CN113619815B - Spacecraft cluster dynamic path planning method - Google Patents

Spacecraft cluster dynamic path planning method Download PDF

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CN113619815B
CN113619815B CN202110893521.4A CN202110893521A CN113619815B CN 113619815 B CN113619815 B CN 113619815B CN 202110893521 A CN202110893521 A CN 202110893521A CN 113619815 B CN113619815 B CN 113619815B
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欧阳一农
方群
张震
宋金丰
上官晔婷
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Xi'an High Intelligent Technology Co ltd
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    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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    • B64G1/00—Cosmonautic vehicles
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Abstract

The invention provides a spacecraft cluster dynamic path planning method, which is characterized in that the nonlinearity of an orbital dynamics equation in a three-dimensional space is stronger, so that the modeling is carried out by considering the space force borne by a spacecraft in the space, the autonomous searching process of the path planning of a spacecraft cluster is carried out by cooperating with a particle swarm algorithm, and the spacecraft cluster path planning taking the fuel optimization as an optimization index can be perfectly finished under the condition of considering the space obstacle and the internal constraint of the spacecraft cluster. The method performs dynamic path planning under the premise of considering the obstacles in the three-dimensional space, and obtains the optimal path under the premise of avoiding the obstacles.

Description

Spacecraft cluster dynamic path planning method
Technical Field
The invention belongs to the field of spacecraft cluster dynamic path planning, and particularly relates to a spacecraft cluster dynamic path planning method.
Background
In recent years, spacecraft clustering systems have become a hot spot for research in the aerospace field, and although spacecraft clustering has been the first focus in the aerospace field, it can be known with reference to development thereof in the aerospace field or ground mission that the use of intelligent spacecraft clustering to perform space mission has a very great prospect, for example: performing observation, containment, handling, or repair tasks on close range targets using a plurality of spacecraft; adopting a plurality of spacecrafts to form a temporary relay communication satellite; or multiple spacecraft validation aggregation, docking or separation techniques, etc.
The problem of spacecraft cluster path planning is a key problem in spacecraft cluster research. The method for designing the spacecraft cluster path by using the particle swarm algorithm is proposed in the document 'research on autonomous formation reconstruction method for satellite formation flight' of the yellow seaside, but possible environmental obstacles are not considered; a robot path planning design is carried out in a two-dimensional environment by applying a particle swarm algorithm and an artificial potential field method in a literature, namely research on a group robot trapping behavior based on the particle swarm algorithm, but the situation in a three-dimensional environment is not considered; thank you to carry out path planning design on unmanned aerial vehicle clusters in a three-dimensional environment in the research on multi-machine crowd body game and coordination control in an confrontation environment, but because a spacecraft is in a space environment, the orbit force borne by the spacecraft and the force borne by the unmanned aerial vehicle are obviously different due to the special environment of the spacecraft.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a spacecraft cluster dynamic path planning method which performs dynamic path planning under the premise of considering obstacles in a three-dimensional space and obtains an optimal path under the premise of avoiding the obstacles.
The invention is realized by the following technical scheme:
a spacecraft cluster dynamic path planning method comprises the following steps:
step 1, determining an initial target point of each member spacecraft according to task requirements;
step 2, establishing a spacecraft dynamics equation in a three-dimensional space, and calculating the motion trail of a target point corresponding to each member spacecraft in a spacecraft cluster according to the initial target point of each member spacecraft to obtain the final target point of each member spacecraft;
step 3, determining constraint conditions in path planning according to task requirements, and establishing a fitness function of each member spacecraft approaching a target point, wherein the fitness function takes the space barrier into consideration, in a three-dimensional space;
step 4, initializing the particle position and speed of the particle swarm algorithm, and calculating the fitness function value of the particle according to the fitness function;
step 5, iterative computation of the individual optimal solution and the global optimal solution of the particle swarm is performed by adopting a particle swarm algorithm; updating the position and the speed of the particle according to the global optimal solution;
step 6, calculating a fitness function value of the particles according to the positions and the speeds of the particles and the fitness function, and outputting an optimal solution if the fitness function value is converged to obtain an optimal path of the spacecraft cluster; and if the fitness function value does not converge, returning to the step 5.
