CN111366136B - Design method of optical ring scanning ultra-wide imaging mode - Google Patents

Design method of optical ring scanning ultra-wide imaging mode Download PDF

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CN111366136B
CN111366136B CN202010158705.1A CN202010158705A CN111366136B CN 111366136 B CN111366136 B CN 111366136B CN 202010158705 A CN202010158705 A CN 202010158705A CN 111366136 B CN111366136 B CN 111366136B
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CN111366136A (en
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王峰
奚瑞辰
岳程斐
李化义
曹喜滨
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Harbin Institute of Technology
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G01C11/02—Picture taking arrangements specially adapted for photogrammetry or photographic surveying, e.g. controlling overlapping of pictures
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Abstract

The invention relates to a design method of an optical ring scanning ultra-wide imaging mode. The method comprises the following steps: designing an included angle gamma between an optical axis of the camera and a whole satellite earth axis; design of spin angular velocity omega of satellite in fast spin modefast(ii) a If the camera can clearly image at the current angular velocity, the method carries outStep three; otherwise, performing the step four; designing a fast spin period TfastOn-off time t of internal cameraon、toff(ii) a Design of spin angular velocity omega of satellite in slow spin modeslow(ii) a Designing a slow rotation period TslowOn-off time t of internal cameraon1、toff1、ton2、toff2(ii) a Designing a phase angle theta of a camera starting time under a variable rotating speed spinning mode0And a boot time τ1(ii) a Designing a satellite spin angular velocity equation when the camera is shut down; if the satellite can stably track the equation, a variable-rotation-speed spinning mode is adopted; otherwise, adopting the slow rotation mode designed in the step five. Each imaging mode of the invention can ensure the integrity of the splicing of the environmental scanning strips; the requirements of the imaging task on the processing, storage and data transmission capabilities of the satellite are reduced.

Description

Design method of optical ring scanning ultra-wide imaging mode
Technical Field
The invention relates to a design method of an optical ring scanning ultra-wide imaging mode, and belongs to the technical field of space satellites.
Background
At present, with the development of aerospace technology, micro-nano satellites are favored by the characteristics of low cost and miniaturization. However, the meter-level resolution low-orbit small satellite cannot meet the requirements of the kilometric-kilometer-level imaging coverage width, and the optical ring scanning ultra-wide imaging is a solution proposed at present. According to the method, an area array optical camera is installed, a certain fixed included angle is formed between the optical axis of the camera and the earth axis of the whole satellite, and the rotation of the whole satellite of the satellite around the earth pointing axis is utilized, so that the camera can realize the ultra-large breadth coverage in the circular scanning imaging.
However, no design scheme is provided for a specific calculation method of an included angle between an optical axis of a camera for optical ring scanning ultra-wide imaging and a whole satellite earth axis, a satellite spin angular velocity and a detailed ring scanning strip splicing mode.
Disclosure of Invention
The invention aims to provide a design method of an optical ring scanning ultra-wide imaging mode. The design method provides three different circular scanning imaging modes aiming at different camera imaging capabilities and different satellite spin angular speed control capabilities, wherein the three different circular scanning imaging modes comprise a fast spinning mode, a slow spinning mode and a variable-rotation-speed spinning mode. Each imaging mode can not only ensure the integrity of the splicing of the circular scanning strips, but also reduce the overlapping area between the circular scanning strips through the design of timing startup and shutdown of the camera in each circular scanning period, thereby reducing the requirements of imaging tasks on the processing capacity, the storage capacity and the data transmission capacity of the satellite. The method solves the problem that no specific calculation method for the included angle between the optical axis of the camera and the earth axis of the whole satellite for optical ring scan ultra-wide imaging, the satellite spin angular velocity and a detailed ring scan strip splicing mode are provided at present.
