1. A multi-satellite single-reconnaissance-target-oriented orbital maneuver optimization method is characterized by comprising the following steps of:

aiming at the problem of orbital maneuver optimization under the condition of multiple stars and multiple scout targets, a multiple optimization target model which simultaneously considers maneuver time, imaging resolution and fuel consumption is established;

solving the multi-optimization target model by using a differential evolution algorithm under an NSGA-II calculation framework, and providing a plurality of non-differential pareto optimal solutions for a user on multiple targets to make decisions;

and selecting the optimal solution as an orbital transfer scheme, and executing a final observation task by each in-orbit satellite.

2. The method for optimizing orbital maneuver oriented to multiple-star single-scout targets according to claim 1, wherein the multiple-optimization target model is as follows:

s.t.

-V≤Δv^j≤V (d)

C^j≤1 (g)

n≤m (i)

i＝1，2，...，n；j＝1，2，...，m

wherein t is_imagThe moment of imaging above the target point, t, for the satellite₀For satellite to receive the mission time, t_sThe illumination start time of the target point, t_eAs the target point illumination end time, D_imagDistance from the target point, H, when the satellite is imaged over the target point_newThe orbital height H of the satellite after the maneuvering orbit change_minTo the lowest permissible rail height, H_maxFor the maximum allowable orbit height, Δ V is the velocity increment required to enable the satellite to reach the target orbit, R is the resolution to be met, V is the maximum velocity increment, A is the lateral swing visible range, T is the maximum maneuvering duration, and i is the targetThe number of punctuation points, j is the number of in-orbit satellites, C is the number of times of orbital transfer of the satellites, w is the number of time windows of the satellites for the target points, n is the total number of the target points, and m is the total number of in-orbit satellites.

3. The method for optimizing orbital maneuver oriented to single-star reconnaissance targets according to claim 1, wherein a population is perturbed by adopting a differential evolution algorithm of real number coding.

4. The method for optimizing the orbital maneuver oriented to the multi-satellite single-scout target according to claim 3, wherein the step of perturbing the population by using a differential evolution algorithm with real number coding comprises: continuously carrying out discretization treatment on the upper layer part of the solution in the solving process; interfering one existing vector in the population by a differential vector calculated by two different vectors selected randomly, and implementing the process on each vector; in the differential evolution algorithm, if the objective function value corresponding to the newly generated vector is better than the parent vector, the new vector replaces the parent vector and enters the next iteration operation.

5. The method for optimizing orbital maneuver oriented to multiple-star single-scout targets according to claim 1, wherein the solution comprises multiple segments and uses a two-layer solution coding structure, each segment contains a task assignment scheme and an orbital transfer scheme for the target point, so that the task assignment and the orbital transfer scheme can evolve together, the upper layer code comprises a satellite number assigned to observe the nth target point, the lower layer code comprises orbital transfer time of the maneuvering satellite, and the satellite performs maneuvering orbital transfer with velocity increment acting on x-axis, y-axis and z-axis of the orbital coordinate system.

6. The method for optimizing orbital maneuver oriented to multiple-star single-scout targets according to claim 1, wherein the calculation of the optimization objective function value adopts a weighted accumulation method, and the weighted method is to use the reciprocal of the constraint value on each target point as a weight value as a user expectation coefficient.

7. The method for optimizing orbital maneuver oriented to multi-satellite single-reconnaissance targets according to claim 1, wherein the constraint conditions comprise maneuver duration constraint, resolution constraint, velocity increment constraint, side-sway visual range constraint, illumination condition constraint, satellite orbit height constraint, orbital transfer times constraint, task completion rate constraint and target point number constraint.

8. The method for optimizing orbital maneuver oriented to multi-satellite single-reconnaissance targets according to claim 1, wherein the numbers of the maneuvering satellites allocated to the target points are not equal in the iteration process, whether a certain satellite can observe a plurality of target points is judged after the iteration is finished, and a greedy method is used for selecting the task allocation and the orbital transfer scheme.

9. The method for optimizing multi-satellite single-scout-oriented orbital maneuver according to claim 8, wherein the selection of the task allocation and orbital transfer scheme by a greedy method comprises: judging whether a situation that one satellite can observe a plurality of target points exists under the current optimal scheme, if so, calculating an objective function value under the situation, and judging whether to replace the current optimal task allocation and orbital transfer scheme according to the size of the objective function value; in the minimization problem, if the calculated objective function value is less than or equal to the current task allocation and orbital transfer scheme, replacing the current optimal task allocation and orbital transfer scheme; otherwise, the current optimal task allocation and the track change scheme are maintained unchanged.

