CN114815872A - Constellation intelligent autonomous orbit control method for collision avoidance - Google Patents
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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: 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 S1 and the artificial potential function. The invention is used in the field of satellite orbit control.
Description
Technical Field
The invention belongs to the field of satellite orbit control, and particularly relates to a constellation intelligent autonomous orbit control method aiming at collision avoidance.
Background
With the increasing complexity of space tasks, the problem of constellation control gradually becomes a hotspot and difficulty in the field of aerospace engineering. The constellation is a carrier for solving space problems in a multi-satellite cooperative mode including satellite clustering, formation and constellation, and compared with a single independent satellite system, the reliability, task diversity, function expandability and other aspects are remarkably improved, so that the method is an important direction for future satellite technology development.
However, the space environment of the constellation is complex, and as the number of satellites increases, the probability of inter-satellite collision of the satellites in the maneuvering process also increases greatly, and how to better integrate maneuvering targets and collision avoidance problems still is a difficult point in the field of current aerospace engineering.
At present, the traditional optimal control problem solving method includes a direct method, an indirect method and a shape method, wherein the direct method directly discretizes state variables and control variables of a system, but the computation amount of the direct method for complex problems is large, the indirect method utilizes an optimal control theory, although a solution with high precision can be obtained, the indirect method is extremely sensitive to an initial value, the shape method is a method for reversely deducing a spacecraft control strategy by estimating a small-thrust-transfer orbit, and although the calculation speed is high, the result precision depends on the selection of the orbit shape. In addition, the traditional maneuvering process including collision avoidance mostly needs to calculate the control rate on the ground and then annotate planets, so that the limitation that the calculation complexity increases along with the increase of the number of the satellites and the potential collision danger caused by delay generated by annotating information on the ground inevitably face, and therefore, the design of an intelligent controller which is flexible, can generate optimal control information in real time and can realize autonomous collision avoidance is needed to be completed.
Disclosure of Invention
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 accuracy of a result depends on the selection of an orbit shape and the like, and provides an intelligent autonomous orbit control method for a constellation aiming at collision avoidance.
A constellation intelligent autonomous orbit control method for avoiding collision specifically comprises the following 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;
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;
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, α);
s2, constructing a satellite constellation thrust intelligent autonomous controller considering collision avoidance based on the neural network model trained in S1 and the artificial potential function; the specific process is as follows:
step 1: constructing a collision avoidance controller by using a potential function;
step 2: 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 risk or not in real time, and if so, 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 risk, and executing step 6
Step 6: and judging whether the current state of the spacecraft meets the state allowable deviation again, if so, finishing the control, if not, 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 finishing the control.
The invention has the beneficial effects that:
the invention provides a design scheme of an optimal spacecraft orbit transfer controller based on a neural network. In the invention, the neural network with a designed structure is trained by utilizing the neural network data generated on the ground so as to realize the purpose of generating optimal control on the satellite intelligently and autonomously, and in addition, the neural network controller is combined with a potential function so as to realize the purpose of avoiding the autonomous collision on the satellite in the constellation maneuvering process. The invention not only can solve the problem that the traditional control needs to be re-planned when disturbance occurs, but also can avoid the trouble that a ground station uploads an instruction to a satellite to wait for a proper window, and the controller also provides an effective design idea for the design problem of the orbit transfer controller of other deep space tasks in the solar system and the problem of autonomous avoidance of inter-satellite collision of a constellation and even a giant constellation.
