CN114115307B - Spacecraft anti-intersection escape pulse solving method based on deep learning - Google Patents
Spacecraft anti-intersection escape pulse solving method based on deep learning Download PDFInfo
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Abstract
The invention discloses a spacecraft anti-intersection escape pulse solving method based on deep learning, which comprises the following steps of: establishing a spacecraft close-range relative motion orbit dynamics model and establishing a relative motion state transfer equation; constructing a double-layer mathematical programming model for describing the optimal escape pulse of the escape spacecraft; a large number of different initial relative states are selected, the size and the direction of the corresponding optimal escape pulse are solved by using a numerical optimization technology, and a series of state quantity-control quantity data pairs are formed; carrying out normalization processing on the data to construct a deep learning sample set; constructing a deep neural network and performing full training; and solving the short-range cross escape pulse by using the deep neural network obtained by final training. The method has the advantages of good escape effect, high calculation speed and the like, can be used for rapidly generating the approximate optimal escape strategy in real time on orbit of the spacecraft in space countermeasure, and can effectively improve the survivability of the spacecraft in future space countermeasure.
Description
Technical Field
The invention relates to the technical field of spacecraft orbit dynamics and control, in particular to a spacecraft anti-intersection escape pulse solving method based on deep learning.
Background
Future on-orbit spacecraft may face non-cooperative intersection of non-own units, and in order to maintain the safety of the spacecraft in space, a close-range anti-intersection escape technology needs to be developed to improve the survivability of the on-orbit spacecraft when facing the threat of close-range non-cooperative intersection. The escape of the spacecraft in the back-cross refers to that the escape spacecraft gets rid of the approach and close-range cross of the tracking spacecraft with the orbital maneuver capability by utilizing the self orbital maneuver capability. The current method mainly comprises a differential countermeasure-based escape game and an optimal index-based pulse maneuver avoidance.
In the chase and flee game based on differential countermeasures, a spacecraft is generally assumed to adopt continuous thrust control, and a chase and flee strategy with both sides being optimal is obtained by solving by a direct method, an indirect method, a semi-direct method and the like, so that the chase and flee game has strict mathematical theory, but has limitation: 1) The theory only solves the saddle point solution, and when the tracking spacecraft does not adopt the saddle point solution, the saddle point solution for the escape spacecraft is not optimal any more, and the engineering significance is limited; 2) Complicated numerical methods are needed for solving the chase-and-evasion game, the solving speed is low, the result can not be obtained rapidly in orbit, and the timeliness is poor. The pulse avoidance technology based on the optimal index is developed from the research related to the space debris collision avoidance, and under the reasonable assumption of state measurement and approach strategies of the tracking spacecraft, the escape maneuvering pulse is optimized, so that the established index is optimal. The core of the method is solving the optimization problem, and currently, global optimization algorithms such as heuristic algorithms and the like are commonly used to avoid trapping local extrema, but the method has the following defects: the numerical optimization algorithm is large in general calculation amount, and escape pulse solving is difficult to realize in real time and rapidly in an on-orbit manner, so that the result that a spacecraft cannot escape in time when facing a non-cooperative intersection threat is possibly caused. Therefore, a new technology capable of generating the anti-intersection escape pulse in real time with higher solving efficiency needs to be developed.
The deep learning technology taking the deep neural network as the main representative model has strong characterization capability and learning capability, and provides a new idea for high-efficiency and real-time solving of the escape of the spacecraft.
Disclosure of Invention
The invention provides a spacecraft anti-intersection escape pulse solving method based on deep learning, which is used for solving anti-intersection escape pulses when a spacecraft faces non-cooperative intersection threats. The method has the advantages that the method is fast in solving speed, good in escape effect and the like, and can be used for generating the escape pulse approximate to the optimal in real time on orbit of the spacecraft.
