a value covering a lower bound of the energy consumed by the scheme,
Figure BDA0001540081940000141
LB2(t) Σ λ (i), u(s) is the target value of the energy consumed by the imaging satellite to perform the s-th coverage mode, SoluList' is the modified coverage scheme, CsFor the s-th overlay mode, λ (i) is the lagrange multiplier corresponding to the i-th mesh;
the energy consumed by the modified coverage scheme, solu (t), is calculated using equation (4):
Figure BDA0001540081940000142
wherein sol (t) is the energy consumed by the modified coverage scheme, SoluList' is the modified coverage scheme, CsEnergy(s) consumed to perform the s coverage mode for the imaging satellite for the s coverage mode;
judging whether the value LB (t) of the lower energy bound is larger than the initial value BestLB of the lower energy bound, and updating the initial value BestLB of the lower energy bound to the value LB (t) of the lower energy bound under the condition that the value LB (t) of the lower energy bound is larger than the initial value BestLB of the lower energy bound;
judging whether the value of the energy solu (t) consumed by the modified coverage scheme is smaller than an initial value BestSolu of energy consumption, and updating the initial value BestSolu of energy consumption with the value of the energy solu (t) consumed by the modified coverage scheme under the condition that the value of the energy solu (t) consumed by the modified coverage scheme is smaller than the initial value BestSolu of energy consumption;
updating the value of the lagrange multiplier using equation (5):
λ '(i) ═ λ (i) + θ' · h (i) formula (5)
Where λ '(i) is the updated value of the lagrangian multiplier, λ (i) is the lagrangian multiplier corresponding to the ith grid, θ' ═ ρ · θ, ρ and θ are initialization coefficients, and ρ and θ may be set to, for example, 2 and 0.999, h (i) ═ 1-v (i), and v (i) is the corrected coverage plan SoluList′Can be connected with grid giNumber of completely covered coverage patterns.
In an embodiment of the present invention, selecting the overlay mode may further include:
setting a set value of an optimality parameter;
judging whether the value of the optimality parameter Gap is smaller than the set value of the optimality parameter;
in the case where it is judged that the value of the optimality parameter Gap is smaller than the set value of the optimality parameter, the modified coverage plan corresponding to the optimality parameter Gap is selected as the coverage plan for covering the rectangular area a.
The set value of the optimality parameter may be set to 0.1, for example.
Embodiments of the present invention also provide a computer-readable storage medium having stored thereon instructions for causing a processor to perform any one of the above-described methods for energy optimization of multiple imaging satellite area coverage when executed by the processor.
Through the implementation mode, the multi-imaging satellite task planning method facing the area coverage is divided into two stages, and the coverage mode generation and the coverage mode selection are separated, so that the method is reasonable in structure and clear in hierarchy; the multi-imaging satellite mission planning method can provide at least one coverage scheme which enables the total energy consumed by a plurality of imaging satellites to be as small as possible.
Although the embodiments of the present invention have been described in detail with reference to the accompanying drawings, the embodiments of the present invention are not limited to the details of the above embodiments, and various simple modifications can be made to the technical solutions of the embodiments of the present invention within the technical idea of the embodiments of the present invention, and these simple modifications all belong to the protection scope of the embodiments of the present invention.
It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. In order to avoid unnecessary repetition, the embodiments of the present invention do not describe every possible combination.
Those skilled in the art can understand that all or part of the steps in the method according to the above embodiments may be implemented by a program to instruct related hardware, where the program is stored in a storage medium and includes several instructions to enable a (may be a single chip, a chip, etc.) or a processor (processor) to execute all or part of the steps in the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In addition, any combination of various different implementation manners of the embodiments of the present invention is also possible, and the embodiments of the present invention should be considered as disclosed in the embodiments of the present invention as long as the combination does not depart from the spirit of the embodiments of the present invention.

