CN114815872B - A Constellation Intelligent Autonomous Orbit Control Method for Collision Avoidance - Google Patents

Abstract

The invention discloses a constellation intelligent autonomous orbit control method for collision avoidance, and relates to a constellation intelligent autonomous orbit control method for collision avoidance. The invention aims to solve the problems that the traditional optimal control problem solving method has large calculation amount and is extremely sensitive to an initial value, or the result precision depends on the selection of the shape of the track, and the like. The process is as follows: s1, constructing a controller neural network model based on deep learning: firstly, the method comprises the following steps: solving the optimal track transfer problem by an indirect method, and constructing an optimal control database; II, secondly, the method comprises the following steps: designing a neural network structure, wherein the neural network structure comprises the number of layers of a neural network, the number of nodes of each layer and an activation function; thirdly, the method comprises the following steps: obtaining an optimal controller model of the spacecraft, and generating an optimal control strategy according to the current and expected state information in real time; and S2, constructing the intelligent autonomous controller of the satellite constellation thrust considering collision avoidance based on the neural network model trained in the S1 and the artificial potential function. The invention is used in the field of satellite orbit control.

Description

A Constellation Intelligent Autonomous Orbit Control Method for Collision Avoidance

technical field

The invention belongs to the field of satellite orbit control, and in particular relates to a constellation intelligent autonomous orbit control method for collision avoidance.

Background technique

With the increasing complexity of space missions, the problem of constellation control has gradually become a hot and difficult point in the field of aerospace engineering. Constellation is a carrier that solves space problems in a multi-satellite coordinated manner, including satellite clusters, formations, and constellations. Compared with a single independent satellite system, it has better reliability, mission diversity, and functional scalability. Significant improvement is an important direction for the development of satellite technology in the future.

However, the space environment in which the constellation is located is complex. With the increase in the number of satellites, the possibility of inter-satellite collisions will also increase significantly during the maneuvering process of the satellites. How to integrate maneuvering targets and collision avoidance problems is still a problem. At present, it is a difficult point in the field of aerospace engineering, but fortunately, with the development of artificial intelligence, big data and other theories, the use of deep neural networks and other methods can greatly reduce the computational burden, and realize the optimal control of real-time intelligent autonomous generation on the star For the purpose of high efficiency, it will provide a new design direction for the on-board intelligent autonomous controller with collision avoidance.

At present, there are direct method, indirect method and shape method for traditional optimal control problems. Among them, the direct method directly discretizes the state variables and control variables of the system, but it has a large amount of calculation for complex problems, and the indirect method The method uses the optimal control theory, although it can obtain a solution with high precision, it is extremely sensitive to the initial value. speed, but the result accuracy depends on the choice of orbital shape. In addition, most of the traditional maneuvering processes involving collision avoidance require the ground to calculate the control rate and then inject the planets. This will inevitably face the limitation that the computational complexity will explode with the increase in the number of satellites, and the potential collision hazard caused by the delay of the information on the ground. , therefore, it is necessary to complete a flexible intelligent controller design that can generate optimal control information in real time and realize autonomous collision avoidance.

Contents of the invention

The purpose of the present invention is to solve the problems that the existing traditional optimal control problem solving method has a large amount of calculation, is extremely sensitive to the initial value, or the result accuracy depends on the selection of the track shape, etc., and proposes a collision avoidance method Constellation Intelligent Autonomous Orbit Control Method.

A specific process of a constellation intelligent autonomous orbit control method for collision avoidance is as follows:

S1. Construct the neural network model of the controller based on deep learning; the specific process is:

Step 1: Solve the optimal orbit transfer problem by the indirect method, and construct the optimal control database;

Step 2: Design the neural network structure, including the number of layers of the neural network, the number of nodes in each layer and the activation function;

Step 3: Obtain the optimal controller model of the spacecraft, and realize the real-time generation of the optimal control strategy (u*,α*) according to the current and expected state information (x _c ,m _c ,x _t );

S2. Based on the neural network model and artificial potential function trained in S1, construct an intelligent autonomous controller for satellite constellation thrust considering collision avoidance; the specific process is:

Step 1: Construct a collision avoidance controller using the potential function;

Step 2: Determine whether the current state of the spacecraft meets the state tolerance; if not, perform step 3; if yes, perform step 4;

Step 3: Use the neural network model trained by S1 to control the spacecraft, and perform step 4;

Step 4: Determine in real time whether there is a collision risk in the current state of the spacecraft. If there is a collision risk in the spacecraft, perform step 5; if there is no collision risk in the spacecraft, perform step 6;

Step 5: Use the potential function to perform collision avoidance maneuver control on the spacecraft until the spacecraft no longer has the risk of collision, go to step 6

Step 6: Judge again whether the current state of the spacecraft satisfies the state allowable deviation. If it is satisfied, the control ends. There is a risk of collision, control ends.