Preferably, step 2 is specifically: calculating a target point motion trail caused by the revolution of the target point by using the formula (1); calculating a target point motion trail caused by the rotation of the target point by using the formulas (2) and (3), and obtaining a motion trail of the target point according to the target point motion trail caused by the revolution of the target point and the target point motion trail caused by the rotation of the target point;
Figure BDA0003196916850000021
wherein the vector v is a velocity vector of the target point; the vector r is a position vector of the target point; the scalar r is the distance from the target point to the center of the track;
Figure BDA0003196916850000022
an acceleration change vector caused by the non-spherical oblate perturbation of the earth;
Figure BDA0003196916850000023
acceleration change vectors caused by solar gravity perturbation;
Figure BDA0003196916850000024
acceleration change vectors caused by perturbation of lunar gravity;
Figure BDA0003196916850000031
acceleration change vectors caused by perturbation of sunlight pressure;
Figure BDA0003196916850000032
wherein, subscript a represents the arrival time of each member spacecraft at the target point, subscript b represents the initial time, [ x, y, z ] represents the position state of the target point under the target system, and R represents a rotation matrix, which is specifically defined as follows:
Figure BDA0003196916850000033
wherein q isi(i ═ 0,1,2,3) represents a quaternion.
Preferably, in step 3, the constraint condition includes a thrust constraint condition of equation (4) and a distance constraint condition of equation (5):
0≤||uk||l≤umax (4)
wherein, | | uk||lRepresents the amplitude of the pulse, u, produced by the kth maneuver of the l spacecraftmaxRepresenting the maximum thrust upper limit that the spacecraft can generate;
Figure BDA0003196916850000034
wherein the content of the first and second substances,
Figure BDA0003196916850000036
representing a minimum distance threshold of the ith spacecraft from the jth spacecraft;
Figure BDA0003196916850000037
representing the current distance between the ith spacecraft and the jth spacecraft;
Figure BDA0003196916850000038
representing the maximum distance threshold of the ith spacecraft from the jth spacecraft.
Further, in step 3, the fitness function of each member spacecraft, which takes the space obstacle into consideration, approaching the target point is as shown in formula (6):
Figure BDA0003196916850000035
wherein alpha is1,α2,α3And epsilon is a weight coefficient, and represents that when the particle swarm iterates to a fixed number of times, the spacecraft exchanges individual information to optimize the total fuel of the spacecraft cluster, the value is 1, and the rest values are 0.
Figure BDA0003196916850000048
The path length that the spacecraft has to travel to date,
Figure BDA0003196916850000049
target point for spacecraftThe length of the path required to be traversed; penaltyi,tAnd representing a penalty function in the obstacle avoidance process.
Further, in step 5, the individual optimal solution in the particle swarm is calculated by using equation (8), and the global optimal solution in the particle swarm is calculated by using equation (9):
Figure BDA0003196916850000041
Figure BDA0003196916850000042
wherein i is the particle number; k is the current iteration number; d is the dimension of the solution;
Figure BDA0003196916850000043
position information of the ith particle on the d-dimensional solution at the k-th iteration;
Figure BDA0003196916850000044
position information of the ith particle on the d-dimensional solution at the k-th iteration;
Figure BDA0003196916850000045
the global optimal solution for the previous k iterations of all particles.
Further, the position and velocity of the particle are updated according to equation (10):
Figure BDA0003196916850000046
wherein the content of the first and second substances,
Figure BDA0003196916850000047
velocity information on a d-dimensional solution for the ith particle at the kth iteration; ω inertial weight; c. C1、c2Is a non-negative constant; r is1、r2Is [0,1 ]]Any constant therebetween.
Further, in step 5, after each iteration of the particle swarm is performed for n times, information is exchanged with global optimal solutions of other particle swarms, and the distance between any two global optimal particles is calculated; if the distance between any two globally optimal particles meets the boundary constraint condition formula (5), the current globally optimal solution is applied to update the positions and the speeds of the particles; otherwise, updating the position and the speed of the particle by using the global optimal solution obtained by the previous iteration; and when the iteration times are not multiples of n, if the boundary constraint condition (5) is met, using the current global optimal solution by each particle swarm, and otherwise, using the global optimal solution obtained by the previous iteration.
