A method for path planning of small satellite constellation formation configuration considering time factor

Abstract

A kind of small satellite constellation formation path planning method considering time factor, introduce time factor on the basis of path point planning in the process of small satellite constellation formation adjustment maneuver, establish satellite motion state function by polynomial interpolation algorithm based on selected path point;With state function as the basis, consider collision, energy loss, path selection and other factors to design comprehensive fitness function, establish genetic algorithm iteration steps, realize the planning of small satellite constellation formation adjustment path.The method of the application comprehensively considers the safety, low energy loss and path selection requirements of small satellite constellation formation adjustment, can quickly complete the small satellite constellation maneuver task, the path is shorter, energy loss is less and has good stability and convergence in the process of maneuver, further improves the real-time and accuracy of small satellite constellation maneuver task.

Description

Technical Field

[0001] This invention belongs to the field of satellite formation flight control and relates to a method for path planning of small satellite constellation formation configuration. Background Technology

[0002] Small satellite constellation formations have solved the problems of high cost, long development cycle, and high economic risk associated with traditional large spacecraft. They provide a space platform foundation for large-scale space missions and offer solutions for high-precision Earth observation, high-precision navigation and positioning, and space warfare. The configuration of spacecraft formations, including small satellite constellations, is fundamental to ensuring the successful completion of spacecraft missions. In complex missions, adjustments to the small satellite constellation configuration are often necessary. Ensuring the safety and stability of the small satellite constellation during these adjustments is crucial. Therefore, finding the optimal maneuver path for small satellite constellation configuration adjustments has become a key research focus.

[0003] Previous research on path planning for satellites and other spacecraft has largely focused on single-spacecraft maneuvering and rendezvous / docking path planning, with single-satellite path planning based on collision probability becoming a mature method for satellite on-orbit maneuvers. However, for constellation formations, each satellite is not an independent entity and must cooperate to complete predetermined tasks. Therefore, on-orbit maneuvers of constellation formations often need to consider the impact of each satellite's maneuvering process on fuel consumption, operational efficiency, and collision probability.

[0004] Genetic algorithms are widely used in path planning due to their flexibility, robustness, and resistance to getting trapped in local optima. However, existing path planning methods based on genetic algorithms only plan critical path points during maneuvers, without considering the time factor. Yet, the time factor has a significant impact on the real-time performance and accuracy of satellite constellation formation path planning, and is a crucial factor that cannot be ignored. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a path planning method for small satellite constellation formation configuration that takes into account the time factor. This method introduces a time variable and comprehensively considers factors such as collision, energy loss, and path selection. It can quickly complete the small satellite constellation formation maneuvering mission. During the maneuver, the path is shorter, the energy loss is less, and it has better stability and convergence. It can significantly improve the real-time performance and accuracy of small satellite constellation formation maneuvering mission.

[0006] The technical solution of this invention is: a path planning method for small satellite constellation configuration that considers time factors, comprising:

[0007] Select satellite S iThe points along the path i = 1, 2, ..., n form a set of positions, which serves as the i-th row of the encoding matrix. The set of positions of the n satellites forms the encoding matrix, which serves as the satellite constellation configuration adjustment path.

[0008] Within the satellite constellation motion region, an initial population containing constellation configuration adjustment paths is randomly generated according to the coding matrix;

[0009] By introducing a time factor, a maneuvering path function is constructed to achieve collision avoidance during the satellite constellation configuration adjustment process. The positions in the encoding matrix are represented by the maneuvering path function that takes the time factor into account.

[0010] Construct a comprehensive fitness function, randomly select individuals using a roulette wheel algorithm based on the comprehensive fitness value of each individual in the population, and perform crossover and mutation on the selected individuals to generate a new generation of population;

[0011] Through multiple iterations, the individual corresponding to the maximum comprehensive fitness value is selected as the optimal path planning choice for the satellite constellation formation.

[0012] Furthermore, the encoding matrix is ​​represented as follows:

[0013]

[0014] For satellite S i The j-th path point in the planned path, j = 1, 2, ... L, is located at... Satellite S i The starting and ending points, The x-axis is the position vector direction from the Earth's center to the center point, and the y-axis is perpendicular to the x-axis and points towards the local horizon from the center point.