The design method of the optical ring scanning ultra-wide imaging mode comprises the following steps:
designing an included angle gamma between an optical axis of a camera and a ground axis of the whole satellite according to the orbital height of the satellite, the requirement of a task on imaging width and the size of a field angle of the camera;
step two, designing the spin angular velocity omega of the satellite in the fast spin mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsfastAnd spin period TfastIf ω isfastEnabling the camera to have enough exposure time and integration time to perform high-resolution imaging, and then performing the third step; if omegafastIf the size is too large, the camera cannot carry out clear imaging, and then the step four is carried out;
step three, in order to reduce the overlapping area between the circular scanning strips, a fast rotation period T is designedfastOn-off time t of internal cameraon、toffNamely, the optical ring scanning ultra-wide imaging mode meeting the design requirement is adopted;
step four, designing the spin angular velocity omega of the satellite in the slow rotation mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsslowAnd a self-selection period Tslow；
Step five, designing a slow rotation period TslowOn-off time t of internal cameraon1、toff1、ton2、toff2；
Designing a variable-rotation-speed spinning mode, wherein in each spinning period in the mode, the spinning angular speed of the satellite when the camera is started is equal to the spinning angular speed omega of the satellite in the slow-rotation modeslowThe satellite spins rapidly when the camera is off so that the spin period is equal to the spin period T of the spin modefastDesigning the phase angle theta of the camera at the time of starting in the mode0And a boot time τ1；
Designing a satellite spin angular velocity equation when the camera is shut down in the variable-rotation-speed spin mode, wherein if the satellite attitude control system can stably track and control the spin angular velocity equation designed in the variable-rotation-speed spin mode, the variable-rotation-speed spin mode designed in the step is an optical ring scanning ultra-wide imaging mode meeting the design requirement; and if the attitude control system of the satellite is not enough to stably track and control the spin angular velocity equation designed by the mode, the slow rotation mode designed in the fifth step is the optical ring scanning ultra-wide imaging mode meeting the design requirement.
Further, in the step one, the included angle γ between the optical axis of the camera and the earth axis of the whole satellite is solved iteratively by the following sine theorem equation:
Figure GDA0003429059910000021
wherein,
Figure GDA0003429059910000022
is the radius of the earth, H is the orbital height, r1Half of the width required for the task, i.e. sweeping the outer radius of the strip around, α is one half field angle of the camera.
Further, in step two, the approximate satellite sub-satellite point moving speed is defined first
Figure GDA0003429059910000031
The following were used:
Figure GDA0003429059910000032
wherein, TorbitThe satellite orbit period is the spin angular velocity omega of the satellite in the fast spin modefastAnd spin period TfastThe calculation is performed by the following equations, respectively:
Figure GDA0003429059910000033
Figure GDA0003429059910000034
wherein r is2In order to sweep the inner radius of the strip in a circular manner,
Figure GDA0003429059910000035
and the minimum overlapping rate of the two adjacent circles of circular scanning strips is obtained.
Further, in step three, the phase angle 0 of the circular scanning stripe is defined, and the theoretical starting time of the j-th circle camera
Figure GDA0003429059910000036
And theoretical shutdown time
Figure GDA0003429059910000037
The solution is iterated through the following equations:
Figure GDA0003429059910000038
Figure GDA0003429059910000039
let the j-th turn 0 phase angle time be
Figure GDA00034290599100000310
Order to
Figure GDA00034290599100000311
To ensure the integrity of the stitching, the camera is rotated for a fast rotation period T, taking into account the actual control error and the speed deviation of the sub-satellite pointsfastInternal boot time tonShould be slightly ahead of the theoretical value t'onShutdown time toffShould be slightly later than the theoretical value t'off。
Further, in step four, the spin angular velocity ω of the satellite in slow spin modeslowAnd a self-selection period TslowThe calculation is performed by the following equations, respectively:
Figure GDA00034290599100000312
Figure GDA0003429059910000041
in the formula,
Figure GDA0003429059910000042
and sweeping the maximum leak rate of the strip for two adjacent circles.