Further, in step 5, the search radius of the particle swarm algorithm is a dynamic search radius, as shown in formula (7),
Figure BDA0003196916850000051
wherein beta is1，β2，β3，β4Are coefficients. By varying the coefficient beta1，β2，β3，β4The search radius R and the varying curvature of the search radius of the particle swarm algorithm may be modified.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a technical scheme for solving the problem of spacecraft cluster dynamic path planning considering space barriers in a three-dimensional space for the first time. Because the trajectory dynamics equation in the three-dimensional space has stronger nonlinearity, the modeling is carried out by considering the space force borne by the spacecraft in the space, the autonomous searching process of the path planning of the spacecraft cluster is carried out by cooperating with the particle swarm algorithm, and the path planning of the spacecraft cluster taking the optimal fuel as the optimization index can be perfectly finished under the condition of considering the space obstacle and the internal constraint of the spacecraft cluster.
Furthermore, when each member spacecraft moves according to the path planning, the relative position inside the cluster is inevitably changed, so that the communication capacity of each member spacecraft is weak or the safety distance exceeds the limit.
Furthermore, compared with the traditional particle swarm algorithm, the method improves the search radius of the particle swarm algorithm, reduces the search range of the particle swarm after approaching the target point, has higher search efficiency, avoids the problem that the optimal solution cannot be found due to an overlarge search area after the spacecraft approaches the target point, optimizes the fuel consumption of the spacecraft cluster through dynamically searching the radius, reduces the fuel consumption, and prolongs the service life of the member spacecraft.
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FIG. 1 is a schematic diagram of a path planning for a member spacecraft in a spacecraft cluster;
FIG. 2 is a flow chart of a spacecraft cluster dynamic path planning solving method provided by the invention, namely a flow chart of dynamic path planning for solving a spacecraft cluster by using a particle swarm algorithm and considering a space obstacle;
FIG. 3 is a path planning implemented by the particle swarm algorithm with dynamic search radius proposed by the present invention;
fig. 4 is a path implemented by solving a path planning problem through a conventional particle swarm algorithm.
Detailed Description
The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.
As shown in fig. 1, when a spacecraft cluster completes a space mission, a reasonable path planning needs to be performed on the spacecraft cluster. Path planning first needs to consider how the target point changes over time; secondly, considering the environmental obstacles to be avoided in the process of reaching a target point by the spacecraft cluster; then, inter-satellite collision in the spacecraft cluster needs to be avoided, and all member spacecrafts are ensured to be in a communication range; finally, whether a planned path designed for the spacecraft cluster is better needs to be considered, and the performance index of the planned path is generally that the maximum maneuvering capacity of each pulse maneuver does not exceed the upper limit of the spacecraft and the total fuel consumption is optimal.
The invention relates to a spacecraft cluster dynamic path planning method, which comprises the following steps:
step 1, determining an initial target point of each member spacecraft according to task requirements.
And 2, calculating the motion trail of the target point corresponding to each member spacecraft in the spacecraft cluster according to the initial target point of each member spacecraft to obtain the final target point of each member spacecraft.
And establishing a spacecraft dynamics equation in a three-dimensional space due to the influence of orbital force on the target. The movement locus of the target point consists of a revolution part and a rotation part, and the numerical integration is carried out on the formula (1) to calculate the movement locus of the target point caused by the revolution of the target point; calculating a target point movement locus caused by target point rotation by using equations (2) and (3):
Figure BDA0003196916850000061
wherein the vector v is a velocity vector of the target point; the vector r is a position vector of the target point; scalar r is the distance of the target point from the center of the orbit;
Figure BDA0003196916850000062
an acceleration change vector caused by the non-spherical oblate perturbation of the earth;
Figure BDA0003196916850000071
acceleration change vectors caused by solar gravity perturbation;
Figure BDA0003196916850000072
acceleration change vectors caused by perturbation of lunar gravity;
Figure BDA0003196916850000073
the acceleration change vector caused by the perturbation of the sunlight pressure.
Figure BDA0003196916850000074
Wherein, subscript a represents the arrival time of each member spacecraft at the target point, subscript b represents the initial time, [ x, y, z ] represents the position state of the target point under the target system, and R represents a rotation matrix, which is specifically defined as follows:
Figure BDA0003196916850000075
wherein q isi(i ═ 0,1,2,3) represents a quaternion.
And obtaining the motion trail of the target point according to the motion trail of the target point caused by the revolution of the target point and the motion trail of the target point caused by the rotation of the target point, thereby obtaining the final target point of each member spacecraft.
And 3, determining constraint conditions in path planning according to task requirements and establishing a fitness function of each member spacecraft approaching a target point.
In order to obtain the path of each member spacecraft, an optimization model needs to be established for solving.