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FIG. 1 is a flow chart of the design of an optimal controller for spacecraft orbit transfer based on a neural network according to the present invention;
FIG. 2 is a flow chart of the operation of the autonomous maneuvering and collision avoidance controller on the spacecraft based on the neural network of the invention;
FIG. 3a is a schematic diagram of the neural network structure of the spacecraft orbit transfer optimal controller based on the neural network 1 of the present invention, wherein L (0) Representing the input layer of a neural network, L (l) Representing the subsequent hidden layer, L (l+1) Representing an output layer;
FIG. 3b is a schematic diagram of the neural network structure of the spacecraft orbit transfer optimal controller based on the neural network 2 according to the present invention;
FIG. 4a is a diagram of satellite distribution after the time of operation of the constellation configuration of the present invention is 0 s;
FIG. 4b shows the constellation configuration of the present invention having an operating time of 9.68X 10 4 s back satellite distribution chart;
FIG. 4c shows the constellation configuration of the present invention having a runtime of 1.94X 10 5 s back satellite distribution chart;
FIG. 4d shows the constellation configuration of the present invention having a runtime of 2.90X 10 5 s rear satellite scoreA cloth situation diagram;
FIG. 4e shows the constellation configuration of the present invention having a runtime of 3.87 × 10 5 s back satellite distribution chart;
FIG. 4f shows the constellation configuration of the present invention having a runtime of 4.84X 10 5 s back satellite distribution chart;
fig. 5 is a relative distance image between spacecrafts according to the present invention.
Detailed Description
The first embodiment is as follows: a constellation intelligent autonomous orbit control method for avoiding collision specifically comprises the following processes:
the invention designs an intelligent controller design based on a neural network. The algorithm overcomes the problems of large calculation amount and the like of the traditional method, the current state and the expected state of the spacecraft are directly used as input quantities, the current optimal control strategy is obtained through a fitted neural network, and the algorithm is combined with a collision avoidance link based on a potential function to realize the design of the intelligent autonomous controller on the satellite with collision avoidance.
Aiming at the defects of the prior art, the invention provides a design scheme of a spacecraft on-satellite autonomous maneuvering and collision avoidance controller based on a neural network, and in order to achieve the purpose, the technical scheme adopted by the invention comprises the following two parts:
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;
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;
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, α);
s2, constructing a satellite constellation low-thrust intelligent autonomous controller considering collision avoidance based on the neural network model trained in S1 and the artificial potential function; the specific process is as follows:
step 1: constructing a collision avoidance controller by using a potential function;
step 2: 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 (inputting the current and expected state information into the neural network model trained in the S1, outputting an optimal control strategy, and controlling the spacecraft based on the optimal control strategy), and executing the step 4;
and 4, step 4: judging whether the current state of the spacecraft has collision risk or not in real time (formula 11), and if so, executing the step 5; if the spacecraft has no collision risk, executing step 6;
and 5: performing collision avoidance maneuver control (formula 12-18) on the spacecraft by using the potential function (performing collision avoidance maneuver control on the state and the like of the spacecraft controlled based on the optimal control strategy in the step 3 by using the potential function to obtain the control rate of each update) until the spacecraft does not have a collision risk, and executing the step 6;
step 6: and judging whether the current state of the spacecraft meets the state allowable deviation again, if so, finishing the control, if not, 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 finishing the control.
The second embodiment is as follows: the first embodiment is different from the first embodiment in that the optimal orbit transfer problem is solved through an indirect method in the first step, and an optimal control database is constructed;
the specific process is as follows:
step one, selecting a dynamic model of the spacecraft as a two-body dynamic model, wherein the adopted two-body dynamic model can be expressed as follows in a cylindrical coordinate system:
wherein D, B is an intermediate variable, 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 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 constant of the central celestial body, and for a near-earth satellite, mu is 398600.4415km 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 can be expressed as:
wherein, t f Is the transfer time of the task;
the initial state and the expected state of the acquisition nominal track are respectively represented as
And
step three, solving 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 initial values and transfer time of the covariates, which are expressed as the optimal solution lambda * ；
Step one, acquiring a group of new nominal orbit initial states
And the expected state
The value of (c):
wherein,
are state quantities given in the form of six numbers; deltax co ，δx to Represents a sufficiently small random quantum;