Claims (9)

1.一种面向区域覆盖的多成像卫星任务规划方法，其特征在于，包括生成覆盖模式和选择覆盖模式，其中生成覆盖模式具体包括以下步骤：1. a multi-imaging satellite mission planning method for area coverage, is characterized in that, comprises generating coverage pattern and selecting coverage pattern, wherein generating cover pattern specifically comprises the following steps: 确定多个成像卫星的成像扫描方向；Determine the imaging scan direction of multiple imaging satellites; 将欲覆盖的矩形区域划分成多个网格，以生成第一网格列表G；Divide the rectangular area to be covered into a plurality of grids to generate a first grid list G; 针对所述多个成像卫星中的每一个成像卫星：For each imaging satellite of the plurality of imaging satellites: 判断所述成像卫星的成像扫描方向是第一倾斜方向还是第二倾斜方向；determining whether the imaging scanning direction of the imaging satellite is a first oblique direction or a second oblique direction; 在判断所述成像卫星的成像扫描方向为所述第一倾斜方向的情况下，以所述第一网格列表G中的任意网格的左上角顶点为基点，根据成像卫星的成像扫描方向将划分的所述多个网格重新排序，以生成第二网格列表LG，In the case of judging that the imaging scanning direction of the imaging satellite is the first oblique direction, taking the upper left vertex of any grid in the first grid list G as the base point, according to the imaging scanning direction of the imaging satellite reordering the divided grids to generate a second grid list LG, 以所述第二网格列表LG中的网格的左上角顶点和右下角顶点为基点，根据所述成像卫星覆盖的条带形区域的宽度确定所述成像卫星的覆盖模式的四个顶点，以形成所述成像卫星的一个覆盖模式，以及遍历所述第二网格列表LG中的网格，以形成所述成像卫星的覆盖模式列表；Taking the upper left corner vertex and the lower right corner vertex of the grid in the second grid list LG as the base point, 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 the imaging satellites, and traverse the grids in the second grid list LG to form a coverage pattern list of the imaging satellites; 在判断所述成像卫星的成像扫描方向为所述第二倾斜方向的情况下，以所述第一网格列表G中的任意网格的右上角顶点为基点，根据成像卫星的成像扫描方向将划分的所述多个网格重新排序，以生成第三网格列表LG，In the case of judging that the imaging scanning direction of the imaging satellite is the second inclined direction, taking the top right vertex of any grid in the first grid list G as the base point, according to the imaging scanning direction of the imaging satellite reordering the divided grids to generate a third grid list LG, 并以所述第三网格列表LG中的网格的右上角顶点和左下角顶点为基点，根据所述成像卫星覆盖的条带形区域的宽度确定所述成像卫星的覆盖模式的四个顶点，以形成所述成像卫星的一个覆盖模式，以及遍历所述第三网格列表LG中的网格，以形成所述成像卫星的覆盖模式列表；And taking the upper right corner vertex and the lower left corner vertex of the grid in the third grid list LG as the base point, according to the width of the strip-shaped area covered by the imaging satellite, determine the four vertices of the coverage mode of the imaging satellite. , to form a coverage pattern of the imaging satellite, and traverse the grids in the third grid list LG to form a coverage pattern list of the imaging satellite; 遍历所述多个成像卫星，以得到覆盖模式集合，该覆盖模式集合包括每个成像卫星的覆盖模式列表；traversing the plurality of imaging satellites to obtain a set of coverage patterns, the set of coverage patterns including a list of coverage patterns for each imaging satellite; 选择覆盖模式具体包括以下步骤：Selecting an overlay mode includes the following steps: 针对所述多个成像卫星中的每一个成像卫星：For each imaging satellite of the plurality of imaging satellites: 设定能量下界的初始值，能量消耗的初始值，迭代次数的上限值，以及拉格朗日乘子序列的初始值；Set the initial value of the lower bound of energy, the initial value of energy consumption, the upper limit of the number of iterations, and the initial value of the Lagrange multiplier sequence; 计算所述成像卫星的覆盖模式的条带形区域的长度；calculating the length of the striped area of the coverage pattern of the imaging satellite; 根据所述成像卫星的覆盖模式的条带形区域的长度计算成像卫星执行所述覆盖模式消耗的能量；Calculate the energy consumed by the imaging satellite to perform the coverage mode according to the length of the strip-shaped area of the coverage mode of the imaging satellite; 建立所述成像卫星消耗的能量最小化的目标函数，以获得所述成像卫星执行覆盖模式消耗的能量目标值；establishing an objective function that minimizes the energy consumed by the imaging satellite to obtain a