Technical Field

The satellite is mainly applied to traffic control in the field of traffic transportation, and provides important basic data support for traffic management, vehicle scheduling, travel navigation and the like through real-time monitoring of vehicles and traffic facilities or acquisition of mobile phone signaling data by the satellite. In addition, the application of the satellite in the aspect of traffic emergency reconnaissance, such as observation of extra-large traffic accidents, detection of damage conditions of traffic infrastructures, prevention and control of traffic disasters and the like, cannot be ignored. For the opposite observation task, the main characteristic is that the satellite moves around the earth on a fixed orbit, which makes the satellite motion less flexible and the time window for each target point is basically fixed. For some tasks with strong burstiness and timeliness, such as a traffic disaster prevention and control observation task, imaging of a target point needs to be completed within a specified time period, and a satellite with a fixed orbit may not be able to complete coverage of the target point within the time period. When an emergency observation task occurs and the task is invisible to a plurality of satellites in orbit at present, in order to meet the requirement of rapid response of the satellites, the satellites can quickly reach the sky of any global target within the time specified by a user after receiving an emergency task instruction, and the satellites in orbit can be maneuvered to complete the remote sensing imaging task.

The satellite has wide application in the traffic field, and many researches are mainly started from optimized deployment in the design of the top layer of the satellite aiming at the application characteristics of the satellite in the traffic problem. The core of the satellite deployment problem facing the traffic reconnaissance task is orbit optimization design, namely, the satellite orbit is reasonably deployed through the optimization design of satellite orbit parameters so as to ensure that the satellite can meet the task requirement within a set time. At present, for most satellite optimization deployment problems, coordinate information of an observation target is used as problem input, and potential user requirements are used as optimization target guidance, so that satellite reconnaissance with large resolution, long observation time or short revisit time is realized.

The multi-star and multi-observation target problem is defined as follows: a plurality of emergent tasks which appear simultaneously are distributed at any position in the global range, meanwhile, a plurality of orbiting satellites with maneuvering capability exist on the earth orbit, but the target point has no time window for each orbiting satellite. The main process of the orbit optimization design of the multi-satellite multi-observation target can be divided into a plurality of parts of demand modeling, structure solving construction, platform simulation and algorithm application for solving better satellite orbit parameters. When the orbit parameters can not meet the task requirements, an orbit maneuver optimization method can be used for improving the satellite coverage rate or reducing the revisit time.

Disclosure of Invention

Aiming at the limitations that the time window of each observation target is fixed in the traditional observation method of the satellite, the position of an emergency observation task of a traffic disaster cannot be determined in advance and the timeliness is strong, and the traditional satellite observation cannot cover certain areas within a specified time period, the invention aims to eliminate the blind area in the observation and complete the emergency observation task, and starts from the design of the top layer of a satellite system and optimizes the configuration of the orbit parameters of the satellite, namely the maneuvering optimization of the satellite orbit. The satellite orbit maneuvering optimization refers to aiming at the sudden observation requirement, an optimization algorithm is utilized, on the basis of a series of constraints such as a task acceptable maximum time constraint, an imaging resolution constraint, an orbital transfer fuel consumption constraint, a satellite platform constraint and the like which are not violated, an optimal satellite orbital transfer parameter is found, so that the observation of a target point can be completed within a specified time after the current in-orbit satellite reaches the target orbit through maneuvering orbital transfer, the target point which is originally invisible within a specified time interval of the task can be observed after the satellite carries out orbital transfer according to the calculated maneuvering scheme, the execution of an observation task has more flexibility and timeliness, and in addition, the in-orbit satellite resources can be fully utilized.

In order to meet the observation requirements of each target point and simultaneously not violate the constraint conditions of each target point, the observation tasks need to be reasonably distributed to the orbiting satellites, so that the satellites distributed with the observation tasks can reach the upper part of the target points to be imaged after maneuvering orbit changing, and the weighting function value of each observation task can be optimal on the optimization target appointed by a user.

The invention discloses a multi-satellite multi-reconnaissance target-oriented track maneuvering optimization method, which comprises the following steps of:

aiming at the problem of the orbital maneuver optimization under the condition of multiple stars and multiple scout targets, a multiple optimization target model which simultaneously considers maneuver time, imaging resolution and fuel consumption is established;

solving the multi-optimization target model by using a differential evolution algorithm under an NSGA-II calculation framework, and providing a plurality of non-differential pareto optimal solutions for a user on multiple targets to make a decision;

and selecting the optimal solution as an orbital transfer scheme, and executing a final observation task by each in-orbit satellite.