Beneficial effects of the present invention:

The invention proposes a neural network-based optimal controller design scheme for spacecraft orbit transfer. In the present invention, the neural network data generated on the ground is used to train the neural network with a well-designed structure, so as to realize the purpose of realizing the real-time intelligence and autonomous generation of the optimal control strategy on the star. In addition, the neural network controller is combined with the potential function , to achieve the purpose of on-board autonomous collision avoidance during constellation maneuvering. The present invention can not only solve the problem of traditional control that needs to be re-planned when disturbances occur, but also avoid the trouble of waiting for an appropriate window due to the ground station uploading instructions to the satellite. Similarly, this controller is also an orbit transfer controller for other deep space missions in the solar system Design problems and constellations and even superstar constellations provide an effective design idea for avoiding interstellar collisions independently.

Description of drawings

Fig. 1 is the optimal controller design flow chart of the spacecraft orbit transfer based on the neural network of the present invention;

Fig. 2 is the working flow diagram of the autonomous maneuvering and collision avoidance controller on the spacecraft star based on the neural network of the present invention;

Fig. 3 a is a schematic diagram of the neural network structure of the optimal controller for the spacecraft orbit transfer based on the neural network 1 of the present invention, wherein, L ⁽⁰⁾ represents the input layer of the neural network, L ⁽¹⁾ represents the subsequent hidden layer, and L ^{(1+ 1)} represents the output layer;

Figure 3b is a schematic diagram of the neural network structure of the optimal controller for spacecraft orbit transfer based on the neural network 2 of the present invention;

Fig. 4 a is the satellite distribution figure after the constellation configuration operation time of the present invention is 0s;

Fig. 4b is a diagram of the distribution of satellites after the running time of the constellation configuration of the present invention is 9.68×10 ⁴ s;

Fig. 4c is a diagram of the distribution of satellites after the running time of the constellation configuration of the present invention is 1.94×10 ⁵ s;

Fig. 4d is a diagram of the distribution of satellites after the running time of the constellation configuration of the present invention is 2.90×10 ⁵ s;

Fig. 4e is a diagram of the distribution of satellites after the running time of the constellation configuration of the present invention is 3.87×10 ⁵ s;

Fig. 4f is a diagram of the distribution of satellites after the running time of the constellation configuration of the present invention is 4.84×10 ⁵ s;

Fig. 5 is an image of the relative distance between spacecraft of the present invention.

Detailed ways

Specific implementation mode one: a constellation intelligent autonomous orbit control method for collision avoidance The specific process is as follows:

The present invention designs an intelligent controller design based on a neural network. This algorithm overcomes the problems of large amount of calculation in the existing traditional methods, directly uses the current state and expected state of the spacecraft as input, and obtains the current optimal control strategy through the fitted neural network, and combines it with the potential function-based collision avoidance Links are combined to realize the intelligent and autonomous controller design on the star with collision avoidance.

The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, and provide a design scheme of autonomous maneuvering and collision avoidance controller on the spacecraft star based on a neural network. In order to achieve the above-mentioned purpose, the technical scheme adopted by the present invention includes the following two parts :

S1. Construct the neural network model of the controller based on deep learning; the specific process is:

Step 1: Solve the optimal orbit transfer problem by the indirect method, and construct the optimal control database;

Step 2: Design the neural network structure, including the number of layers of the neural network, the number of nodes in each layer and the activation function;

Step 3: Obtain the optimal controller model of the spacecraft, and realize the real-time generation of the optimal control strategy (u*,α*) according to the current and expected state information (x _c ,m _c ,x _t );

S2. Based on the neural network model and artificial potential function trained in S1, construct a satellite constellation low-thrust intelligent autonomous controller considering collision avoidance; the specific process is:

Step 1: Construct a collision avoidance controller using the potential function;

Step 2: Determine whether the current state of the spacecraft meets the state tolerance; if not, perform step 3; if yes, perform step 4;