[0015] Furthermore, the initial population containing the constellation configuration adjustment path is represented as follows:

[0016]

[0017] Furthermore, the maneuver path function is expressed in Newton interpolation polynomial form as follows:

[0018] f i (t)=f i [t1]+f i [t1,t2](t-t1)+…+f i [t1,t2,…,t L ](t-t1)…(tt L-1 )

[0019] g i (t)=g i [t1]+g i[t1,t2](t-t1)+…+g i [t1,t2,…,t L ](t-t1)…(tt L )

[0020] Where f i (t) represents the constructed x-direction maneuvering path function of satellite Si, g i (t) is the y-direction maneuvering path function of satellite Si, f i [t1,t2,…,t L ] and g i [t1,t2,…,t L ] represents the (L-1)th order difference quotient, t1, t2, ..., t L This represents the time corresponding to L different positions.

[0021] Furthermore, the comprehensive fitness function, which integrates the three factors of no collisions, short path, and low energy loss, is expressed as:

[0022]

[0023] k = 1, 2, ..., m, where m is the number of individuals in the population. m i For satellite S i quality l i w is the length of the satellite's maneuver path. i The weighting function is based on satellite mass. For satellite S p and S q The minimum distance between them, r pq This is the minimum safe zone between satellites in the formation.

[0024] Furthermore, the aforementioned random selection of individuals using the roulette wheel algorithm specifically refers to:

[0025] First, calculate the relative fitness value of each individual in the population. Then, select individuals by comparing the relative fitness value with a randomly generated random number R in the interval [0,1]. The specific relative fitness value is as follows:

[0026]

[0027] If so:

[0028]

[0029] Then select individual I k .

[0030] Furthermore, the crossover is based on two-point crossover, where two parent generations are selected from the population with a crossover probability, and then the selected parent generations are exchanged to produce offspring. Preferably, the crossover probability P1 = 50%.

[0031] Furthermore, the mutation specifically involves: for the selected individual, randomly changing the numerical code of a certain node of the selected individual according to the mutation probability. Preferably, the mutation probability P2 = 2%.

[0032] The advantages of this invention compared to the prior art are:

[0033] (1) The method of the present invention introduces the time factor into the genetic algorithm, uses Newton polynomial interpolation based on the random search path points to realize the construction of the maneuver path function, establishes a comprehensive fitness function based on the collision-free constraint fitness function, the shortest path fitness function, and the fitness function with the least energy loss, and completes the design of the genetic algorithm. It makes full use of the advantages of the genetic algorithm in terms of flexibility, robustness and the fact that the search is not easy to get trapped in local optima. It comprehensively considers the collision, path and energy problems in the satellite constellation maneuver process and can complete the satellite constellation formation maneuver mission well.

[0034] (2) The small satellite constellation formation path planning method proposed in this invention, which takes into account the time factor, has good stability and convergence. Since the time factor in the maneuver process is fully considered, the planned path has high application value in global path offline search. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 A schematic diagram of satellite constellation formation configuration adjustments;

[0037] Figure 3 This is a schematic diagram of the relative reference coordinate system for the small satellite constellation formation of the present invention;

[0038] Figure 4 This is a satellite constellation path diagram planned using a genetic algorithm in an embodiment of the present invention;

[0039] Figure 5 This is a satellite constellation path diagram using Newton's polynomial interpolation in an embodiment of the present invention;

[0040] Figure 6 This is a graph showing the change in fitness values ​​during the iterative process of the genetic algorithm in this embodiment of the invention. Detailed Implementation

[0041] The present invention will now be described in further detail with reference to the accompanying drawings.

[0042] like Figure 1 The diagram shown is an overall flowchart of a small satellite constellation formation path planning method considering time factors according to the present invention, which includes the following steps:

[0043] (1) Establish a relative dynamics model of small satellite constellation formation.

[0044] Assume a satellite formation consists of n small satellites, each tracking a designated center point to maintain the formation's configuration. When configuration adjustments are required, the satellites change their configuration by adjusting their relative positions to the center point. A diagram illustrating satellite constellation configuration adjustments is shown below. Figure 2 .

[0045] For satellite constellation formations, a relative reference coordinate system o-xyz is defined, with the origin o being the center point of the satellite constellation. The x-axis follows the position vector direction from the Earth's center to the center point, the y-axis is perpendicular to the x-axis and points towards the local horizon at the center point, and the z-axis, together with the x and y axes, forms a right-handed coordinate system. The relative reference coordinate system for a small satellite constellation is as follows: Figure 3 As shown.