In the embodiment of the invention, the constraint condition adopts a thrust constraint condition of an expression (4) and a distance constraint condition of an expression (5):
0≤||uk||l≤umax (4)
wherein, | | uk||lRepresents the amplitude of the pulse, u, produced by the kth maneuver of the l spacecraftmaxRepresenting the upper limit of the maximum thrust that can be generated by the spacecraft.
Figure BDA0003196916850000076
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003196916850000078
representing a minimum distance threshold of the ith spacecraft from the jth spacecraft;
Figure BDA0003196916850000077
representing the current distance between the ith spacecraft and the jth spacecraft;
Figure BDA0003196916850000083
representing the maximum distance threshold of the ith spacecraft from the jth spacecraft.
Since the space obstacle tends to have a spin motion, the space obstacle is described as a space envelope sphere and is regarded as an unreachable domain.
Then, a fitness function taking the obstacle into consideration is established as shown in the formula (6):
Figure BDA0003196916850000081
wherein alpha is1,α2,α3And epsilon is a weight coefficient, and represents that when the particle swarm evolves to a fixed number of times, the spacecraft exchanges individual information to optimize the total fuel of the spacecraft cluster, and the value is 1, and the rest values are 0.
Figure BDA0003196916850000084
The path length that the spacecraft has to travel to date,
Figure BDA0003196916850000085
the length of a path which the spacecraft needs to pass to reach a target point; dependencyi,tAnd representing a penalty function in the obstacle avoidance process, namely the penalty function of meeting the obstacle in the path planning.
And 4, initializing the particle swarm algorithm and designing the dynamic search radius of the particle swarm algorithm.
Initializing a particle swarm algorithm, giving information such as the number of particles in a particle swarm and the number of iterations according to an actual task background, initializing particle position information and velocity information, and limiting the position and the velocity of the particles. The search radius of the particle swarm algorithm is improved, the search radius of the particle swarm algorithm is designed to be a dynamic radius, and as shown in formula (7), the situation that the spacecraft searches for an optimal solution in the process of gradually approaching the target point to cause a great amount of useless maneuvering of the spacecraft is avoided through continuous reduction of the search radius.
Figure BDA0003196916850000082
Wherein, beta1，β2，β3，β4Are coefficients. By varying the coefficient beta1，β2，β3，β4The search radius R and the varying curvature of the search radius of the particle swarm algorithm may be modified.
And 5, calculating the individual optimal solution and the global optimal solution of the particle swarm according to the particle swarm algorithm obtained in the step 4. So as to record the passing state of each particle and the whole particle swarm, and is convenient to find the optimal value.
Calculating a particle fitness function by using an equation (6), calculating an individual optimal solution in the particle swarm by using an equation (8), and calculating a global optimal solution of the particle swarm by using an equation (9):
Figure BDA0003196916850000091
Figure BDA0003196916850000092
and exchanging information with the global optimal solution of other particle swarms after the particle swarms iterate n (generally taking 6) times, and calculating the distance between any two global optimal particles. If the distance between any two globally optimal particles meets the boundary constraint condition formula (5), applying the current globally optimal solution; otherwise, the global optimal solution obtained by the previous iteration is used, so that the spacecraft is ensured to meet the distance constraint. In addition, when the iteration number is not a multiple of n, if the boundary constraint condition (5) is met, each particle swarm uses the current global optimal solution; otherwise, the global optimal solution obtained by the previous iteration is used. And updating the position and velocity of the particle according to equation (10):
Figure BDA0003196916850000093
the meanings of the symbols in the formulae (8), (9) and (10) are shown in Table 1.
TABLE 1 meanings of symbols in formulae (8), (9) and (10)
Figure BDA0003196916850000094
Figure BDA0003196916850000101
By designing a global optimal solution exchanged by a certain particle swarm and other particle swarms, the cooperative function among different particle swarms is realized, so that the minimum total fuel consumption is ensured, and the influence of an optimal value found by a certain particle swarm on the results of other particle swarms is avoided, thereby causing local optimization. Meanwhile, in order to reduce excessive consumption of computing resources, information is exchanged between particle groups only when each iteration is performed n times.
Step 6, calculating a fitness function value of the particles by using the formula (6) according to the positions and the speeds of the particles, and outputting an optimal solution if the fitness function value is converged and proves that the particle swarm has searched an optimal path; and if the fitness function value is not converged, repeating the steps 5 and sequentially executing the re-searching until the fitness function value is converged. Judging whether the particle swarm algorithm iterates to an optimal value or not by calculating a fitness function, if so, proving that the particle swarm has searched an optimal path, and outputting a result; if not, the re-search continues with the iteration.