Further, in the fifth step, two times of power-off and two times of power-on are performed in each circle, and the theoretical power-on and power-off time of the j-th circle of camera is respectively
Figure GDA0003429059910000043
Wherein, the lower corner mark on is the time of starting up, the lower corner mark off is the time of shutting down, 1, 2 represent the time successively, solve through the following equation iteration:
Figure GDA0003429059910000044
Figure GDA0003429059910000045
Figure GDA0003429059910000046
Figure GDA0003429059910000047
wherein k is defined as: a right half-ring which is formed by a fourth quadrant of the (m) -1 th ring and a first quadrant of the m-th ring together, and a left half-ring which is formed by a second quadrant and a third quadrant of the n-th ring together are spliced with each other so as to fill a hollow part in the middle of the n-1 th ring, and then k is equal to n-m,
let the 0 phase angle time of the j-th turn be
Figure GDA0003429059910000048
Order to
Figure GDA0003429059910000049
To ensure the integrity of the stitching, the camera is rotated for a slow rotation period T, taking into account the actual control error and the speed deviation of the sub-satellite pointslowInternal shutdown time toff1、toff2Should be slightly later than the theoretical value t'off1、t′off2At the time of start-upon1、ton2Should be slightly ahead of the theoretical value t'on1、t′on2。
Further, in the sixth step, the theoretical value θ 'of the phase angle at the time of starting the camera in one cycle'0The iterative calculation is obtained by the following formula:
Figure GDA0003429059910000051
phase angle theta at actual camera turn-on time taking into account actual control errors0Is slightly less than theoretical value theta'0，
Theoretical value tau 'of camera startup time length'1Can be calculated by the following formula:
Figure GDA0003429059910000052
considering the actual control error, the actual camera turn-on duration tau1Should be slightly greater than theoretical value tau'1。
Further, in step seven, the state vector x (t) is defined as follows:
Figure GDA0003429059910000053
let u (t) then be the angular acceleration of the satellite, t0The following energy optimization problem is solved for the starting moment of one period by the Pontryagin maximum principle:
Figure GDA0003429059910000054
Figure GDA0003429059910000055
obtaining a satellite spin angular velocity equation omega of a camera in a shutdown stage*(t)t∈[t0+τ1,t0+Tfast]。
The main advantages of the invention are: the invention provides a design method of an optical ring scanning ultra-wide imaging mode. In the invention, three different circular scanning imaging modes are provided aiming at different camera imaging capabilities and different satellite spin angular speed control capabilities, wherein the three different circular scanning imaging modes comprise a fast spinning mode, a slow spinning mode and a variable-rotation-speed spinning mode. Each imaging mode can not only ensure the integrity of the splicing of the circular scanning strips, but also reduce the overlapping area between the circular scanning strips through the design of timing startup and shutdown of the camera in each circular scanning period, thereby reducing the requirements of imaging tasks on the processing capacity, the storage capacity and the data transmission capacity of the satellite.
Drawings
FIG. 1 is a flow chart of a design method of an optical ring scan ultra-wide imaging mode according to the present invention;
FIG. 2 is a schematic diagram of optical ring scan ultra-wide imaging;
FIG. 3 is a schematic view of the circular sweep width;
FIG. 4 is a diagram illustrating a minimum overlap ratio in fast spin mode;
FIG. 5 is a diagram illustrating a long-term startup of a fast-rotation mode camera;
FIG. 6 is a diagram illustrating a long-term startup of a fast-rotation mode camera;
FIG. 7 is a schematic diagram of quadrant and 0 phase angle definitions;
FIG. 8 is a schematic diagram illustrating the design result after reducing the overlap area of the circular scanning stripes in the fast rotation mode;
FIG. 9 is a schematic diagram of the maximum leak rate in slow-spin mode;
FIG. 10 is a schematic diagram of a slow-rotation mode camera with long-term power-on (narrow field of view);
FIG. 11 is a schematic diagram of a slow-rotation mode camera with long-term power-on (wide field of view);
FIG. 12 is a schematic diagram showing the design result of reducing the overlap area of the circular scanning stripes in the slow rotation mode;
FIG. 13 is a schematic diagram showing the design results of the variable spin mode.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Referring to fig. 1-2, the present invention provides a method for designing an optical ring scanning ultra-wide imaging mode, comprising the following steps:
designing an included angle gamma between an optical axis of a camera and a ground axis of the whole satellite according to the orbital height of the satellite, the requirement of a task on imaging width and the size of a field angle of the camera;
step two, designing the spin angular velocity omega of the satellite in the fast spin mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsfastAnd spin period TfastIf ω isfastEnabling the camera to have enough exposure time and integration time to perform high-resolution imaging, and then performing the third step; if omegafastIf the size is too large, the camera cannot carry out clear imaging, and then the step four is carried out;
step three, in order to reduce the overlapping area between the circular scanning strips, a fast rotation period T is designedfastOn-off time t of internal cameraon、toffNamely, the optical ring scanning ultra-wide imaging mode meeting the design requirement is obtained;
step four, designing the spin angular velocity omega of the satellite in the slow rotation mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsslowAnd a self-selection period Tslow；
Step five, designing a slow rotation period TslowOn-off time t of internal cameraon1、toff1、ton2、toff2；
Designing a variable-rotation-speed spinning mode, wherein in each spinning period in the mode, the spinning angular speed of the satellite when the camera is started is equal to the spinning angular speed omega of the satellite in the slow-rotation modeslowThe satellite spins rapidly when the camera is off so that the spin period is equal to the spin period T of the spin modefastDesigning the phase angle theta of the camera at the time of starting in the mode0And a boot time τ1；
Designing a satellite spin angular velocity equation when the camera is shut down in the variable-rotation-speed spin mode, wherein if the satellite attitude control system can stably track and control the spin angular velocity equation designed in the variable-rotation-speed spin mode, the variable-rotation-speed spin mode designed in the step is an optical ring scanning ultra-wide imaging mode meeting the design requirement; and if the attitude control system of the satellite is not enough to stably track and control the spin angular velocity equation designed by the mode, the slow rotation mode designed in the fifth step is the optical ring scanning ultra-wide imaging mode meeting the design requirement.