[0046] According to the CW formula, a motion model of a satellite constellation can be established by knowing only the orbital parameters of the central orbit and the relative initial conditions of each satellite. The relative dynamic model of a small satellite constellation based on the CW formula is as follows:

[0047]

[0048] In the formula ω n Let (x, y, z) be the average angular velocity of the center orbit of the formation, and (x, y, z) be the relative position of the satellites with respect to the center point. Assuming the satellite constellation moves within the same orbital plane, subsequent path planning can be studied within the two-dimensional plane xoy.

[0049] (2) The design uses a real number matrix to implement the encoding method of individuals in the genetic algorithm.

[0050] The genetic algorithm uses real-number matrices to encode individuals, and selects satellite S. i The points along the path i = 1, 2, ..., n form a set of positions, which is the i-th row of the encoding matrix. The set of positions of n satellites forms an individual encoding matrix, which is the satellite constellation configuration adjustment path.

[0051] The initial and adjusted configurations of the satellite constellation are known, that is, the configurations of satellite S... i The starting and ending points are known. Assume the satellite formation configuration adjustment is completed after time T. Divide time T into L-1 segments, and take... Time Satellite S i Location This is the j-th path point in the planned path. Where, location... Satellite S i The starting and ending points of satellite S i Location description The designed encoding method is as follows:

[0052]

[0053] For example, in the simulation, there are n=6 spacecraft in the satellite constellation formation, with initial positions as follows: The final positions are as follows:

[0054] (3) Within the satellite constellation motion region, an initial population containing constellation configuration adjustment paths is randomly generated according to the coding matrix.

[0055] Within the satellite constellation's motion region, m individuals are randomly generated according to the coding matrix. Each individual represents a set of paths for adjusting the satellite constellation configuration, denoted as I. k k = 1, 2, ..., m. The individual coding matrix has n rows, representing the n satellites in the satellite constellation formation. Each row has L position vectors, representing L path points in each path, where the L path points include the starting point. and the end point

[0056] To ensure that the path does not loop during satellite constellation maneuvers, during individual satellite generation, the process is designed to target satellite S. i The L-2 randomly generated path points are arranged in ascending order of their y-coordinates, which is for individual I. k Each line in the text contains:

[0057] The initial population generated is as follows:

[0058]

[0059]

[0060] In the simulation, the population size is m = 200, and the number of path points in the satellite constellation path planning is L = 10.

[0061] (4) Construct path functions to achieve collision avoidance during satellite constellation configuration adjustment.

[0062] To avoid collisions during satellite constellation configuration adjustments, a time factor is introduced to establish a maneuver path function.

[0063] As can be seen from the definition of the encoding matrix, for satellite S i have:

[0064]

[0065]

[0066] In the formula, f i (t) represents the x-direction path function of satellite Si within the constructed xoy plane; g i (t) is the path function in the y-direction.

[0067] To facilitate the updating of the interpolation basis function when path points are added or removed, this invention establishes a path function in the form of a Newton interpolation polynomial using the Newton method.

[0068] For the path function f i (t) The difference quotient table is constructed as shown in Table 1:

[0069] Table 1: Difference Quotient Table

[0070]

[0071] In the table, the definition of the k-th order difference quotient is established according to the definition of Newton interpolation, and we have:

[0072]

[0073] The final encoding function for the x-direction path function obtained based on Newton interpolation is as follows:

[0074] f i (t)=f i [t1]+f i [t1,t2](t-t1)+…+f i [t1,t2,…,t L ](t-t1)…(tt L-1 )

[0075] Similarly, Newton interpolation can be used to perform path function g. i (t) Construct the difference quotient table and obtain:

[0076]

[0077] The final encoding function for the y-direction path function obtained based on Newton interpolation is as follows:

[0078] g i (t)=g i [t1]+g i [t1,t2](t-t1)+…+g i [t1,t2,…,t L ](t-t1)…(tt L )

[0079] Based on the above formula, the previously obtained coding matrix I can be constructed into a coding function matrix.

[0080]

[0081] Here, the encoding matrix I is converted into a function representation; where f i (t) represents x, g i (t) represents y.