target value of energy consumed by the imaging satellite to perform the coverage mode; 计算所述成像卫星执行所述覆盖模式列表中的每一个覆盖模式消耗的能量目标值，并从所述覆盖模式列表中选择消耗的能量目标值最小的一个覆盖模式；Calculate the energy target value consumed by the imaging satellite to execute each coverage mode in the coverage mode list, and select one coverage mode with the smallest energy consumption target value from the coverage mode list; 遍历所述多个成像卫星，以选择每一个成像卫星的消耗的能量目标值最小的一个覆盖模式，以形成一个覆盖方案；traversing the plurality of imaging satellites to select a coverage mode with the smallest energy consumption target value of each imaging satellite to form a coverage scheme; 修正所述覆盖方案，以获得修正后的覆盖方案；modifying the coverage scheme to obtain a revised coverage scheme; 更新所述能量下界的初始值，所述能量消耗的初始值；Update the initial value of the lower bound of energy, the initial value of the energy consumption; 根据更新后的能量下界的初始值和更新后的能量消耗的初始值计算所述修正后的覆盖方案的最优性参数的值；Calculate the value of the optimality parameter of the revised coverage scheme according to the updated initial value of the lower bound of energy and the updated initial value of energy consumption; 通过更新所述拉格朗日乘子的值来更新所述目标函数，基于更新的目标函数重新选择每一个成像卫星的消耗的能量目标值最小的一个覆盖模式，以形成一个覆盖方案，针对新形成的覆盖方案重新计算所述最优性参数的值；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 energy consumption target value of each imaging satellite is reselected to form a coverage scheme for the new The formed coverage scheme recalculates the value of the optimality parameter; 多次更新所述拉格朗日乘子的值，在所述拉格朗日乘子的值的更新次数达到所述迭代次数的上限值的情况下，从选择和重新选择的多个覆盖方案中选择所述最优性参数的值最小的覆盖方案，作为用于覆盖所述矩形区域的覆盖方案。updating the value of the Lagrangian multiplier multiple times, and in the case where the number of updates of the value of the Lagrangian multiplier reaches the upper limit of the number of iterations, select and reselect multiple overlays from Among the schemes, the covering scheme with the smallest value of the optimality parameter is selected as the covering scheme for covering the rectangular area. 2.根据权利要求1所述的多成像卫星任务规划方法，其特征在于，以所述第一网格列表G中的任意网格的左上角顶点为基点，根据成像卫星的成像扫描方向将划分的所述多个网格重新排序，以生成第二网格列表LG具体包括：2. The multi-imaging satellite mission planning method according to claim 1, characterized in that, taking the upper left corner vertex of any grid in the first grid list G as a base point, according to the imaging scanning direction of the imaging satellite, it will be divided into The reordering of the plurality of grids to generate a second grid list LG specifically includes: 从所述第一网格列表G中任意选择一个网格，在所述成像卫星的成像扫描直线上确定与选择的网格的左上角顶点的距离为设定值的第一参考点和第二参考点，其中所述第一参考点位于所述第二参考点的右下方；A grid is arbitrarily selected from the first grid list G, and a first reference point and a second reference point whose distance from the upper left vertex of the selected grid is a set value are determined on the imaging scanning line of the imaging satellite. a reference point, wherein the first reference point is located at the lower right of the second reference point; 以所述第一参考点为起点，所述第二参考点为终点确定参考向量，以所述第一参考点为起点，以所述第一网格列表G中的任意网格的左上角顶点为终点确定一向量，计算该向量在所述参考向量上的投影；Take the first reference point as the starting point and the second reference point as the end point to determine a reference vector, take the first reference point as the starting point, and take the upper left corner vertex of any grid in the first grid list G Determine a vector for the end point, and calculate the projection of the vector on the reference vector; 遍历所述第一网格列表G中的网格，获得向量投影列表；Traverse the grids in the first grid list G to obtain a vector projection list; 将所述向量投影列表中的投影按照降序排列，以对所述第一网格列表G中的网格重新排序，构造所述第二网格列表LG；Arrange the projections in the vector projection list in descending order to reorder the grids in the first grid list G to construct the second grid list LG; 以所述第一网格列表G中的任意网格的右上角顶点为基点，根据成像卫星的成像扫描方向将划分的所述多个网格重新排序，以生成第三网格列表LG具体包括：Taking the upper right corner vertex of any grid in the