Step 3: Use the neural network model trained by S1 to control the spacecraft (at this time, input the current and expected state information of the neural network model trained by S1, output the optimal control strategy, and control the spacecraft based on the optimal control strategy control), perform step 4;

Step 4: judge in real time whether there is a collision risk in the current state of the spacecraft (Formula 11), if there is a collision risk in the spacecraft, then perform step 5; if there is no collision risk in the spacecraft, then perform step 6;

Step 5: Use the potential function to perform collision-avoidance maneuver control on the spacecraft (Formula 12-18) (use the potential function to perform collision-avoidance maneuver control on the state of the spacecraft based on the optimal control strategy in step 3, and obtain each update control rate), until the spacecraft is no longer at risk of collision, go to step 6;

Step 6: Judge again whether the current state of the spacecraft satisfies the state allowable deviation. If it is satisfied, the control ends. There is a risk of collision, control ends.

Specific embodiment two: the difference between this embodiment and specific embodiment one is that in the first step, the optimal orbit transfer problem is solved by the indirect method, and the optimal control database is constructed;

The specific process is:

Step 11, the dynamic model of the spacecraft is selected as a two-body dynamic model, and the adopted two-body dynamic model can be expressed in the cylindrical coordinate system as:

Among them, D and B are intermediate variables, and the expressions are as follows:

为状态x关于时间的一阶导数；x＝[r,θ,z,v_r,v_θ,v_z]^T，r、θ和z分别是航天器的径向距离、方位角和高度；v_r、v_θ和v_z分别表示r、θ和z关于时间的一阶导数；R为航天器中心到中心天体之间的距离，

T_max为航天器的最大推力，I_sp和g₀分别表示推进器的比冲和地球的平均重力加速度；u为发动机的实际推力与最大推力的比值，u∈[0,1]；α＝[α_r,α_θ,α_z]^T是推力方向，α_r、α_θ、α_z分别为推力方向在径向，主法向和次法向上的分量；m为航天器质量；μ是中心天体的引力常量，对于近地卫星μ＝398600.4415km³/s²；上角标“T”代表矩阵转置；t为时间；in,

is the first derivative of state x with respect to time; x=[r,θ,z,v _r ,v _θ ,v _z ] ^T , r, θ and z are the radial distance, azimuth and height of the spacecraft respectively; v _r , v _θ and v _z represent the first derivatives of r, θ and z with respect to time respectively; R is the distance from the center of the spacecraft to the central celestial body,

T _max is the maximum thrust of the spacecraft, I _sp and g ₀ respectively represent the specific impulse of the propeller and the average acceleration of gravity of the earth; u is the ratio of the actual thrust of the engine to the maximum thrust, u∈[0,1]; α = [α _r ,α _θ ,α _z ] ^T is the thrust direction, α _r , α _θ , and α _z are the components of the thrust direction in the radial direction, the main normal direction and the subnormal direction respectively; m is the mass of the spacecraft; μ is the center The gravitational constant of the celestial body, for the near-earth satellite μ=398600.4415km ³ /s ² ; the superscript "T" stands for matrix transposition; t is time;

Step 1 and 2, the index J of the time-free fuel optimal control problem can be expressed as:

Among them, t _f is the transfer time of the task;

和

The initial state and desired state to obtain the nominal orbit are expressed as

and

Step 13. Based on the initial state and expected state of the nominal orbit, use the indirect method to solve the time-free fuel optimal control problem, and obtain the initial value of the co-state variable and the transition time, expressed as the optimal solution Λ ^* ;

与期望状态

的值：Step 14. Obtain the initial state of a new set of nominal orbits

and desired state

value of:

均为以六根数形式给出的状态量；δx_co，δx_to表示足够小的随机小量；in,

Both are state quantities given in the form of hexagrams; δx _co , δx _to represent small enough random quantities;

的初始值；Step 15. Use the optimal solution Λ ^* as the optimal solution in the new state

initial value;

与期望状态

的值，利用间接法对时间自由的燃料最优控制问题进行求解，得到新的协态变量初值和转移时间，表示为新状态下最优解

Initial state based on the new nominal orbit

and desired state

The value of , using the indirect method to solve the time-free fuel optimal control problem, get the initial value of the new costate variable and transition time, expressed as the optimal solution in the new state

Step 16. Repeat steps 14 and 15 to obtain multiple optimal solutions, which correspond to multiple optimal trajectories;

When δx _co and δx _to are small enough, the shooting method for solving the indirect method converges quickly;

Establish a neural network database, sample each optimal trajectory obtained at M time discrete points, and obtain the current and expected state-optimal control action pair (x _c , m _c , x _t , U*) by sampling;

Multiple sets of current and expected state-optimal control action pairs (x _c , m _c , x _t , U*) are obtained by sampling multiple optimal trajectories, and an optimal control database is established;

Where x _c , m _c are the current state of the spacecraft, x _t is the desired state, and U* is the optimal control.