[0082] (5) Construct a comprehensive fitness function by considering the three factors of no collisions, short path, and low energy loss:

[0083] A fitness function is established to evaluate the generated individuals. Since satellite constellations need to complete maneuvers without collisions to adjust their configuration, collision-free maneuvers are the most important factor in finding the optimal path.

[0084] Construct a collision-free constraint fitness function:

[0085] For satellite S p S q Based on the constructed path function, the minimum distance between the two can be obtained as:

[0086]

[0087] To facilitate the design of the path planning algorithm, it is assumed that the orbital parameters of each satellite in the satellite constellation are known, and the minimum safe zone between each satellite is simplified to a radius of r. pq A sphere.

[0088] Determine satellite S p S q Did any collision occur during the maneuver?

[0089]

[0090] In the formula, r pq The minimum safe zone between satellites in the formation; sig(l pq ) is the collision function, and its result is 0 or 1, representing collision and no collision respectively.

[0091] The above formula is the collision function between two satellites. For constellation formations, it is:

[0092]

[0093] In the formula, function P represents the collision function between satellites n and n-1 in the satellite formation, and its safe distance is still the minimum safe area r between the satellites in the formation. pq less than r pqThen it is a collision (0), greater than r pq Then it is safe (1).

[0094] Establish a collision-free constraint fitness function:

[0095]

[0096] In the simulation, the safe distance between satellite constellations is r = 10m.

[0097] Construct the fitness function with the shortest path:

[0098] To ensure that the satellite constellation can achieve configuration adjustments with fewer path maneuvers, it is necessary to establish a fitness function with the shortest path.

[0099] For satellite S i Based on the constructed path function, the maneuver path length can be obtained as follows:

[0100]

[0101] In the formula, f i (t), g i (t) represents the path function. Taking its derivative yields the velocity function, and integrating it over time T gives the maneuver path length based on the path function, i.e., the maneuver path of the satellite over time T.

[0102] Because the satellites in a satellite constellation have different masses, the energy lost during maneuvers along the same path also varies. Therefore, a weighting function based on satellite mass is introduced here:

[0103]

[0104] In the formula m i For satellite S i The mass of the satellites is m = 100 kg in the simulation. Therefore, the comprehensive path fitness function for satellite constellation formation maneuvers is:

[0105]

[0106] In the formula l i w is the length of the satellite's maneuver path. i This is a weighting function based on satellite quality. A larger fitness function indicates a longer path.

[0107] Construct the fitness function with minimum energy loss:

[0108] For satellite S i Based on the constructed path function, the energy loss during the maneuver can be obtained as follows:

[0109]

[0110] In the formula, f i (t), g i The second derivative of (t) represents acceleration; mi is the satellite mass; motorized to The required energy loss is the integral along this path.

[0111] The overall energy fitness function for a satellite constellation formation is:

[0112]

[0113] To achieve the integration of the above three fitness functions, a comprehensive comparison is performed on all m individuals in the population.

[0114] For individual I in the population k There is a comprehensive fitness function:

[0115]

[0116] In the formula, the path fitness function, the energy fitness function, and the ratio of all individuals in the population can be used to achieve a comprehensive comparison between the two; and multiplying the comprehensive result by the collision-free fitness function can guarantee the premise of no collision during the maneuver. From the comprehensive fitness function, it can be seen that when the fitness is 0, the path does not satisfy the collision-free constraint. When the fitness is not 0, the larger the fitness, the better the path performance.

[0117] (6) Based on the overall fitness value of each individual in the population, individuals are randomly selected using the roulette wheel algorithm, and the selected individuals are crossovered and mutated to generate a new generation of the population:

[0118] The selection method is based on the roulette wheel algorithm. First, the relative fitness value of each individual in the population is calculated. Then, an individual is selected by comparing a randomly generated number R within the [0,1] interval with its relative fitness value. The specific relative fitness value is as follows:

[0119]

[0120] If so:

[0121]

[0122] Then select individual I k .

[0123] The crossover method is based on two-point crossover, and its purpose is to generate new solutions. Two parents are selected from the population with a certain probability, and then the selected parents are exchanged to produce offspring. This certain probability is called the crossover probability. In genetic algorithms, constant or variable probabilities are often used, or specific values ​​can be selected based on experience. In the simulation, the crossover probability selected based on experience is P1 = 50%.