Further, the multiple optimization objective model is as follows:

-V≤Δv^j≤V (d)

C^j≤1 (g)

n≤m (i)

i＝1，2，...，n；j＝1，2，...，m

wherein t is_imagThe moment of imaging above the target point, t, for the satellite₀For satellite to receive the mission time, t_sAs the target point illumination start time, t_eAs the target point illumination end time, D_imagDistance from the target point when the satellite is imaged over the target point, H_newThe orbital height H of the satellite after the maneuvering orbit change_minTo allow the lowest track height, H_maxIn order to obtain the maximum allowable orbit height, Δ V is the speed increment required by the satellite to reach the target orbit, R is the resolution required to be met, V is the maximum speed increment, a is the sidesway visible range, T is the maximum maneuvering duration, i is the target point sequence number, j is the in-orbit satellite sequence number, C is the satellite orbital transfer frequency, w is the time window number of the satellite to the target point, n is the total number of the target points, and m is the total number of the in-orbit satellites.

Further, a real number coded differential evolution algorithm is adopted to disturb the population.

Further, the step of perturbing the population by using a differential evolution algorithm with real number coding comprises: continuously carrying out discretization treatment on the upper layer part of the solution in the solving process; interfering one existing vector in the population by a differential vector calculated by two different vectors selected randomly, and implementing the process on each vector; in the differential evolution algorithm, if the target function value corresponding to the newly generated vector is better than the parent vector, the new vector replaces the parent vector to enter the next iteration operation.

Further, the solution comprises a plurality of segments and uses a double-layer solution coding structure, each segment comprises a task allocation scheme and an orbit change scheme aiming at the target point, so that the task allocation and the orbit change schemes can be jointly evolved, the upper layer code comprises a satellite number allocated to observe the nth target point, the lower layer code comprises the orbit change time of the mobile satellite, and the satellite performs the speed increment acting on the x axis, the y axis and the z axis of the orbit coordinate system when in the mobile orbit change.

Furthermore, a weighted accumulation method is adopted for calculating the optimized objective function value, and the weighted method is to take the reciprocal of the constraint value on each target point as a weight value and take the reciprocal as a user expectation coefficient.

Further, the constraint conditions comprise maneuvering duration constraint, resolution constraint, speed increment constraint, side swing visual range constraint, illumination condition constraint, satellite orbit height constraint, orbit changing times constraint, task completion rate constraint and target point number constraint.

Further, the mobile satellite numbers allocated to the target points are not equal in the iteration process, whether a certain satellite can observe a plurality of target points is judged after the iteration is finished, and a task allocation and orbital transfer scheme is selected by using a greedy avaricious method.

Further, the selecting the task allocation and the orbital transfer scheme by a greedy method comprises the following steps: judging whether a situation that one satellite can observe a plurality of target points exists under the current optimal scheme, if so, calculating an objective function value under the situation, and judging whether to replace the current optimal task allocation and orbital transfer scheme according to the magnitude of the objective function value; in the minimization problem, if the calculated objective function value is less than or equal to the current task allocation and orbital transfer scheme, replacing the current optimal task allocation and orbital transfer scheme; otherwise, the current optimal task allocation and the track change scheme are maintained unchanged.

Compared with the prior art, the invention has the following beneficial effects:

1) the task allocation and orbital transfer scheme co-evolutionary computation framework designed by the invention needs to consider the task allocation problem in the situation.

2) The task allocation evaluation method considering the user expectation satisfaction is provided, and the problem that the quality degrees of all task allocation schemes are difficult to compare under the condition of multiple stars and multiple reconnaissance targets is solved.

3) Experiments prove that the original on-orbit satellite without a time window at a target point can finish the observation of a task point after being subjected to orbit maneuver optimization and orbital transfer to an expected orbit, and meanwhile, the completion quality and timeliness of the task can be guaranteed.

Drawings

FIG. 1 is a flow chart of a method for optimizing a multi-star multi-scout-target oriented orbit maneuver according to the present invention;

FIG. 2 is a schematic diagram of an encoding structure of a multi-satellite multi-target problem solution according to the present invention;

FIG. 3 is a flow chart of the NSGA-II algorithm of the present invention;

FIG. 4 is a non-dominated sorting hierarchy breakdown diagram of the present invention;

FIG. 5 is a view showing the crowdedness of an individual i according to the present invention;

FIG. 6 is a diagram of the elite strategy procedure of the present invention;

FIG. 7 is a multi-optimization objective model solution distribution graph simultaneously considering maneuver length-imaging resolution-fuel consumption;

FIG. 8 is a diagram of target points and initial positions of satellites in example 2 of the multi-satellite and multi-target problem;

FIG. 9 considers multiple optimization objective model solution profiles of maneuver duration-imaging resolution-fuel consumption simultaneously.