first grid list G as the base point, reordering the divided grids according to the imaging scanning direction of the imaging satellite to generate the third grid list LG specifically includes: : 从所述第一网格列表G中任意选择一个网格，在所述成像卫星的成像扫描直线上确定与选择的网格的右上角顶点的距离为设定值的第一参考点和第二参考点，其中所述第一参考点位于所述第二参考点的左下方；A grid is arbitrarily selected from the first grid list G, and a first reference point and a second reference point whose distance from the top-right vertex of the selected grid is a set value are determined on the imaging scanning line of the imaging satellite. a reference point, wherein the first reference point is located at the lower left of the second reference point; 以所述第一参考点为起点，所述第二参考点为终点确定参考向量，以所述第一参考点为起点，以所述第一网格列表G中的任意网格的右上角顶点为终点确定一向量，计算该向量在所述参考向量上的投影；Take the first reference point as the starting point and the second reference point as the end point to determine a reference vector, take the first reference point as the starting point, and take the upper right corner vertex of any grid in the first grid list G Determine a vector for the end point, and calculate the projection of the vector on the reference vector; 遍历所述第一网格列表G中的网格，获得向量投影列表；Traverse the grids in the first grid list G to obtain a vector projection list; 将所述向量投影列表中的投影按照降序排列，以对所述第一网格列表G中的对应的网格重新排序，构造所述第三网格列表LG。The projections in the vector projection list are arranged in descending order to reorder the corresponding grids in the first grid list G to construct the third grid list LG. 3.根据权利要求2所述的多成像卫星任务规划方法，其特征在于，在所述成像卫星的成像扫描直线上的与所述选择的网格的左上角顶点的距离为设定值的两个点采用方程组(1)表示：3. The multi-imaging satellite mission planning method according to claim 2, wherein the distance from the upper left corner vertex of the selected grid on the imaging scanning line of the imaging satellite is two of the set value. A point is represented by equation system (1):
Figure FDA0003246241050000041
Figure FDA0003246241050000041
 其中，x代表经度，y代表纬度，xl<x1(z)<xr，x1(z)和y1(z)分别为所述选择的网格的左上角顶点的经度值和纬度值，xl和xr分别为所述两个点的经度值，R为所述设定值，A、B、C均为成像卫星的成像扫描直线的参数；Wherein, x represents longitude, y represents latitude, x l <x 1 (z)<x r , x 1 (z) and y 1 (z) are the longitude and latitude of the upper left corner vertex of the selected grid, respectively value, x l and x r are respectively the longitude values of the two points, R is the set value, and A, B, and C are the parameters of the imaging scanning line of the imaging satellite; 在所述成像卫星的成像扫描直线上的与所述选择的网格的右上角顶点的距离为设定值的两个点采用方程组(2)表示：The two points on the imaging scanning line of the imaging satellite whose distance from the upper right corner vertex of the selected grid is the set value are expressed by equation (2):
Figure FDA0003246241050000042
Figure FDA0003246241050000042
 其中，x代表经度，y代表纬度，xl<x2(z)<xr，x2(z)和y2(z)分别为所述选择的网格的右上角顶点的经度值和纬度值，xl和xr分别为所述两个点的经度值，R为所述设定值，A、B、C均为成像卫星的成像扫描直线的参数。Wherein, x represents longitude, y represents latitude, x l <x 2 (z)<x r , x 2 (z) and y 2 (z) are the longitude and latitude of the upper right corner vertex of the selected grid, respectively value, x l and x r are the longitude values of the two points respectively, R is the set value, and A, B, and C are all parameters of the imaging scanning line of the imaging satellite. 4.根据权利要求3所述的多成像卫星任务规划方法，其特征在于，以所述第二网格列表LG中的网格的左上角顶点和右下角顶点为基点，根据所述成像卫星覆盖的条带形区域的宽度确定所述成像卫星的覆盖模式的四个顶点，以形成所述成像卫星的一个覆盖模式，以及遍历所述第二网格列表LG中的网格，以形成所述成像卫星的覆盖模式列表具体包括：4. The multi-imaging satellite mission planning method according to claim 3, wherein, taking the upper left corner vertex and the lower right corner vertex of the grid in the second grid list LG as base points, according to the imaging satellite coverage The width of the strip-shaped area determines the four vertices of the coverage pattern of the imaging satellite to form a coverage pattern of the imaging satellite, and traverses the grids in the