In the preferred embodiment of this section, in step one, the included angle γ between the optical axis of the camera and the earth axis of the whole star is solved iteratively by the following sine theorem equation:
Figure GDA0003429059910000081
wherein,
Figure GDA0003429059910000082
is the radius of the earth, H is the orbital height, r1Half of the width required for the task, i.e. sweeping the outer radius of the strip around, α is one half field angle of the camera.
In the preferred embodiment of this section, in step two, the approximate satellite sub-satellite point movement speed is first defined
Figure GDA0003429059910000083
The following were used:
Figure GDA0003429059910000084
wherein, TorbitThe satellite orbit period is the spin angular velocity omega of the satellite in the fast spin modefastAnd spin period TfastThe calculation is performed by the following equations, respectively:
Figure GDA0003429059910000085
Figure GDA0003429059910000086
wherein r is2To sweep the inner radius of the strip, as shown with reference to figure 3,
Figure GDA0003429059910000087
the minimum overlapping rate of the two adjacent circles of sweeping strips is defined as shown in fig. 4.
Before proceeding to step three, the sweeping trajectory obtained by the design of step two is shown in fig. 5 and 6.
In this section, the bestIn an alternative embodiment, referring to FIG. 7 in step three, the phase angle 0 of the circular sweep stripe and the theoretical turn-on time of the jth camera turn are defined
Figure GDA0003429059910000088
And theoretical shutdown time
Figure GDA0003429059910000089
The solution is iterated through the following equations:
Figure GDA00034290599100000810
Figure GDA00034290599100000811
let the j-th turn 0 phase angle time be
Figure GDA00034290599100000812
Order to
Figure GDA00034290599100000813
To ensure the integrity of the stitching, the camera is rotated for a fast rotation period T, taking into account the actual control error and the speed deviation of the sub-satellite pointsfastInternal boot time tonShould be slightly ahead of theoretical value t'onTime of shutdown toffShould be slightly later than theoretical value t'off。
The circular scan strip resulting from the step three design is shown in FIG. 8.
In the preferred embodiment of this section, in step four, the satellite spin angular velocity ω in slow spin modeslowAnd a self-selection period TslowThe calculation is performed by the following equations, respectively:
Figure GDA0003429059910000091
Figure GDA0003429059910000092
in the formula,
Figure GDA0003429059910000093
the maximum leak rate of the sweeping strips for two adjacent circles is defined as shown in fig. 9.
Before the step five, the circular scanning track designed by the step four is shown in fig. 10 and 11.