Detailed Description

The invention is further described with reference to the accompanying drawings, which are not intended to be limiting in any way, and any alterations or substitutions based on the teachings of the invention are intended to fall within the scope of the invention.

As shown in fig. 1, the method for optimizing a multi-satellite multi-scout-target oriented orbit maneuver disclosed by the invention comprises the following steps:

aiming at the problem of the orbital maneuver optimization under the condition of multiple stars and multiple scout targets, a multiple optimization target model which simultaneously considers maneuver time, imaging resolution and fuel consumption is established;

solving the multi-optimization target model by using a differential evolution algorithm under an NSGA-II calculation framework, and providing a plurality of non-differential pareto optimal solutions for a user on multiple targets to make a decision;

and selecting the optimal solution as an orbital transfer scheme, and executing a final observation task by each in-orbit satellite.

In order to avoid increasing the complexity of the problem, aiming at the emphasis point and the application direction of the invention, some secondary factors are omitted by grasping the main problem, and certain simplification and assumption are made on the problem background:

(1) satellite fuel supply is not considered in the whole process. In addition, the maneuvering measures adopted by the invention for the satellite are in-plane orbit transfer which saves fuel, namely, the change of the satellite phase is realized by adjusting parameters such as the satellite orbit height, the eccentricity and the like on the basis of not changing the satellite inclination angle and the ascent intersection point.

(2) It is assumed that the satellites in orbit all carry optical loads that can only observe the target in the presence of visible light. Besides illumination, other factors such as cloud layer thickness and weather can also influence the optical satellite imaging, and are not considered. Furthermore, each satellite carries only one sensor.

(3) During the whole task process time length, the time of some short segments is not considered, such as the processing time of the satellite on the task information, the ignition time of the satellite and the like.

(4) Because the altitude of the target point is far from the height of the satellite orbit, the altitude of the target point is ignored and calculated according to the height of the sea level.

(5) In the invention, the configuration among satellites is not considered, the priority and master-slave relation does not exist among the satellites, each satellite independently exists, and any satellite can independently perform orbital maneuver.

(6) The invention does not consider the range of the target, and all the observation targets are regarded as point targets, namely, the satellite can completely observe and image through the sky of the target point once without observing for many times and splicing images.

(7) In order to avoid the situation that the normal service life of the satellite is affected by observing and imaging a series of target points by repeatedly changing the orbit of a certain or some satellites, in this embodiment, it is limited that each satellite changes the orbit at most once.

(8) Because the number of the on-orbit candidate satellites is limited and each satellite is limited to change the orbit at most once, in order to ensure the completion rate of the task and observe each target point, the number of the specified target points in the embodiment is not more than the number of the on-orbit satellites.

(9) Since the target point may be distributed at any position in the global range, the uniformity of the distribution cannot be guaranteed, in the embodiment, only the satellite has a yaw angle, but the adjustment of the yaw attitude of the satellite is not considered.

(10) In this embodiment, each target point can self-set up a constraint limit according to its own property.

The present invention makes the following explanation for some concept problems involved in the modeling process:

(1) the maneuvering time is as follows: the maneuvering time is defined in the present study as the total time from the start of the satellite's observation mission until the satellite images the target point.

(2) Imaging resolution ratio: the resolution of the satellite is expressed by a distance unit, which represents that objects within the resolution distance cannot be distinguished during imaging, only one pixel point is used for representing, and only two objects with the distance above the resolution value can be distinguished in the image, so that the smaller the resolution value is, the higher the imaging precision is.

(3) Speed increment: the change in satellite orbit imparts an impulse to the satellite based on the adjustment to the satellite velocity, which in this study represents the magnitude of the adjustment to the satellite velocity. The velocity increments are vectors, and the signs represent the magnitude of the adjustment in different directions.