second grid list LG to form the The list of coverage modes of imaging satellites specifically includes: 在所述第二网格列表LG中任意选择一个第一网格，在通过所述第一网格的左上角顶点且与所述成像卫星的成像扫描方向垂直的直线上确定与成像扫描直线的距离等于所述成像卫星覆盖的条带形区域的宽度的一半的第一顶点和第二顶点；A first grid is arbitrarily selected from the second grid list LG, and a line that passes through the upper left corner of the first grid and is perpendicular to the imaging scanning direction of the imaging satellite is determined. distances from first and second vertices equal to half the width of the strip-shaped area covered by the imaging satellite; 在第二网格列表LG中选择一个第二网格，所述第二网格在所述第二网格列表LG中的编号大于等于所述第一网格的编号，在通过所述第二网格的右下角顶点且与所述成像卫星的成像扫描方向垂直的直线上确定与所述成像扫描直线的距离等于所述成像卫星覆盖的条带形区域的宽度的一半的第三顶点和第四顶点；Select a second grid in the second grid list LG. The number of the second grid in the second grid list LG is greater than or equal to the number of the first grid. The lower right corner vertex of the grid and the line perpendicular to the imaging scanning direction of the imaging satellite determine the third vertex and the third vertex whose distance from the imaging scanning line is equal to half the width of the strip-shaped area covered by the imaging satellite. four vertices; 以所述第一顶点、第二顶点、第三顶点和第四顶点为顶点，形成所述成像卫星的一个覆盖模式；Taking the first vertex, the second vertex, the third vertex and the fourth vertex as vertexes, a coverage pattern of the imaging satellite is formed; 对于所述第一网格和所述第二网格依次遍历所述第二网格列表LG中的网格，获得所述成像卫星的基础覆盖模式列表；For the first grid and the second grid, sequentially traverse the grids in the second grid list LG to obtain a basic coverage mode list of the imaging satellite; 在所述基础覆盖模式列表中添加一个虚拟的覆盖模式，以获得所述成像卫星的覆盖模式列表，所述虚拟的覆盖模式被定义为不覆盖任何网格，消耗的能量或者时间为零的覆盖模式；Add a dummy overlay pattern to the base overlay pattern list to obtain the imaging satellite overlay pattern list, the dummy overlay pattern is defined as overlay that does not cover any grid, consumes zero energy or time model; 以所述第三网格列表LG中的网格的右上角顶点和左下角顶点为基点，根据所述成像卫星覆盖的条带形区域的宽度确定所述成像卫星的覆盖模式的四个顶点，以形成所述成像卫星的一个覆盖模式，以及遍历所述第三网格列表LG中的网格，以形成所述成像卫星的覆盖模式列表具体包括：Taking the upper right corner vertex and the lower left corner vertex of the grid in the third 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 the imaging satellite, and traverse the grids in the third grid list LG, to form a coverage pattern list of the imaging satellite specifically includes: 在所述第三网格列表LG中任意选择一个第一网格，在通过所述第一网格的右上角顶点且与该成像扫描直线方程垂直的直线上确定与所述成像扫描直线的距离等于该成像卫星覆盖的条带形区域的宽度的一半的第一顶点和第二顶点；A first grid is arbitrarily selected from the third grid list LG, and the distance to the imaging scanning straight line is determined on a straight line that passes through the upper right corner vertex of the first grid and is perpendicular to the imaging scanning straight line equation a first vertex and a second vertex equal to half the width of the strip-shaped area covered by the imaging satellite; 在所述第三网格列表LG中选择一个第二网格，所述第二网格在所述第二网格列表LG中的编号大于等于所述第一网格的编号，在通过所述第二网格的左下角顶点且与该成像卫星的成像扫描方向垂直的直线上确定与所述成像扫描直线的距离等于该成像卫星覆盖的条带形区域的宽度的一半的第三顶点和第四顶点；A second grid is selected in the third grid list LG, and the number of the second grid in the second grid list LG is greater than or equal to the number of the first grid. On the lower left corner vertex of the second grid and a line perpendicular to the imaging scanning direction of the imaging satellite, determine the third vertex and the third vertex whose distance from the imaging scanning line is equal to half the width of the strip-shaped area covered by the imaging satellite. four vertices; 以所述第一顶点、第二顶点、第三顶点和第四顶点为顶点，形成所述成像卫星的一个覆盖模式；Taking the first vertex, the second vertex, the third vertex and the fourth vertex as vertexes, a coverage pattern of the imaging satellite is formed; 对于所述第一网格和所述第二网格依次遍历所述第三网格列表LG中的网格，获得所述成像卫星的基础覆盖模式列表；For the first grid and the second grid, sequentially traverse the grids in the third grid list LG to obtain a basic coverage mode list of the imaging satellite; 在所述基础覆盖模式列表中添加一个虚拟的覆盖模式，以获得所述成像卫星的覆盖模式列表，所述虚拟的覆盖模式被定义为不覆盖任何网格，消耗的能量或者时间为零的覆盖模式。