[0124] The mutation method involves randomly transforming the value of a node on a selected individual according to a certain probability. The simplest method is to change the numerical code of a node, such as changing 0 to 1 or 1 to 0. This process simulates the genetic mutation process in biology, thereby generating new individuals. The probability used in the selection process is the mutation probability. Different algorithms using different mutation probabilities will have varying convergence. In this patent, based on experience, the mutation probability is chosen as P² = 2%.

[0125] (7) Repeat steps (5) and (6) for multiple iterations, and use the individual with the maximum fitness value as the final estimate to complete the optimal path planning and selection for the small satellite constellation formation.

[0126] The algorithm stopped iterating after 1000 generations in the simulation.

[0127] from Figure 4 As can be seen from the algorithm designed in this invention, after 100 iterations, the optimal path point is selected. From... Figure 5 It can be seen that the path curve based on Newton's polynomial interpolation meets the requirements for adjusting the satellite constellation formation configuration. From Figure 6 As can be seen, the genetic algorithm designed in this invention iterated to find the optimal path after about 310 generations. Therefore, the algorithm provided by this invention is suitable for path planning in small satellite constellation configurations, exhibiting excellent stability and convergence. Because it fully considers the time factor during maneuvers, the planned path has high application value in offline global path search.

Claims

1. A path planning method for small satellite constellation configurations that considers time factors, characterized in that... include: Select Satellite The points along the path form a set of locations, which serves as the first position in the encoding matrix. OK, The location sets of individual satellites form a coding matrix, which serves as the path for adjusting the satellite constellation configuration. Within the satellite constellation motion region, an initial population containing constellation configuration adjustment paths is randomly generated according to the coding matrix; By introducing a time factor, a maneuvering path function is constructed to achieve collision avoidance during the satellite constellation configuration adjustment process. The positions in the encoding matrix are represented by the maneuvering path function that takes the time factor into account. Construct a comprehensive fitness function, randomly select individuals using a roulette wheel algorithm based on the comprehensive fitness value of each individual in the population, and perform crossover and mutation on the selected individuals to generate a new generation of population; Through multiple iterations, the individual corresponding to the maximum comprehensive fitness value is selected as the optimal path planning choice for the satellite constellation formation; The encoding matrix is ​​represented as follows: For satellite The first in the planned path Path points, ,Location , Satellites The starting and ending points, ,coordinate The axis is along the direction of the position vector from the Earth's center to the center point. shaft and The axis is perpendicular to the local horizon and points towards the center point. The initial population containing the constellation configuration adjustment path is represented as follows: The maneuvering path function is expressed in Newton interpolation polynomial form as follows: in For the construction of satellites of x Directional maneuver path function, For satellite of y Directional maneuver path function, and Denotes the (L-1)th order difference quotient, This represents the time corresponding to L different positions.

2. The method for planning the formation configuration of a small satellite constellation considering time factors according to claim 1, characterized in that: The comprehensive fitness function integrates three factors: collision-free, short path, and low energy loss, and is expressed as follows: m is the number of individuals in the population. , , For satellite quality , The length of the satellite's maneuver path. The weighting function is based on satellite mass. , , , , , For satellite and The minimum distance between them This is the minimum safe zone between satellites in the formation.

3. The method for planning the formation configuration of small satellite constellations considering time factors according to claim 2, characterized in that: The aforementioned method of randomly selecting individuals using a roulette wheel algorithm specifically refers to: First, calculate the relative fitness value of each individual in the population, based on randomly generated numbers in the interval [0,1]. R Individuals were selected by comparing them with their relative fitness, the specific relative fitness value being: If so: Then select an individual .

4. The method for planning the formation configuration of small satellite constellations considering time factors according to claim 3, characterized in that: The crossover is based on two-point crossover, where two parent generations are selected from the population with crossover probability, and then the selected parent generations are exchanged to produce offspring.

5. The method for planning the formation configuration of small satellite constellations considering time factors according to claim 4, characterized in that: The crossover probability P 1 = 50%.

6. The method for planning the formation configuration of small satellite constellations considering time factors according to claim 3, characterized in that: The mutation refers specifically to: for the selected individual, randomly changing the numerical code of a certain node of the selected individual according to the mutation probability.

7. The method for planning the formation configuration of small satellite constellations considering time factors according to claim 6, characterized in that: The mutation probability P 2 = 2%.

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