TABLE 1 multiple stars Single Observation target problem variable notation

The multi-star and multi-reconnaissance target problem has a plurality of target points and different acceptable constraint values for each target point, so that the calculation of an objective function is more complicated compared with a multi-star single observation target. Because tasks need to be allocated in the problem, if a simple method of accumulating function values on all target points is adopted to calculate the objective function values of the multi-satellite multi-reconnaissance target problem, the situation that the target function values are equal under some task allocation schemes may occur, and the advantages and the disadvantages of the schemes are difficult to compare. Taking the maneuver time as the optimization target as an example, if there are two targets, the first target may receive the maneuver length constraint value of 12 hours, and the second target may receive the maneuver length of 15 hours. In the first case, the maneuvering time for observing the target point I is 10 hours, and the maneuvering time for observing the target point II is 8 hours; in the second case, the observation of the first target point takes 8 hours, while the observation of the target point takes 10 hours of maneuver length. The accumulated maneuvering time of the two maneuvering optimization schemes is 18 hours, and the quality degrees of the two schemes are consistent on the whole, so that comparison cannot be made. Therefore, to avoid such a situation, in the present embodiment, a weighted accumulation method is adopted for the calculation of the optimization objective function value. The weighting rule takes the reciprocal of the constraint value on each target point as a weight value, and the weight value is taken as a user expectation coefficient, and the weighting coefficient is multiplied to reflect the degree to which the task completion conditions on different target points meet the user expectation value.

The orbit maneuvering task modeling method under the condition of simultaneously considering maneuvering time, imaging resolution, fuel consumption and multiple optimization targets for the multi-satellite and multi-target problem is as follows, wherein length units, duration units and speed units in all variables are meters/second:

simultaneously considering a problem model with maneuvering time-imaging resolution-fuel consumption multiple optimization objectives:

optimizing the target: and simultaneously, the fastest maneuver, the minimum fuel consumption and the optimal imaging resolution are taken as targets, so that a plurality of undifferentiated pareto optimal solutions are obtained for the user to select.

Constraint conditions are as follows: firstly, maneuvering duration constraint; secondly, restricting the resolution; thirdly, speed increment constraint; fourthly, restricting the visual range of the side swing; lighting condition constraint; sixthly, satellite orbit height constraint; seventhly, restricting the track changing times; eighthly, restricting task completion rate; and ninthly, restricting the number of the target points.

The mathematical model is established as follows:

-V≤Δv^j≤V (d)

C^j≤1 (g)

n≤m (i)

i＝1，2，...，n；j＝1，2，...，m

the problem background studied in this embodiment is a multi-satellite and multi-observation target problem, and besides the optimal orbital transfer scheme needs to be calculated for each mobile satellite, observation task allocation needs to be performed, that is, it is determined which satellite observes which target point, but the combination manner of task allocation between the satellites and the target points will exponentially increase with the increase of the number of satellites and the number of target points. Therefore, in the present embodiment, a two-layer coding mode is adopted for the structure of the solution in the algorithm, so as to better correspond the observation task with the maneuvering optimization scheme.

The specific coding structure of a solution in the multi-star multi-observation target problem is shown in fig. 2. The largest rectangle in the figure represents the individual, and the rectangle is composed of n segments (divided by thick black lines in the figure) and represents each task point from the target point 1 to the target point n. Wherein each segment contains a task allocation scheme and a tracking scheme for the target point. Satellite in upper layer coding_{i_n}Denotes the satellite number assigned to observe the nth target point, t in the lower layer code_{c_n}Representing the orbital transfer time, Δ v, of the mobile satellite_{x_n}、Δv_{y_n}、Δv_{z_n}Respectively representing the velocity increment acting on the x-axis, the y-axis and the z-axis of the orbit coordinate system when the satellite performs maneuvering orbit transfer. t is t_{c_n}Also needs to be satisfied at t₀，t₀+Tⁱ]Within a time range of Δ v_{x_n}、Δv_{y_n}、Δv_{z_n}Is required to be in the range of [ -V, V]Within the interval. Although a situation that a certain satellite after reaching the target orbit can observe a plurality of target points in sequence may occur in the problem, the probability of the situation occurring in a short time period expected by the emergency observation task is relatively low, and in order to save the computing resources, the computing mechanism in the iterative process of the embodiment ensures that the mobile satellite numbers allocated to the target points are not equal, that is, satellite numbers are not equal, namely, satellite numbers are distributed to the target points₁≠satellite₂≠…≠satellite_{i_n}. And after the iteration is finished, judging whether a certain satellite can observe a plurality of target points or not, and selecting a task allocation and orbital transfer scheme by using a greedy method. The method comprises the following specific steps: because there is a certain probability that a certain satellite can observe a plurality of target points after reaching a target orbit in the problem, for the optimal task allocation and orbital transfer scheme obtained after iteration, it needs to be judged whether there is a situation that a satellite can observe a plurality of target points under the current optimal scheme, if so, an objective function value under the situation is calculated, and whether the current optimal task allocation and orbital transfer scheme are replaced is judged according to the size of the objective function value, in the minimization problem, if the objective function value calculated under the situation is smaller than or equal to the target function valueReplacing the current optimal task allocation and orbital transfer scheme in the current task allocation and orbital transfer scheme; otherwise, the current optimal task allocation and the track change scheme are maintained unchanged.