Add a dummy overlay pattern to the base overlay pattern list to obtain the imaging satellite overlay pattern list, the dummy overlay pattern is defined as overlay that does not cover any grid, consumes zero energy or time model. 5.根据权利要求4所述的多成像卫星任务规划方法，其特征在于，通过所述第一网格的左上角顶点且与成像卫星的成像扫描方向垂直的直线上的与成像扫描直线的距离等于该成像卫星覆盖的条带形区域的宽度的一半的第一顶点和第二顶点采用方程组(3)来表示：5. The multi-imaging satellite mission planning method according to claim 4, wherein the distance to the imaging scanning straight line on a straight line that passes through the upper left corner vertex of the first grid and is perpendicular to the imaging scanning direction of the imaging satellite The first and second vertices equal to half the width of the strip-shaped area covered by the imaging satellite are expressed by equation (3):
Figure FDA0003246241050000061
Figure FDA0003246241050000061
 其中，x代表经度，y代表纬度，C1(i)＝A·y1(i)-B·x1(i)，x1(i)和y1(i)分别为所述第一网格的左上角顶点的经度值和纬度值，wj为与第j个成像卫星成像的条带形区域的宽度，A、B、C均为成像卫星的成像扫描直线的参数，第一顶点和第二顶点分别表示为U1(x1,i,y1,i)和U2(x2,i,y2,i)，x1,i和y1,i分别为所述第一顶点的经度值和纬度值，x2,i和y2,i分别为所述第二顶点的经度值和纬度值；Wherein, 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 network The longitude value and latitude value of the upper left corner vertex of the grid, 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 vertices 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 the first vertices, respectively The longitude value and latitude value of x 2,i and y 2,i are respectively the longitude value and latitude value of the second vertex; 通过所述第二网格的右下角顶点且与所述成像卫星的成像扫描方向垂直的直线上确定与所述成像扫描直线的距离等于所述成像卫星覆盖的条带形区域的宽度的一半的第三顶点和第四顶点采用方程组(4)来表示：A line that passes through the lower right corner vertex of the second grid and is perpendicular to the imaging scan direction of the imaging satellite determines a distance from the imaging scan line equal to half the width of the strip-shaped area covered by the imaging satellite The third vertex and the fourth vertex are represented by equation system (4):
Figure FDA0003246241050000071
Figure FDA0003246241050000071
 其中，x代表经度，y代表纬度，C4(k)＝A·y4(k)-B·x4(k)，x4(k)和y4(k)分别为所述第二网格的右下角顶点的经度值和纬度值，wj为与第j个成像卫星成像的条带形区域的宽度，A、B、C均为成像卫星的成像扫描直线的参数，所述第三顶点和第四顶点分别表示为U3(x3,i,y3,i)U4(x4,i,y4,i)，x3,i和y3,i分别为所述第三顶点的经度值和纬度值，x4,i和y4,i分别为所述第四顶点的经度值和纬度值；Wherein, 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 network The longitude value and latitude value of the lower right corner vertex of the grid, wj 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, and the third The vertex and the fourth vertex are respectively denoted 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 third The longitude value and latitude value of the vertex, x 4,i and y 4,i are respectively the longitude value and latitude value of the fourth vertex; 通过所述第一网格的右上角顶点且与成像卫星的成像扫描方向垂直的直线上的与所述成像扫描直线的距离等于该成像卫星覆盖的条带形区域的宽度的一半的第一顶点和第二顶点采用方程组(5)来表示：A first vertex on a line that passes through the upper right corner vertex of the first grid and is perpendicular to the imaging scan direction of the imaging satellite at a distance from the imaging scan line equal to half the width of the strip-shaped area covered by the imaging satellite and the second vertex are represented by the system of equations (5):
Figure FDA0003246241050000072
Figure FDA0003246241050000072