In the preferred embodiment of this part, in step five, there are two times of power-off and two times of power-on in each turn, and the theoretical power-on and power-off time of the j-th turn of camera is respectively
Figure GDA0003429059910000094
Wherein, the lower corner mark on is the time of starting up, the lower corner mark off is the time of shutting down, 1, 2 represent the time successively, solve through the following equation iteration:
Figure GDA0003429059910000095
Figure GDA0003429059910000096
Figure GDA0003429059910000097
Figure GDA0003429059910000098
wherein k is defined as: a right half ring formed by the fourth quadrant of the (m-1) th ring and the first quadrant of the (m) th ring together, and a left half ring formed by the second quadrant and the third quadrant of the (n) th ring together are spliced with each other so as to fill the hollow part in the middle of the (n-1) th ring, and k is n-m,
let the j-th turn 0 phase angle time be
Figure GDA0003429059910000101
Order to
Figure GDA0003429059910000102
To ensure the integrity of the stitching, the camera is rotated for a slow rotation period T, taking into account the actual control error and the sub-satellite point speed deviationslowInternal shutdown time toff1、toff2Should be slightly later than theoretical value t'off1、t′off2At the time of start-upon1、ton2Should be slightly ahead of theoretical value t'on1、t′on2。
The circular scan strip resulting from the step five design is shown in fig. 12.
In the preferred embodiment of this part, in step six, the theoretical value θ 'of the phase angle at the time of starting the camera in one period'0The iterative calculation is obtained by the following formula:
Figure GDA0003429059910000103
phase angle theta at actual camera turn-on time taking into account actual control errors0Should be slightly less than the theoretical value theta'0，
Theoretical value tau 'of camera startup time length'1Can be calculated by the following formula:
Figure GDA0003429059910000104
considering the actual control error, the actual camera turn-on duration tau1Should be slightly greater than theoretical value tau'1。
In the preferred embodiment of this section, in step seven, the state vector x (t) is first defined as follows:
Figure GDA0003429059910000105
let u (t) then be the angular acceleration of the satellite,t0solving the following energy optimization problem for the start time of one cycle by means of the Pontryagin maximum principle:
Figure GDA0003429059910000111
Figure GDA0003429059910000112
obtaining a satellite spin angular velocity equation omega of a camera in a shutdown stage*(t)t∈[t0+τ1,t0+Tfast]。
The circular scanning strip designed by the step seven is shown in fig. 13.

Claims (8)

1. The design method of the optical ring scanning ultra-wide imaging mode is characterized by comprising the following steps of:
designing an included angle gamma between an optical axis of a camera and a ground axis of the whole satellite according to the orbital height of the satellite, the requirement of a task on imaging width and the size of a field angle of the camera;
step two, designing the spin angular velocity omega of the satellite in the fast spin mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsfastAnd spin period TfastIf ω isfastEnabling the camera to have enough exposure time and integration time to perform high-resolution imaging, and then performing the third step; if omegafastIf the size is too large, the camera cannot carry out clear imaging, and then the step four is carried out;
step three, in order to reduce the overlapping area between the circular scanning strips, a fast rotation period T is designedfastOn-off time t of internal cameraon、toffNamely, the optical ring scanning ultra-wide imaging mode meeting the design requirement is obtained;
step four, designing the spin angular velocity omega of the satellite in the slow rotation mode according to the gamma value designed in the step one and the requirement of the minimum overlapping rate between the two adjacent circle scanning stripsslowAnd selecting weekPeriod Tslow；
Step five, designing a slow rotation period TslowOn-off time t of internal cameraon1、toff1、ton2、toff2；
Designing a variable-rotation-speed spinning mode, wherein in each spinning period in the mode, the spinning angular speed of the satellite when the camera is started is equal to the spinning angular speed omega of the satellite in the slow-rotation modeslowThe satellite spins rapidly when the camera is off so that the spin period is equal to the spin period T of the spin modefastDesigning the phase angle theta of the camera at the starting time in the mode0And a boot time τ1；
Designing a satellite spin angular velocity equation when the camera is shut down in the variable-rotation-speed spin mode, wherein if the satellite attitude control system can stably track and control the spin angular velocity equation designed in the variable-rotation-speed spin mode, the variable-rotation-speed spin mode designed in the step is an optical ring scanning ultra-wide imaging mode meeting the design requirement; and if the attitude control system of the satellite is not enough to stably track and control the spin angular velocity equation designed by the mode, the slow rotation mode designed in the fifth step is the optical ring scanning ultra-wide imaging mode meeting the design requirement.
2. The design method of the optical ring scanning ultra-wide imaging mode according to claim 1, wherein in the step one, an included angle γ between an optical axis of the camera and a ground axis of the whole star is solved iteratively by the following sine theorem equation:
Figure FDA0002404989830000021
wherein,
Figure FDA0002404989830000022
is the radius of the earth, H is the orbital height, r1Half of the width required for the task, i.e. sweeping the outer radius of the strip around, α is one half field angle of the camera.