step one or five, the optimal solution Λ 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 is solved by an indirect method to obtain a new initial value and transfer time of the covariate variable, 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;
when δ x co ，δx to When the time is small enough, the target practice of solving the indirect method is converged quickly;
establishing a neural network database, sampling each obtained optimal track in M time discrete points, and sampling 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 c ,m c Is the current state of the spacecraft, x t U is the optimal control for the desired state.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the second step is different from the first or second specific embodiment in that a neural network structure is designed, including the number of layers of the 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]The output of the neural network 2 model is the radial thrust direction angle and the sub-normal thrust direction angle [ theta ] r ,θ z ] T Wherein, theta 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 ω and an offset b, and a Mean Square Error (MSE) between training data and a network prediction result is used 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, it is proposed that,
for the neural network to expect output, | | | | represents a two-norm of the vector;
parameters in the neural network are trained by using an Adam optimization algorithm, and the learning rate is set to be 0.0001.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between the first embodiment and the third embodiment is that the optimal controller model of the spacecraft is obtained in the third stepNow based on the current and expected state information (x) 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, 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 primary normal direction and the secondary normal direction are respectively represented, so that the optimal control strategy (u, alpha) is as follows:
other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the present embodiment is different from one of the first to fourth embodiments in that the collision avoidance controller is constructed by using a potential function in step 1; the specific process is as follows:
setting the safety constraints of a spacecraft is expressed as:
||r min ||＞L (10)
wherein r is min Representing the nearest distance between two spacecrafts, and L representing the minimum distance allowed between the spacecrafts;
the repulsion potential of a spacecraft to its nearest neighbor is:
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 distance between two spacecrafts is less than or equal to d, the two spacecrafts are considered to have no collision risk 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:
S＝Aα ui
T＝Bα ui (15)
W＝0
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
By means of the acceleration direction vector under the earth center inertia coordinate system, a cylindrical coordinate system can be obtainedLower acceleration direction vector alpha o-rθz ＝[α r ,α θ ,α z ] T The following were used:
α r ＝a x cosθ+a y sinθ
α θ ＝-a x sinθ+a y cosθ (17)
α z ＝a z
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:
other steps and parameters are the same as those in one of the first to fifth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is 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 as follows:
wherein, | Δ r |, | Δ θ |, | Δ z |, | Δ v |, and 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;
if the current state of the spacecraft is less than or equal to the allowable deviation, the spacecraft still can be in a state ofCan avoid the maneuver deviating from the expected state of the spacecraft due to collision, and at the moment, in order to avoid the frequent switch state switching of the controller, the state is allowed to deviate to start the limit
And a stop limit
The form of (1) 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.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
an orbital plane in a large constellation is selected, assuming that the phases of the orbital plane are uniformly distributed among 100 satellites. Each satellite has a mass of 270kg, and adopts an electric propeller and a specific impulse I sp 3000s, the maximum thrust T that can be provided max 100mN, an initial semi-major axis common to the spacecraft a 7378km, an eccentricity e 0.1, and a common orbit inclination i, a ascent crossing ascension (RAAN) omega, a near-location argument omega and a true near-point angle
All are 0, the maximum time of the limiting task is 4.841 multiplied by 10 5 s, the satellite is adjusted according to its initial phase
The numbers from small to large are 1-100, five satellites are randomly selected from the numbers to rearrange the phases, and the numbers of the selected satellites are [1,23,58,75 and 88]]And rearranged to [58,88,1,23,75 ] by orbital maneuver]。
TABLE 1 Artificial potential function parameters and control limits
The satellite position change during the maneuver is shown in fig. 4a, 4b, 4c, 4d, 4e, 4f, where the number 12345 corresponds to the selected satellite number [1,23,58,75,88 ]:
passing through 4.841X 10 5 The s satellite realizes the configuration reconstruction, and the minimum relative distance change between the spacecrafts is shown in figure 5: and after the control evasion link is executed, the minimum distance between the spacecrafts is 10.12km which is larger than a given 10km boundary, and under the condition that potential function collision evasion control is not carried out, the total fuel consumption of 0.08kg-0.31kg of fuel required by the spacecrafts for completing the process is 1.1863kg, and the minimum distance between the spacecrafts is 8.28km which is smaller than the given 10km collision boundary.