 其中，x代表经度，y代表纬度，C2(i)＝A·y2(i)-B·x2(i)，x2(i)和y2(i)分别为所述第一网格的右上角顶点的经度值和纬度值，wj为与第j个成像卫星成像的条带形区域的宽度，A、B、C均为成像卫星的成像扫描直线的参数，第一顶点和第二顶点分别表示为U1(x1,i,y1,i)和U2(x2,i,y2,i)，x1,i和y1,i分别为所述第一顶点的经度值和纬度值，x2,i和y2,i分别为所述第二顶点的经度值和纬度值；Wherein, 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 network The longitude value and latitude value of the upper right corner vertex of the grid, 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 vertices 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 the first vertices, respectively The longitude value and latitude value of x 2,i and y 2,i are respectively the longitude value and latitude value of the second vertex; 通过所述第二网格的左下角顶点且与成像卫星的成像扫描方向垂直的直线上的与所述成像扫描直线的距离等于该成像卫星覆盖的条带形区域的宽度的一半的第三顶点和第四顶点采用方程组(6)来表示：A third vertex on a line that passes through the lower left corner vertex of the second grid and is perpendicular to the imaging scan direction of the imaging satellite at a distance from the imaging scan line equal to half the width of the strip-shaped area covered by the imaging satellite and the fourth vertex are represented by the system of equations (6):
Figure FDA0003246241050000081
Figure FDA0003246241050000081
 其中，x代表经度，y代表纬度，C3(k)＝A·y3(k)-B·x3(k)，x3(k)和y3(k)分别为所述第二网格的左下角顶点的经度值和纬度值，wj为与第j个成像卫星成像的条带形区域的宽度，A、B、C均为成像卫星的成像扫描直线的参数，所述第三顶点和第四顶点分别表示为U3(x3,i,y3,i)U4(x4,i,y4,i)，x3,i和y3,i分别为所述第三顶点的经度值和纬度值，x4,i和y4,i分别为所述第四顶点的经度值和纬度值。Wherein, 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 network The longitude value and latitude value of the lower left corner vertex of the grid, wj 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, and the third The vertex and the fourth vertex are respectively denoted 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 third The longitude value and the latitude value of the vertex, x 4,i and y 4,i are the longitude value and the latitude value of the fourth vertex, respectively. 6.根据权利要求5所述的多成像卫星任务规划方法，其特征在于，修正覆盖方案，获得修正后的覆盖方案具体可以包括以下步骤：6. The multi-imaging satellite mission planning method according to claim 5, wherein, revising the coverage scheme, and obtaining the revised coverage scheme can specifically include the following steps: 判断所述覆盖方案是否能够完全覆盖所述矩形区域中的网格；judging whether the covering scheme can completely cover the grid in the rectangular area; 在判断所述覆盖方案不能完全覆盖所述矩形区域中的网格的情况下，在所述覆盖方案中找出条带形区域最接近未被覆盖的网格的待替换覆盖模式，在与所述待替换覆盖模式对应的成像卫星的覆盖模式列表中选择条带形区域与所述待替换覆盖模式的条带形区域最接近的覆盖模式来在所述覆盖方案中替换所述待替换覆盖模式。In the case of judging that the coverage scheme cannot completely cover the grids in the rectangular area, find out the coverage mode to be replaced in the coverage scheme with the strip-shaped area closest to the uncovered grids, In the coverage mode list of the imaging satellite corresponding to the coverage mode to be replaced, select the coverage mode with the strip-shaped area that is closest to the strip-shaped area of the coverage mode to be replaced to replace the coverage mode to be replaced in the coverage scheme . 7.根据权利要求6所述的多成像卫星任务规划方法，其特征在于，采用拉格朗日松弛技术建立的成像卫星消耗的能量最小化的目标函数采用式(2)表示：7. The multi-imaging satellite mission planning method according to claim 6, wherein the objective function of minimizing the energy consumed by the imaging satellite established by the Lagrangian relaxation technique is represented by formula (2):
Figure FDA0003246241050000082
Figure FDA0003246241050000082
 其中，u(s)为所述成像卫星执行第s个覆盖模式消耗的能量的目标值，energy(s)＝ls·dj，energy(s)为所述成像卫星执行第s个覆盖模式消耗的能量，ls为第s个覆盖模式的条带形区域的长度，dj为第j个成像卫星消耗的能量与第s个覆盖模式的条带形区域的长度的比例系数，G′为所述第二网格列表LG和所述第三网格列表LG构成的网格集合，λ(i)为与第i个网格对应的拉格朗日乘子，WC[s,i]被定义为在判断第s个覆盖模式完整覆盖了第i个网格的情况下，WC[s,i]＝1，在判断第s个覆盖模式没有完整覆盖了第i个网格的情况下，WC[s,i]＝0。Wherein, u(s) is the target value of the energy consumed by the imaging satellite to perform the s-th coverage mode, energy(s)= ls ·d j , and energy(s) is the s-th coverage mode performed by the imaging satellite Energy consumed, ls is the length of the strip-shaped area of the s -th coverage mode, d j is the proportional coefficient of the energy consumed by the j-th imaging satellite and the length of the strip-shaped area of the s-th coverage mode, G′ is the grid set formed by the second grid list LG and the third grid list LG, λ(i) is the Lagrange multiplier corresponding to the i-th grid, WC[s,i] It is defined as WC[s,i]=1 when it is judged that the s-th covering mode completely covers the i-th grid, and when it is judged that the s-th covering mode does not completely cover the i-th grid , WC[s,i]=0. 