Other steps and parameters are the same as those in Embodiment 1.

Specific embodiment three: the difference between this embodiment and specific embodiment one or two is that the neural network structure is designed in the step two, including the number of layers of the neural network, the number of nodes and the activation function of each layer;

The specific process is:

The neural network model of the controller is a feedforward fully connected neural network, including neural network 1 model and neural network 2 model;

The inputs of the neural network 1 and 2 models of the controller are both the current state and the desired state of the spacecraft [x _c ; m _c ; x _t ], and the output of the neural network 1 model of the controller is the spacecraft thrust amplitude u∈[0 ,1], the output of the neural network 2 model is the radial thrust direction angle and the subnormal thrust direction angle [θ _r ,θ _z ] ^T , where θ _r ∈[-π,π], θ _z ∈[-π /2,π/2] have:

Neural network 1 sequentially includes an input layer, 3 hidden layers, and an output layer. Each hidden layer contains 128 neurons, and the Sigmoid function is selected as the activation function of the output layer, and ReLU is selected as the activation function in the hidden layer; The neural network 2 sequentially includes an input layer, 9 hidden layers, and an output layer. Each hidden layer contains 128 neurons. The Tanh function is selected as the activation function of the output layer, and ReLU is selected as the activation function in the hidden layer;

The neural network is parameterized by weight ω and bias b, using the mean square error (MSE) between the training data and the network prediction results as the loss function:

为神经网络期望输出，|| ||表示向量的二范数；Among them, Net represents the neural network that needs to be trained, and N is the total number of samples used for training. X _i is the input data,

is the expected output of the neural network, || || represents the two-norm of the vector;

The Adam optimization algorithm is used to train the parameters in the neural network, and the learning rate is set to 0.0001.

Other steps and parameters are the same as those in Embodiment 1 or Embodiment 2.

Specific Embodiment 4: The difference between this embodiment and one of specific embodiments 1 to 3 is that the optimal controller model of the spacecraft is obtained in the step 3, and the real-time basis of the current and expected state information (x _c , m _c , x _t ) to generate the optimal control strategy (u*,α*); the specific process is:

Extract the data in the database as the training set, input the training set into the constructed controller neural network model 1, 2, train the constructed controller neural network model, obtain two trained neural network models, and obtain the optimal control of the spacecraft device model;

为：Input the current and expected state information [x _c ; m _c ; x _t ] into the trained neural network models 1 and 2, the output of the trained neural network model 1 is u _net , and the output of the trained neural network model 2 is [θ _r ,θ _z ] ^T , the thrust direction vector received by the spacecraft at this time

for:

分别表示神经网络计算得到的推力方向在径向，主法向和次法向上的分量，因此最优控制策略(u*,α*)为：In the formula,

represent the components of the thrust direction calculated by the neural network in the radial direction, the main normal direction and the subnormal direction respectively, so the optimal control strategy (u*,α*) is:

Other steps and parameters are the same as those in Embodiments 1 to 3.

Specific embodiment five: the difference between this embodiment and one of specific embodiments one to four is that in the step 1, a potential function is used to construct a collision avoidance controller; the specific process is:

Setting the safety constraints of the spacecraft is expressed as:

||r _min ||＞L (10)

Where r _min represents the shortest distance between the two spacecraft, and L represents the minimum distance allowed between the spacecraft;

The repulsion potential of the closest spacecraft to the spacecraft is:

表示对函数求取梯度，当两航天器之间最近距离大于d₀时，认为两航天器间无碰撞的风险，当两航天器之间最近距离小于等于d₀时，认为两航天器间有碰撞的风险，F_o(x_i,x_j)为最终斥力场对航天器产生的斥力幅值；Among them, U _o (xi _, x _j ) is the repulsive force potential of the spacecraft j closest to the spacecraft i suffered by the spacecraft i, x _i , x _j are the states of the two spacecraft i and j, and d ₀ is the repulsive force Field radius, k is the repulsion gain coefficient;

means to calculate the gradient of the function, when the shortest distance between the two spacecraft is greater than d ₀ , it is considered that there is no risk of collision between the two spacecraft, and when the shortest distance between the two spacecraft is less than or equal to d ₀ , it is considered that there is a risk of collision between the two spacecraft The risk of collision, F _o ( _xi , x _j ) is the magnitude of the repulsive force generated by the final repulsive field on the spacecraft;