For the problem model considering maneuvering time, imaging resolution and fuel consumption multiple optimization targets at the same time, the differential evolution algorithm under the multi-target algorithm NSGA-II calculation framework is adopted for solving in the embodiment.

The multi-objective optimization problem is defined as: the vector of control variables is determined in the feasible region such that a set of objective function values are maximized or minimized as simultaneously as possible. In most cases, the targets optimized simultaneously are interactive and conflicting, and the problem of optimizing the trajectory maneuver is mainly reflected in that, for example, in order to image the target point more quickly or to make the imaging resolution higher, the trajectory needs to be adjusted to a greater extent, and therefore the amount of fuel consumed by the trajectory change is greater; or to save fuel consumption, the trajectory is adjusted to a small extent only on the basis of the observation of the target point, in which case the imaging resolution or the task time may need to be sacrificed. In order to optimize multiple targets on the whole, three mutually conflicting sub-targets of maneuvering duration, imaging resolution and fuel consumption need to be comprehensively considered, namely, each sub-target is compromised, so that the problem of simultaneously considering maneuvering time-imaging resolution-fuel consumption multiple optimization targets is solved by selecting an NSGA-II algorithm framework.

The flow of the NSGA-II algorithm is divided into three parts: firstly, randomly generating an initial parent population containing N individuals, and carrying out non-dominated sorting on the individuals in the parent population; then, calculating the crowding degree of each individual in the population, determining the level of the individual according to the crowding degree of the individual, selecting proper individuals by using a selection operator, putting the individuals into a mating pool, and performing operations such as crossing, mutation and the like on the individuals in the pool to generate an offspring population; and finally, merging the parent population and the child population, selecting new N individuals through an elite strategy operation, taking the new individuals as new parents, and continuously repeating the process until the algorithm termination condition is met, wherein the flow chart is shown in fig. 3.

NSGA-II is a fast non-dominated sorting genetic algorithm, and a real number coded differential evolution algorithm is adopted to replace the genetic algorithm to disturb the population in the invention. The steps of disturbing the population by using a differential evolution algorithm of real number coding are as follows: since the upper layer code of the solution represents the mobile satellite numbers assigned to the target points, which are discrete integers, and the mutation operation in the differential evolution algorithm is mainly applied to the continuous search space, the upper layer part of the solution needs to be converted between continuous and discrete types, and a discretization coding method based on sorting is used herein. The upper-layer solution can not maintain a discrete state all the time under the mutation operation, but the elements in the solution still have size difference, the elements in the upper-layer solution are arranged in an ascending order based on the difference, and the position of the elements in the original solution after the ordering is used as the codes in the discrete space. For example, the upper layer solution is subjected to mutation operation to obtain [3.9, 1.4, 2.6, 4.3, 6.2], the ordered solution is [1.4, 2.6, 3.9, 4.3, 6.2], and the upper layer solution is encoded into [3, 1, 2, 4, 5] in discrete space.

Firstly, the upper layer part of the solution is continuously discretized in the solving process. Then, one existing vector in the population is disturbed by a difference vector calculated for two different vectors chosen at random, and the process is carried out for each vector. Since the random perturbation among the vectors can be carried out independently, the differential evolution algorithm is a parallel algorithm. In the differential evolution algorithm, if the objective function value corresponding to the newly generated vector is better than the parent vector, the new vector will replace the parent vector and enter the next iteration operation.

Three major advantages of solving the multi-objective problem by using the NSGA-II algorithm framework are a rapid non-dominated sorting strategy, an individual crowding degree and an elite strategy, which are specifically described as follows.

(1) Fast non-dominated ranking policy

In NSGA-II, the non-dominated ranking of the initial population is based on the number of layers i in which the individuals in the population are located_rankTo proceed with. Specifically, theIn other words, it is dependent on the pareto optimal solution of the population to operate: first, all individuals in the pareto optimal solution are assigned to the first level, i.e., i_rank1 is ═ 1; then removing individuals in the first level from the population, continuously searching pareto optimal solutions (non-sub-distribution solution sets) for the rest populations, and distributing the found pareto optimal solutions into a second level, namely i_rank2; the above operations are repeated until the individuals in the entire population are all stratified, with the same non-dominant ordering for individuals in the same stratum.