And 7: and obtaining the optimal solution of the spacecraft cluster path planning problem.
Fig. 2 is a flowchart of a method for solving a spacecraft cluster dynamic path planning proposed by the present invention, and the process of steps 1-3 is not shown in the diagram. FIG. 3 is a path plan obtained by the particle swarm algorithm using dynamic search radius proposed by the present invention; fig. 4 is a path plan obtained by a conventional particle swarm. Compared with the prior art, the traditional particle swarm algorithm has the advantages that due to the fact that the search radius is fixed, the optimal solution is difficult to find near a target point, a large amount of track fluctuation occurs, fuel consumption is increased due to excessive maneuvering, the service life of a spacecraft is shortened, and a large amount of cost loss is caused; the method provided by the invention has the advantages that the search radius is continuously reduced, so that the optimal solution can be easily found when the particle swarm approaches a target point, the track is stable, the maneuvering times are reduced, the fuel consumption and the spacecraft loss are reduced, and a large amount of economic cost is saved.
The invention not only can reach the dynamic target point under the premise of considering the collision avoidance constraint of the space spacecraft (the minimum value in the formula (5)), the maximum communication distance constraint (the maximum value in the formula (5)) and the obstacle constraint, but also improves the traditional particle swarm algorithm, so that the fuel consumption of a spacecraft cluster is optimized, and the fuel consumption is reduced.
In the application process of the method, users can set different member spacecraft target points according to actual conditions to simulate different forms of space tasks; although the spacecraft distance constraint and the thrust constraint are taken as examples for discussion in the presentation process of the invention, different obstacle avoidance areas can be designed, target points and constraint conditions can be changed according to different space task requirements in the actual process so as to respond to space tasks with different requirements, and the method can be used for solving the dynamic path planning problem.
Although the present invention is demonstrated by the general embodiments to effectively solve the problem of planning a dynamic path of a spacecraft cluster in a three-dimensional space in consideration of space obstacles and to make the planned path tend to be optimal, the present invention can be easily generalized to the path planning problem of other different tasks. Accordingly, those skilled in the art can readily devise many modifications and equivalents of the disclosed methods and techniques without departing from the spirit and scope of the invention. However, any simple modification, equivalent change and modification made to the above general embodiments or similar works according to the technical essence of the present invention are still within the scope of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.

Claims (8)

1. A spacecraft cluster dynamic path planning method is characterized by comprising the following steps:
step 1, determining an initial target point of each member spacecraft according to task requirements;
step 2, establishing a spacecraft dynamics equation in a three-dimensional space, and calculating the motion trail of a target point corresponding to each member spacecraft in a spacecraft cluster according to the initial target point of each member spacecraft to obtain the final target point of each member spacecraft;
step 3, determining constraint conditions in path planning according to task requirements and establishing a fitness function of each member spacecraft approaching a target point, wherein the fitness function takes the space obstacles into consideration, in a three-dimensional space;
step 4, initializing the particle position and speed of the particle swarm algorithm, and calculating the fitness function value of the particle according to the fitness function;
step 5, iterative computation of the individual optimal solution and the global optimal solution of the particle swarm is performed by adopting a particle swarm algorithm; updating the position and the speed of the particles according to the global optimal solution;
step 6, calculating a fitness function value of the particles according to the positions and the speeds of the particles and the fitness function, and outputting an optimal solution if the fitness function value is converged to obtain an optimal path of the spacecraft cluster; if the fitness function value is not converged, returning to the step 5;
and 7, obtaining an optimal solution of the spacecraft cluster path planning problem.