Suppose the direction of tangential acceleration received by spacecraft i is α _ui , therefore, it can be expressed as:

Where a _i represents the semi-major axis of the i-th spacecraft, a _j represents the semi-major axis of the spacecraft closest to the i-th spacecraft, and da ₀ is to prevent thrust direction oscillation caused by too small semi-major axis difference;

In order to transfer the tangential acceleration direction vector to the cylindrical coordinate system, the direction vector is first transposed into the radial direction S, the transverse direction T and the normal direction W of the orbital surface, and the intermediate variables A and B are expressed as follows:

Have:

S＝Aα _ui

T = Bα _ui (15)

W=0

表示真近点角；where e represents the orbital eccentricity,

Indicates the true anomaly angle;

Therefore, to transfer [S,T,W] ^T to the geocentric inertial coordinate system, there are:

和

分别表示绕x,z轴将矢量旋转角

的旋转矩阵；Ω表示升交点赤经，i表示轨道倾角，ω表示近地点幅角；

分别代表-Ω、-i或

In the formula, a _x , a _y , a _z represent the acceleration components of the spacecraft in the earth-centered inertial coordinate system;

and

Respectively represent the rotation angle of the vector around the x and z axes

The rotation matrix of ; Ω represents the right ascension of the ascending node, i represents the orbital inclination, and ω represents the argument of perigee;

represent -Ω, -i or

By means of the acceleration direction vector in the earth-centered inertial coordinate system, the acceleration direction vector α _o-rθz =[α _r ,α _θ ,α _z ] ^T in the cylindrical coordinate system can be obtained as follows:

α _r ＝a _x cosθ+a _y sinθ

α _θ ＝-a _x sinθ+a _y cosθ (17)

α _z =a _z

In the formula, α _r , α _θ , and α _z are the components of the thrust direction in the radial direction, the main normal direction and the subnormal direction respectively

The acceleration obtained by this method is summed with the acceleration obtained by the neural network controller, and the control rate of the spacecraft that needs to avoid collision can be obtained, namely:

Other steps and parameters are the same as one of the specific embodiments 1 to 5.

Specific Embodiment 6: The difference between this embodiment and one of Specific Embodiments 1 to 5 is that the allowable deviation of the state of the spacecraft in the steps 2 to 6 is given in the form of cylindrical coordinates, and the specific representation of the state deviation of the spacecraft as follows:

与期望状态

的偏差量，rem(p,q)表示p除以q所得的余数；In the formula, |Δr|, |Δθ|, |Δz|, |Δv _r |, |Δv _θ | and |Δv _z | represent the current state

and desired state

The amount of deviation, rem(p,q) represents the remainder obtained by dividing p by q;

与停止极限

的形式给出；If the current state of the spacecraft is less than or equal to the allowable deviation, it is still possible to deviate from the expected state of the spacecraft due to collision avoidance maneuvers.

with stop limit

given in the form;

When all the state deviations of the spacecraft are less than or equal to the stop limit, it is considered that the state allowable deviation is satisfied; when any state deviation of the spacecraft is greater than the start limit, it is considered that the state allowable deviation is no longer satisfied;

The start limits are all greater than the stop limits.

Other steps and parameters are the same as one of the specific embodiments 1 to 5.

Adopt the following examples to verify the beneficial effects of the present invention:

Embodiment one:

均为0，限制任务的最大时间为4.841×10⁵s，将卫星按照其初始相位

由小到大编号为1～100，从中随机选出五颗卫星重新排布相位，选择的卫星编号为[1,23,58,75,88]，并通过轨道机动将其重新排布为[58,88,1,23,75]。Select an orbital plane in a large constellation, assuming that 100 satellites are evenly distributed in phase of this orbital plane. Each satellite has a mass of 270kg, uses electric propulsion, specific impulse _Isp = 3000s, and can provide the maximum thrust _Tmax = 100mN. The common initial semi-major axis of the spacecraft is a = 7378km, the eccentricity e = 0.1, and the common orbital inclination i, right ascension of ascending node (RAAN)Ω, argument of perigee ω and true anomaly

are all 0, limit the maximum time of the mission to 4.841×10 ⁵ s, set the satellite according to its initial phase

Numbers from small to large are 1 to 100, from which five satellites are randomly selected to rearrange their phases. The selected satellites are numbered [1, 23, 58, 75, 88], and are rearranged as [ 58,88,1,23,75].