An example of the hierarchical division of individuals in a population is shown in fig. 4: in the non-dominated sorting, two parameters need to be calculated for each individual i in the population, namely the number n of individuals dominating i in the population_iAnd a set S of solutions in the population that are dominated by i_i. In the first step n needs to be calculated for each individual_iAnd S_iFinding n in the population_i0, and put it into the first non-dominant level; the second step is to traverse the solution set S that it governs for each individual k in the first non-governing level_k，S_kEach of the individuals l performs n individually_l＝n_l-1, i.e. to solve the solution S_kThe dominant solution number of the middle individual minus 1, since the individual k has already been divided into the first non-dominant hierarchy. If n is present_lIf 0, the individual/is saved to the second non-dominant level and the above steps are repeated for the individuals in the second non-dominant level until the entire population is stratified.

(2) Congestion degree calculation

The diversity of the population and the distribution characteristics in the solution space are critical to the optimization performance of the NSGA-ii algorithm, in which individuals with good performance and low aggregation density are usually retained as parents to participate in the evolution process of the next generation. In the process, the crowding degree of the population individual is calculated, and the crowding degree can be measured by a crowding distance, wherein the crowding degree of the population individual i is defined as the average distance between the individual and two adjacent individuals in a uniform non-dominant level on each sub-objective function,in the two-dimensional solution space, which is represented by the maximum rectangular perimeter surrounding the individual i but not including other individuals, as shown in fig. 5, the calculation process of the individual crowdedness degree is as follows: first, the congestion degree is initialized to make all the individuals have the congestion degree I_i0; then, ordering the individuals in the same level according to the sub-objective function values; the crowdedness of two individuals located at the edge of the hierarchy is set to infinity, and the crowdedness of the remaining individuals located in the middle can be calculated by equation 2:

wherein f (& ltM & gt.) is the function value at the mth target,andand sorting the maximum value and the minimum value of the layer of individuals according to the ascending order of the mth objective function. Respectively repeating the steps for each objective function in the multi-objective optimization model to obtain the crowdedness of each individual, namely i_distance＝I_i。

After the above operations of non-dominant ranking and congestion degree calculation, each individual in the population has a non-dominant ranking (i.e. the level i where the individual is located after the non-dominant ranking_rank) And degree of congestion i_distanceAnd two attributes, by which the quality between individuals can be judged. For any two individuals i and j in the population, if the two individuals are not at the same level, i_rank＜j_rankIn which case individual i is considered superior to individual j; if i_rank＝j_rankThe assessment is made according to the individual's crowdedness, e.g. i_distance＞j_distanceThat is, the crowdedness of the individual i is greater than that of the individual j, which also represents that the individual i is better than the individual j.

(3) Elite strategy

The flow of the elite reservation strategy is shown as a figure6, in the Elite preservation strategy, the parent population P is first identified_tAnd the offspring population Q_tSynthesis of a population R of size 2N_t(i.e., R)_t＝P_t∪Q_t) Then for the new population R_tAnd performing rapid non-dominated sorting and congestion degree calculation operation, and selecting the optimal N individuals as new parent population. The mechanism that the parent individuals and the child individuals compete together to generate the new population can inherit effective information in the evolution process, so that excellent individuals are reserved, and the function of further improving the performance of the algorithm is achieved.

The following experiments were conducted to verify the technical effects of the present invention.

In order to verify the effectiveness of the model and the algorithm under different environments, the embodiment is provided with two cases, the first case is that the number of target points is equal to the number of satellites, and the second case is that the number of the target points is less than the number of the satellites, and the multi-optimization target model which simultaneously considers maneuvering duration, resolution and fuel consumption under the two cases is solved and analyzed.

Example one

Example scene settings

In this example, three orbiting satellites are provided, and six initial orbits and target point position information of each satellite are shown in tables 2 and 3:

TABLE 2 initial orbit six numbers of in-orbit satellite for multi-satellite single reconnaissance target problem

TABLE 3 position information of target points of multi-satellite single scout target problem example

Target weaveNumber (C)	Latitude	Longitude (G)
			1	0°	Western-style menses at 62 °
2	North latitude 41 °	Dongding Jing 70 °
			3	50 degree of south latitude	Xijing 146 °
4	North latitude 45 °	Dongding Jing 116 °

For the maneuvering time constraint and the resolution constraint of the satellite, since different constraint thresholds can be set for different target point task properties, the embodiment draws up two types of constraint values for different target points, as shown in table 4:

TABLE 4 Multi-Star Multi-Observation problem EXAMPLE 1 different target Point constraint value settings

Analysis of results

The part takes the maneuvering duration-imaging resolution-fuel consumption as an optimization model to solve the problem.