2. The spacecraft cluster dynamic path planning method according to claim 1, wherein step 2 specifically comprises: calculating a target point motion trail caused by the revolution of the target point by using the formula (1); calculating a target point motion trail caused by target point rotation by using the formulas (2) and (3), and obtaining a target point motion trail according to the target point motion trail caused by target point revolution and the target point motion trail caused by target point rotation;
Figure FDA0003632352730000011
wherein the vector v is a velocity vector of the target point; the vector r is a position vector of the target point; scalar r is the distance of the target point from the center of the orbit;
Figure FDA0003632352730000021
an acceleration change vector caused by the non-spherical oblate perturbation of the earth;
Figure FDA0003632352730000022
acceleration change vectors caused by solar gravity perturbation;
Figure FDA0003632352730000023
acceleration change vectors caused by perturbation of lunar gravity;
Figure FDA0003632352730000024
acceleration change vectors caused by the perturbation of the sunlight pressure;
Figure FDA0003632352730000025
wherein, subscript a represents the arrival time of each member spacecraft at the target point, subscript b represents the initial time, [ x, y, z ] represents the position state of the target point under the target system, and R represents a rotation matrix, which is specifically defined as follows:
Figure FDA0003632352730000026
wherein q isi(i ═ 0,1,2,3) represents a quaternion.
3. A spacecraft constellation dynamic path planning method according to claim 1, wherein in step 3, the constraints comprise a thrust constraint of equation (4) and a distance constraint of equation (5):
0≤||uk||l≤umax (4)
wherein, | | uk||lRepresents the amplitude of the pulse, u, produced by the kth maneuver of the l spacecraftmaxRepresenting the maximum thrust upper limit that the spacecraft can generate;
Figure FDA0003632352730000027
wherein the content of the first and second substances,
Figure FDA0003632352730000028
representing a minimum distance threshold of the ith spacecraft from the jth spacecraft;
Figure FDA0003632352730000029
representing the current distance between the ith spacecraft and the jth spacecraft;
Figure FDA00036323527300000210
representing the maximum distance threshold of the ith spacecraft from the jth spacecraft.
4. A spacecraft cluster dynamic path planning method according to claim 3, wherein in step 3, the fitness function of each member spacecraft approaching the target point taking into account the space obstacle is as shown in formula (6):
Figure FDA0003632352730000031
wherein alpha is1,α2,α3The weight coefficient is epsilon, which indicates that when the particle swarm iterates to a fixed number of times, the spacecraft exchanges individual information to optimize the total fuel of the spacecraft cluster, the value is 1, and the rest values are 0;
Figure FDA0003632352730000032
the path length that the spacecraft has to travel to date,
Figure FDA0003632352730000033
the length of a path which the spacecraft needs to pass to reach a target point; dependencyi,tAnd representing a penalty function in the obstacle avoidance process.
5. The spacecraft cluster dynamic path planning method of claim 3, wherein in step 5, the individual optimal solution in the particle swarm is calculated by using the formula (8), and the global optimal solution in the particle swarm is calculated by using the formula (9):
Figure FDA0003632352730000034
Figure FDA0003632352730000035
wherein i is the particle number; k is the current iteration number; d is the dimension of the solution;
Figure FDA0003632352730000036
position information of the ith particle on the d-dimensional solution at the k-th iteration;
Figure FDA0003632352730000037
the individual optimal solution of the previous k iterations of the ith particle is obtained;
Figure FDA0003632352730000038
the global optimal solution for all the previous k iterations of the particle.
6. A spacecraft constellation dynamic path planning method according to claim 5, characterized in that the position and velocity of the particles are updated according to equation (10):
Figure FDA0003632352730000039
wherein the content of the first and second substances,
Figure FDA00036323527300000310
velocity information on a d-dimensional solution for the ith particle at the kth iteration; ω inertial weight; c. C1、c2Is a non-negative constant; r is a radical of hydrogen1、r2Is [0,1 ]]Any constant therebetween.
7. The spacecraft cluster dynamic path planning method of claim 3, wherein in step 5, the particle swarm exchanges information with global optimal solutions of other particle swarms after iterating for n times each time, and the distance between any two global optimal particles is calculated; if the distance between any two globally optimal particles meets the boundary constraint condition formula (5), the current globally optimal solution is applied to update the positions and the speeds of the particles; otherwise, updating the position and the speed of the particle by using the global optimal solution obtained by the previous iteration; and when the iteration times are not multiples of n, if the boundary constraint condition expression (5) is met, each particle swarm uses the current global optimal solution, otherwise, the global optimal solution obtained by the previous iteration is used.
8. The spacecraft cluster dynamic path planning method of claim 3, wherein in step 5, the search radius of the particle swarm algorithm is a dynamic search radius as shown in formula (7),
Figure FDA0003632352730000041
wherein, beta1，β2，β3，β4As a coefficient, by varying the coefficient beta1，β2，β3，β4The search radius R and the varying curvature of the search radius of the particle swarm algorithm may be modified.
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