Table 1 Artificial potential function parameters and control limits

The satellite position changes during maneuvering are shown in Figures 4a, 4b, 4c, 4d, 4e, and 4f, where the number 12345 corresponds to the selected satellite number [1, 23, 58, 75, 88]:

After 4.841×10 ⁵ s satellites realized the configuration reconstruction, the change of the minimum relative distance between the spacecraft is shown in Figure 5: the minimum distance between the spacecraft is 10.12km after the execution of the control avoidance link, which is greater than the given 10km boundary , without potential function collision avoidance control, the fuel required for the spacecraft to complete the above process is 0.08kg-0.31kg, the total fuel consumption is 1.1863kg and the minimum distance between spacecraft is 8.28km, which is less than the given collision boundary of 10km .

At the same time, the fuel consumption of spacecraft maneuvering with collision avoidance is 0.09kg-0.32kg, and the total fuel consumption is 1.2917kg. It can be seen that the artificial intelligence controller based on the potential function has reasonable energy consumption, and at the same time proves the effectiveness of the collision avoidance algorithm.

Moreover, compared with the indirect method, which takes about 2000s to calculate on average, the neural network only needs about 100s to calculate a complete trajectory, and the average neural network controller only needs 0.0095s to calculate the control amount once. It also shows sufficient advantages in computing time.

The present invention can also have other various embodiments, without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all Should belong to the scope of protection of the appended claims of the present invention.

Claims (4)

1. A constellation intelligent autonomous orbit control method aiming at collision avoidance is characterized by comprising the following steps: the method comprises the following specific processes:

s1, constructing a controller neural network model based on deep learning; the specific process is as follows:

the method comprises the following steps: solving the optimal track transfer problem by an indirect method, and constructing an optimal control database;

the specific process is as follows:

step one, selecting a dynamic model of the spacecraft as a two-body dynamic model, and expressing the adopted two-body dynamic model in a cylindrical coordinate system as follows:

wherein D and B are intermediate variables, and the expression is as follows:

wherein,

is the first derivative of state x with respect to time; x = [ r, theta, z, v = _r ,v _θ ,v _z ] ^T R, θ and z are the radial distance, azimuth and altitude of the spacecraft, respectively; v. of _r 、v _θ And v _z Representing the first derivatives of r, θ and z with respect to time, respectively; r is the distance from the center of the spacecraft to the central celestial body,

T _max maximum thrust of the spacecraft, I _sp And g ₀ Respectively representing the specific impulse of the propeller and the average gravity acceleration of the earth; u is the ratio of the actual thrust to the maximum thrust of the engine, and u belongs to [0,1 ]]；α＝[α _r ,α _θ ,α _z ] ^T Is the direction of thrust, α _r 、α _θ 、α _z The components of the thrust direction in the radial direction, the primary normal direction and the secondary normal direction are respectively; m is the spacecraft mass; mu is the gravitational force of the central celestial bodyAmount, μ =398600.4415km for a near earth satellite ³ /s ² (ii) a The superscript "T" represents the matrix transposition; t is time;

the second step, time-free index J of the fuel optimal control problem is expressed as:

wherein, t _f Is the transfer time of the task;

the initial state and the expected state of the nominal track are respectively represented as

And

step three, solving the index J of the time-free fuel optimal control problem by using an indirect method based on the initial state and the expected state of the nominal orbit to obtain the initial value of the co-modal variable and the transfer time, which are expressed as the optimal solution Lambda ^* ；

Step one and four, acquiring the initial state of a group of new nominal tracks

And the expected state

The value of (c):

wherein, δ x _co ，δx _to Represents a sufficiently small random quantity;

step one or five, the optimal solution lambda is obtained ^* As an optimal solution for solving the new state

An initial value of (1);

initial state based on new nominal track

And the expected state

The time-free fuel optimal control problem J is solved by using an indirect method to obtain a new initial value and transfer time of the co-state variables, which are expressed as an optimal solution in a new state