8.根据权利要求7所述的多成像卫星任务规划方法，其特征在于，所述更新所述能量下界的初始值，所述能量消耗的初始值具体包括以下步骤：8. The multi-imaging satellite mission planning method according to claim 7, wherein the updating the initial value of the energy lower bound, the initial value of the energy consumption specifically comprises the following steps: 采用式(3)计算覆盖方案消耗的能量下界的值LB(t)：Use formula (3) to calculate the value LB(t) of the lower bound of energy consumed by the coverage scheme: LB(t)＝LB1(t)+LB2(t) 式(3)LB(t)=LB 1 (t)+LB 2 (t) Equation (3) 其中，LB(t)为覆盖方案消耗的能量下界的值，
Figure FDA0003246241050000091
LB2(t)＝∑λ(i)，u(s)为所述成像卫星执行第s个覆盖模式消耗的能量的目标值，λ(i)为与第i个网格对应的拉格朗日乘子；Among them, LB(t) is the value of the lower bound of energy consumed by the coverage scheme,
Figure FDA0003246241050000091
LB 2 (t)=∑λ(i), u(s) is the target value of energy consumed by the imaging satellite to perform the s-th coverage mode, and λ(i) is the Lagrangian corresponding to the i-th grid day multiplier; 采用式(4)计算修正后的覆盖方案消耗的能量solu(t)：Equation (4) is used to calculate the energy solu(t) consumed by the revised coverage scheme:
Figure FDA0003246241050000092
Figure FDA0003246241050000092
 其中，solu(t)为修正后的覆盖方案消耗的能量，SoluList′为所述修正后的覆盖方案列表，Cs为第s个覆盖方案，energy(s)为所述成像卫星执行第s个覆盖模式消耗的能量；where, solu(t) is the energy consumed by the revised coverage scheme, SoluList' is the revised coverage scheme list, C s is the sth coverage scheme, and energy(s) is the sth coverage scheme performed by the imaging satellite. The energy consumed by the coverage mode; 判断所述能量下界的值是否大于所述能量下界的初始值，在判断所述能量下界的值大于所述能量下界的初始值的情况下，将所述能量下界的初始值更新为所述能量下界的值；Judging whether the value of the energy lower bound is greater than the initial value of the energy lower bound, and in the case of judging that the value of the energy lower bound is greater than the initial value of the energy lower bound, update the initial value of the energy lower bound to the energy the value of the lower bound; 判断所述修正后的覆盖方案消耗的能量的值是否小于所述能量消耗的初始值，在判断所述修正后的覆盖方案消耗的能量的值小于所述能量消耗的初始值的情况下，将所述能量消耗的初始值更新为所述修正后的覆盖方案消耗的能量的值；Determine whether the value of the energy consumed by the revised coverage scheme is less than the initial value of the energy consumption, and in the case of judging that the value of the energy consumed by the revised coverage scheme is less than the initial value of the energy consumption, use The initial value of the energy consumption is updated to the value of the energy consumed by the revised coverage scheme; 采用式(5)更新拉格朗日乘子的值：Use formula (5) to update the value of the Lagrange multiplier: λ′(i)＝λ(i)+θ′·h(i) 式(5)λ′(i)=λ(i)+θ′·h(i) Equation (5) 其中，λ′(i)为更新后的拉格朗日乘子的值，λ(i)为与第i个网格对应的拉格朗日乘子，θ′＝ρ·θ，ρ和θ均为初始化系数，h(i)＝1-v(i)，v(i)为修正后的覆盖方案中能够将第i个网格完全覆盖的覆盖模式的个数。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), and v(i) is the number of coverage patterns that can completely cover the i-th grid in the revised coverage scheme. 9.根据权利要求8所述的多成像卫星任务规划方法，其特征在于，采用式(6)计算所述修正后的覆盖方案的最优性参数的值：9. The multi-imaging satellite mission planning method according to claim 8, characterized in that, formula (6) is used to calculate the value of the optimality parameter of the modified coverage scheme:
Figure FDA0003246241050000101
Figure FDA0003246241050000101
 其中，BestLB为更新后的能量下界的初始值，BestSolu更新后的能量消耗的初始值，Gap为修正后的覆盖方案的最优性参数的值。Among them, BestLB is the initial value of the updated energy lower bound, BestSolu is the initial value of the updated energy consumption, and Gap is the value of the optimality parameter of the revised coverage scheme.
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