(1) Multiple optimization objectives simultaneously considering maneuver duration-imaging resolution-fuel consumption

The multiple optimization target model considering maneuvering duration, imaging resolution and fuel consumption simultaneously is solved by using a differential evolution algorithm under an NSGA-II calculation framework, and the conditions of the multiple pareto optimal solutions on spatial distribution are shown in FIG. 7:

each solution in the pareto solution set provides a user with a non-differentiated task allocation scheme and an orbital transfer scheme for the user to make decisions. The assignment of the tasks in the solutions and the maneuvering times, imaging resolutions and velocity increments required to perform the observation tasks at the different target points on the mobile satellites are shown in table 5.

TABLE 5 EXAMPLE 1 multiple optimization target case results

Example two

Example scene settings

The example assumes that the time point of the satellite receiving the observation task is consistent with that of the example 1, and is the Beijing time 2020-12-0114: 00: 00. In the present embodiment, four orbiting satellites are provided, the four orbiting satellites need to observe three target points distributed at different positions in a global range, and all the three target points are invisible on initial orbits of the four satellites, so that part of the satellites need to be selected from four selected satellites to perform maneuvering orbital transfer and complete observation tasks. The initial six orbital numbers of each satellite and the unified constraint values that need to be satisfied for orbital transfer are shown in tables 6 and 7, respectively.

TABLE 6 Multi-satellite Multi-target problem EXAMPLE 2 initial orbit six numbers of in-orbit satellites

TABLE 7 Multi-Star Multi-object problem example 2 unified constraint values required for orbital transfer

Category of constraint	Constraint value
		Target point illumination time	Local time is 6:00:00 to 18:00:00
Satellite side-swing visual range	45°
		Velocity delta constraint	The velocity increment is not more than 300m/s

The target task points in the present example can be distributed at any position in the global scope, and in order to verify the effectiveness of the algorithm under various conditions, three target points are set up in the present example, which are respectively located on the high latitude, the middle latitude and the low latitude of the southern hemisphere and the northern hemisphere, and the longitudes of the target points are also distributed uniformly between the west longitude 180 degrees and the east longitude 180 degrees. The target basic information and the constraint values formulated for the task properties of each target point are shown in table 8.

TABLE 8 Multi-Star Multi-object problem calculation example 2 target Point location information and specific constraint value settings

The relationship between the position of the satellite at the time of the reception task and the target points is shown in fig. 8:

analysis of results

The method takes the maneuvering duration-imaging resolution-fuel consumption as an optimization model, solves the problems, and displays and analyzes a selection scheme, a task allocation scheme and other solution results of the executed task satellite in the following text.

(1) Multiple optimization objectives simultaneously considering maneuver duration-imaging resolution-fuel consumption

The multiple optimization target model considering maneuvering duration, imaging resolution and fuel consumption simultaneously is solved by using a differential evolution algorithm under an NSGA-II calculation framework, and the conditions of the multiple pareto optimal solutions on spatial distribution are shown in FIG. 9:

each solution in the pareto solution set provides a user with a non-differentiated task allocation scheme and an orbital transfer scheme for the user to make decisions. The assignment of the tasks to the solutions and the maneuvering times, imaging resolutions, and velocity increments required to perform the observation tasks at the different target points on the mobile satellites are shown in table 9.

TABLE 9 EXAMPLE 2 multiple optimization target case results

The method sets two application examples in different environments, solves and analyzes a multi-optimization target model which simultaneously considers maneuvering time, imaging resolution and fuel consumption under the condition of multi-satellite and multi-reconnaissance targets by utilizing a differential evolution algorithm under a classical multi-target algorithm NSGA-II calculation framework, and the solved result fully proves the effectiveness of the multi-satellite and multi-reconnaissance target orbit maneuvering optimization method designed by the invention.

Compared with the prior art, the invention has the following beneficial effects:

1) the task allocation and orbital transfer scheme co-evolutionary computation framework designed by the invention needs to consider the task allocation problem in the situation.

2) The task allocation evaluation method considering the user expectation satisfaction is provided, and the problem that the quality degrees of all task allocation schemes are difficult to compare under the condition of multiple stars and multiple reconnaissance targets is solved.

3) Experiments prove that the original on-orbit satellite without a time window at a target point can finish the observation of a task point after being subjected to orbit maneuver optimization and orbital transfer to an expected orbit, and meanwhile, the completion quality and timeliness of the task can be guaranteed.

The above embodiment is an implementation manner of the present invention, but the implementation manner of the present invention is not limited by the above embodiment, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be regarded as equivalent replacement manners, which are included in the protection scope of the present invention.