Step six, repeating the step four and the step five to obtain a plurality of optimal solutions, wherein the optimal solutions correspond to a plurality of optimal tracks;

sampling each obtained optimal track in M time discrete points to obtain a current and expected state-optimal control brake pair (x) _c ,m _c ,x _t ,U*)；

Obtaining a plurality of groups of current and expected state-optimal control brake pairs (x) by sampling a plurality of optimal tracks _c ,m _c ,x _t U), building an optimal control database;

wherein x is _c ,m _c Is the current state of the spacecraft, x _t In the expected state, U is the optimal control;

step two: designing a neural network structure, wherein the neural network structure comprises the number of layers of a neural network, the number of nodes of each layer and an activation function; the specific process is as follows:

the neural network model of the controller is a feedforward fully-connected neural network and comprises a neural network 1 model and a neural network 2 model;

the inputs of the neural network 1 and 2 models of the controller are the current state and the expected state [ x ] of the spacecraft _c ；m _c ；x _t ]The output of the neural network 1 model of the controller is the thrust amplitude u E [0,1 ] of the spacecraft]Neural netThe output of the collateral 2 model is a radial thrust direction angle and a sub-normal thrust direction angle [ theta ] _r ,θ _z ] ^T Wherein, θ _r ∈[-π,π]，θ _z ∈[-π/2,π/2]Comprises the following steps:

the neural network 1 sequentially comprises an input layer, a 3-layer hidden layer and an output layer, wherein each hidden layer comprises 128 neurons, a Sigmoid function is selected as an activation function of the output layer, and a ReLU is selected as an activation function in the hidden layer;

the neural network 2 sequentially comprises an input layer, 9 hidden layers and an output layer, wherein each hidden layer comprises 128 neurons, a Tanh function is selected as an activation function of the output layer, and a ReLU is selected as an activation function in the hidden layer;

the neural network is parameterized by a weight omega and an offset b, and the mean square error between training data and a network prediction result is taken as a loss function:

where Net represents the neural network that needs to be trained, N is the total number of samples used for training, X _i In order to input the data, the data is,

for the neural network to expect output, | | | | represents a two-norm of the vector;

training parameters in the neural network by using an Adam optimization algorithm, and setting the learning rate to be 0.0001;

step three: obtaining an optimal controller model of the spacecraft to realize real-time operation according to the current and expected state information (x) _c ,m _c ,x _t ) Generating an optimal control strategy (u, a); the specific process is as follows:

extracting data in a database as a training set, inputting the training set into the constructed controller neural network models 1 and 2, and training the constructed controller neural network models to obtain two trained neural network models and obtain an optimal spacecraft controller model;

associating current and expected state information [ x ] _c ；m _c ；x _t ]Inputting the trained neural network models 1 and 2, and outputting the trained neural network model 1 as u _net The output of the trained neural network model 2 is [ theta ] _r ,θ _z ] ^T Thrust direction vector to which the spacecraft is subjected at the moment

Comprises the following steps:

in the formula,

the components of the thrust direction calculated by the neural network in the radial direction, the main normal direction and the secondary normal direction are respectively represented, so that the optimal control strategy (u, α) is as follows:

s2, constructing a satellite constellation thrust intelligent autonomous controller considering collision avoidance based on the neural network model trained in the S1 and the artificial potential function; the specific process is as follows:

step 1: constructing a collision avoidance controller by using a potential function;

and 2, step: judging whether the current state of the spacecraft meets the state allowable deviation or not; if not, executing the step 3; if yes, executing step 4;

and step 3: controlling the spacecraft by using the neural network model trained in the S1, and executing the step 4;

and 4, step 4: judging whether the current state of the spacecraft has collision risks or not in real time, and if the current state of the spacecraft has collision risks, executing the step 5; if the spacecraft has no collision risk, executing step 6;

and 5: utilizing the potential function to carry out collision avoidance maneuvering control on the spacecraft until the spacecraft does not have collision risks, and executing the step 6;

and 6: and judging whether the current state of the spacecraft meets the state allowable deviation or not again, if so, ending the control, otherwise, returning to the step 2, repeating the step 2 to the step 6 until all the current states of the spacecraft meet the state allowable deviation and no collision risk exists, and ending the control.