3. The method as claimed in claim 1, wherein in step two, the approximate satellite sub-satellite point movement speed is defined first
Figure FDA0002404989830000023
The following:
Figure FDA0002404989830000024
wherein, TorbitThe satellite orbit period is the spin angular velocity omega of the satellite in the fast spin modefastAnd spin period TfastThe calculation is performed by the following equations, respectively:
Figure FDA0002404989830000025
Figure FDA0002404989830000026
wherein r is2In order to sweep the inner radius of the strip in a circular manner,
Figure FDA0002404989830000027
and scanning the minimum overlapping rate of the strips for two adjacent circles.
4. The method as claimed in claim 1, wherein in step three, a phase angle of 0 of the circular scanning bar and a theoretical turn-on time of the jth circle of the camera are defined
Figure FDA0002404989830000028
And theoretical shutdown time
Figure FDA0002404989830000029
By passingThe following equations are solved iteratively:
Figure FDA00024049898300000210
Figure FDA00024049898300000211
let the j-th turn 0 phase angle time be
Figure FDA00024049898300000212
Order to
Figure FDA00024049898300000213
To ensure the integrity of the stitching, the camera is rotated for a fast rotation period T, taking into account the actual control error and the speed deviation of the sub-satellite pointsfastInternal boot time tonShould be slightly ahead of theoretical value t'onShutdown time toffShould be slightly later than theoretical value t'off。
5. The method as claimed in claim 1, wherein in step four, the spin angular velocity ω of the satellite in slow rotation mode is set to be ωslowAnd a self-selection period TslowThe calculation is performed by the following equations, respectively:
Figure FDA0002404989830000031
Figure FDA0002404989830000032
in the formula,
Figure FDA0002404989830000033
sweeping the maximum leakage of the strip for two adjacent circlesThe seam ratio.
6. The method as claimed in claim 1, wherein in step five, there are two power-off times and two power-on times in each turn, and the theoretical power-on and power-off times of the j-th turn of the camera are set as
Figure FDA0002404989830000034
Figure FDA0002404989830000035
Wherein, the lower corner mark on is the time of starting up, the lower corner mark off is the time of shutting down, 1, 2 represent the time successively, solve through the following equation iteration:
Figure FDA0002404989830000036
Figure FDA0002404989830000037
Figure FDA0002404989830000038
Figure FDA0002404989830000039
wherein k is defined as: a right half ring formed by the fourth quadrant of the (m-1) th ring and the first quadrant of the (m) th ring together, and a left half ring formed by the second quadrant and the third quadrant of the (n) th ring together are spliced with each other so as to fill the hollow part in the middle of the (n-1) th ring, and k is n-m,
let the j-th turn 0 phase angle time be
Figure FDA0002404989830000041
Order to
Figure FDA0002404989830000042
To ensure the integrity of the stitching, the camera is rotated for a slow rotation period T, taking into account the actual control error and the speed deviation of the sub-satellite pointslowInternal shutdown time toff1、toff2Should be slightly later than theoretical value t'off1、t′off2At the time of start-upon1、ton2Should be slightly ahead of theoretical value t'on1、t′on2。
7. The design method for optical ring scan ultra-wide band imaging mode according to claim 1, wherein in step six, the theoretical value θ 'of the phase angle at the moment of turning on the camera in one period'0The calculation is iteratively performed by:
Figure FDA0002404989830000043
phase angle theta at actual camera turn-on time taking into account actual control errors0Is slightly less than theoretical value theta'0，
Theoretical value tau 'of camera startup time length'1Can be calculated by the following formula:
Figure FDA0002404989830000044
considering the actual control error, the actual camera turn-on duration tau1Should be slightly greater than theoretical value tau'1。
8. The method as claimed in claim 1, wherein in step seven, the state vector x (t) is defined as follows:
Figure FDA0002404989830000045
let u (t) then be the angular acceleration of the satellite, t0The following energy optimization problem is solved for the starting moment of one period by the Pontryagin maximum principle:
Figure FDA0002404989830000051
Figure FDA0002404989830000052
obtaining a satellite spin angular velocity equation omega of a camera in a shutdown stage*(t)t∈[t0+τ1,t0+Tfast]。
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