Meanwhile, the fuel consumption of the spacecraft maneuver containing collision avoidance is 0.09kg-0.32kg, and the total fuel consumption is 1.2917 kg. It can be seen that the artificial intelligence controller based on the potential function has reasonable energy consumption, and meanwhile, the effectiveness of the collision avoidance algorithm is proved.
And compared with an indirect method of which the average duration needs about 2000s of calculation time, the method has the advantages that the calculation of a complete track by the neural network is only about 100s, and the control quantity of the average neural network controller is only 0.0095s every time the controller calculates. It also represents a sufficient advantage in terms of computation time.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (6)
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;
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;
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, α);
s2, constructing a satellite constellation thrust intelligent autonomous controller considering collision avoidance based on the neural network model trained in S1 and the artificial potential function; the specific process is as follows:
step 1: constructing a collision avoidance controller by using a potential function;
step 2: 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 risk or not in real time, and if so, 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;
step 6: and judging whether the current state of the spacecraft meets the state allowable deviation again, if so, finishing the control, if not, 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 finishing the control.
2. The intelligent constellation autonomous trajectory control method for collision avoidance according to claim 1, characterized in that: in the first step, an optimal track transfer problem is solved through an indirect method, and an optimal control database is constructed;
the specific process is as follows:
step one, selecting a dynamic model of the spacecraft as a two-body dynamic model, wherein the adopted two-body dynamic model can be expressed as follows in a cylindrical coordinate system:
wherein D, B is an intermediate variable, 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 Respectively in the radial direction of thrustThe components in the directions, primary normal and secondary normal; m is the spacecraft mass; mu is the gravitational constant of the central celestial body, and for a near-earth satellite, mu is 398600.4415km 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 can be expressed as:
wherein, t f Is the transfer time of the task;
the initial state and the expected state of the acquisition 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 and the transfer time of the covariate, which are expressed as the optimal solution Lambda * ；
Step one, acquiring a group of new nominal orbit initial states
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 is obtainedΛ * As an optimal solution Λ for solving the new state new* 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 an indirect method to obtain a new initial value and transfer time of the covariate, 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 c ,m c Is the current state of the spacecraft, x t U is the optimal control for the desired state.
3. The intelligent constellation autonomous trajectory control method for collision avoidance according to claim 1 or 2, characterized in that: designing a neural network structure in the second step, wherein the neural network structure comprises the number of layers of the 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;
input of neural network 1,2 model of controllerAre both 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]The output of the neural network 2 model is the radial thrust direction angle and the sub-normal thrust direction angle [ theta ] r ,θ z ] T Wherein, theta 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 ReLU is selected as the activation function in the hidden layer;
the neural network 2 sequentially comprises an input layer, 9 layers of hidden layers and an output layer, wherein each layer of 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 adopted 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 the two-norm of the vector;
parameters in the neural network are trained by using an Adam optimization algorithm, and the learning rate is set to be 0.0001.
4. Constellation intelligence for collision avoidance as recited in claim 3An autonomous orbit control method, characterized by: 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, 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 primary normal direction and the secondary normal direction are respectively represented, so that the optimal control strategy (u, alpha) is as follows:
5. the intelligent constellation autonomous trajectory control method for collision avoidance according to claim 4, wherein: in the step 1, a collision avoidance controller is constructed by utilizing 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 Representing the nearest distance between two spacecrafts, and L representing the minimum distance allowed between the spacecrafts;
the repulsion potential of a spacecraft to its nearest neighbor is:
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 distance between two spacecrafts is less than or equal to d, the two spacecrafts are considered to have no collision risk 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 halfThe thrust direction oscillation generated by the undersize difference of the long shafts;
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 ascent intersection right ascension, 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:
6. the intelligent constellation autonomous trajectory control method for collision avoidance according to claim 5, wherein: 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 |, and r |、|Δv θ i and | Δ v z Respectively representing the current state
Date of andinspection 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 (1) is given; when all state deviations of the spacecraft are smaller than or equal to the stopping limit, the state allowable deviation is considered to be met, and when any state deviation of the spacecraft is larger than the starting limit, the state allowable deviation is considered to be not met any more;
the start limits are each greater than the stop limits.
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