2. The intelligent constellation autonomous trajectory control method for collision avoidance according to claim 1, characterized in that: the optimal controller model of the spacecraft is obtained in the third step, and the current and expected state information (x) is obtained in real time _c ,m _c ,x _t ) Generating an optimal control strategy (u, α); the specific process is as follows:

extracting data in a database as a training set, inputting the training set into the constructed controller neural network models 1 and 2, and training the constructed controller neural network models to obtain two trained neural network models and obtain an optimal spacecraft controller model;

comparing current and expected state information [ x ] _c ；m _c ；x _t ]Inputting the trained neural network models 1 and 2, and outputting the trained neural network model 1 as u _net The output of the trained neural network model 2 is [ theta ] _r ,θ _z ] ^T Thrust direction vector to which the spacecraft is subjected at the moment

Comprises the following steps:

in the formula,

the components of the thrust direction calculated by the neural network in the radial direction, the main normal direction and the secondary normal direction are respectively represented, so that the optimal control strategy (u, α) is as follows:

3. the intelligent constellation autonomous trajectory control method for collision avoidance according to claim 2, characterized in that: in the step 1, a collision avoidance controller is constructed by using a potential function; the specific process is as follows:

setting the safety constraints of a spacecraft is expressed as:

||r _min ||＞L (10)

wherein r is _min The minimum distance between two spacecrafts is represented, and L represents the minimum distance allowed between the spacecrafts;

the repulsion force of a spacecraft closest to the spacecraft is as follows:

wherein, U _o (x _i ,x _j ) Is the repulsive force, x, of a spacecraft j closest to the spacecraft i _i ,x _j Is the state of the i, j two spacecrafts, d ₀ Is the repulsive force field radius, and k is the repulsive force gain coefficient;

representing the gradient of the function, when the closest distance between two spacecrafts is greater than d ₀ When the two spacecrafts are in use, the risk of collision is considered to be avoided,when the closest distance between the two spacecrafts is less than or equal to d ₀ When there is a risk of collision between two spacecraft, F _o (x _i ,x _j ) The amplitude of the repulsion force generated by the final repulsion field to the spacecraft;

assuming that the direction of the tangential acceleration experienced by the spacecraft i is alpha _ui Thus, it can be expressed as:

wherein a is _i Denotes the semi-major axis of the ith spacecraft, a _j Denotes the semi-major axis, da, of the spacecraft closest to the ith spacecraft ₀ To prevent the thrust direction oscillation generated by the over-small difference of the semi-major axes;

in order to transfer the tangential acceleration direction vector to the cylindrical coordinate system, firstly, the direction vector is transposed to the radial direction S, and in the transverse direction T and the orbital plane normal direction W, the intermediate variables A and B are expressed as follows:

comprises the following steps:

wherein e represents the orbital eccentricity and the orbital eccentricity,

representing true proximal angles;

thus, will [ S, T, W] ^T Transfer to the geocentric inertial frame, with:

in the formula, a _x 、a _y 、a _z Representing the acceleration component of the spacecraft in a geocentric inertial coordinate system;

and

representing the angle of rotation of a vector about the x, z axes, respectively

The rotation matrix of (a); omega represents the ascension of the intersection point, i represents the track inclination angle, and omega represents the argument of the perigee;

respectively represent-omega, -i or

Obtaining the acceleration direction vector alpha under the cylindrical coordinate system by the acceleration direction vector under the earth center inertia coordinate system _o-rθz ＝[α _r ,α _θ ,α _z ] ^T The following were used:

in the formula, alpha _r 、α _θ 、α _z Components of thrust direction in radial direction, primary normal direction and secondary normal direction, respectively

The acceleration obtained by the method is summed with the acceleration obtained by the neural network controller, and the control rate of the collision avoidance spacecraft can be obtained, namely:

4. the intelligent constellation autonomous trajectory control method for collision avoidance according to claim 3, characterized in that: the state allowable deviation of the spacecraft in the steps 2 to 6 is given in the form of cylindrical coordinates, and the state deviation of the spacecraft is specifically expressed in the following manner:

wherein, | Δ r |, | Δ θ |, | Δ z |, | Δ v |, etc _r |、|Δv _θ I and | Δ v _z Respectively representing the current state

And the expected state

Rem (p, q) represents the remainder of dividing p by q;

biasing the state allowed to start to limit

And a stop limit

The form of (b) is given; when all state deviations of the spacecraft are smaller than or equal to the stopping limit, considering that the state allowable deviation is met, and when any state deviation of the spacecraft is larger than the starting limit, considering that the state allowable deviation is not met any more;

the start limits are each greater than the stop limits.

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