In order to achieve the above purpose, the invention provides a spacecraft anti-intersection escape pulse solving method based on deep learning, which specifically comprises the following steps:
s1: establishing an orbit dynamics model of the spacecraft close-range relative motion, defining the relative position and the relative speed as state variables, and constructing a relative motion state transfer equation;
S2: according to the relative motion state transfer equation in the step S1, taking the escape speed pulse size and direction of the escape spacecraft as an optimization variable, and tracking the optimal speed pulse consumption of the spacecraft for completing the intersection as an objective function, and constructing a double-layer mathematical programming model;
s3: a large number of different initial relative states are selected, the size and the direction of the corresponding optimal escape speed pulse of the escape spacecraft are solved by using a numerical optimization technology according to the double-layer mathematical programming model in the step S2, and a series of state quantity-control quantity data pairs are formed;
s4: carrying out normalization processing on a sample set for constructing deep learning by using the state quantity-control quantity data in the S3, and dividing the sample set into a training set, a verification set and a test set;
s5: constructing a deep neural network comprising a plurality of hidden layers, training the deep neural network by using the training set in the step S4, and taking the network with the minimum mean square error on the verification set as the finally obtained deep neural network;
s6: and inputting the relative state of the currently measured tracking spacecraft to the escape spacecraft into the depth neural network finally obtained in S5, and outputting the back-intersection escape pulse.
In one possible implementation manner, in the method for solving the escape pulse of the spacecraft based on deep learning provided by the invention, step S1 specifically includes:
Under the full central gravitational field of the earth, the escaped spacecraft flies in a nearly circular orbit, and the spacecraft is tracked nearby. Selecting a virtual point which performs circular orbit motion near the two spacecrafts, subtracting the relative motion equations of the tracking spacecraft and the escape spacecraft relative to the virtual point respectively to obtain a motion equation of the tracking spacecraft relative to the escape spacecraft, wherein the motion equation can be described as follows by using a Clohessy-Wiltshire equation:
wherein x, y, z represent three components of a position vector of the tracking spacecraft relative to the escape spacecraft in a virtual point orbit coordinate system, ω represents a circular orbit angular rate of the virtual point, f ix ,f iy ,f iz For a control acceleration applied on the spacecraft, i=p, E, P denotes the tracking spacecraft and E denotes the escape spacecraft.
Let state variablesControl amount u= [ f Px -f Ex ,f Py -f Ey ,f Pz -f Ez ] T T represents a transpose; the above equation of relative motion can be written as:
wherein the method comprises the steps ofIs a constant matrix.
According to the theory of ordinary differential equations, the relative motion state transfer equation can be obtained by solving the differential equation:
wherein t is 0 For initial time, X 0 As the initial phaseFor the state, Φ (t, t 0 ) For the state transition matrix, let v=ω (t-t 0 ) The state transition matrix is expressed as:
in one possible implementation manner, in the method for solving the deep learning-based spacecraft anti-intersection escape pulse provided by the invention, the step S2 includes two sub-steps:
S201, carrying out mathematical modeling on a mode of tracking the approach and intersection of multiple pulses of a spacecraft, and constructing a bottom mathematical programming model, wherein an objective function is the total speed pulse size of the intersection of the multiple pulses, and optimization variables are the time of each speed pulse, the size of each speed pulse and the direction of each speed pulse.
S202, carrying out mathematical modeling on an escape mode of an escape spacecraft, and constructing an upper-layer mathematical programming model, wherein an objective function is an optimal value of the bottom-layer mathematical programming model, and an optimization variable is the direction and the size of an escape pulse.
The step S201 specifically includes:
writing out a relative motion state transfer equation when the tracking spacecraft orbits in a pulse control mode and the escape spacecraft does not orbit according to the formula (3):
wherein t is i To track the moment of the spacecraft pulse maneuver, i=1, …, M is the total number of tracking spacecraft pulse maneuvers, Δv Pi To track the velocity pulse vector of the ith maneuver of the spacecraft, it contains three components:
Δv Pi ＝[Δv Pi cosβcosα,Δv Pi cosβsinα,Δv Pi sinβ] T (6)
wherein Deltav Pi For the i-th speed pulse, alpha and beta are respectively the i-th speed pulse vector under the virtual point orbit coordinate systemAzimuth and elevation.
For convenience of representation, the subscript P of the velocity pulse is omitted here, and the M times of pulse time and the vector of the previous M-2 times of velocity pulse are taken as optimization variables and expressed as [ t ] 1 ,…,t M ,Δv 1 ,…,Δv M-2 ] T 4M-6 optimization variables in total, taking the total speed increment of M pulses as an optimization target, and the expression is as follows:
after the last pulse, the constraint that the positions and the speeds of the tracking spacecraft and the escape spacecraft are the same is considered, and the constraint is naturally established by introducing the specific relation between the last two pulses and the optimization variable, specifically:
considering tracking the natural flight of the segment of the spacecraft after the M-1 th pulse and before the M th pulse, the state transition can be expressed as:
X(t M )＝Φ(t M ,t M-1 )X(t M-1 ) (8)
written as a form of block matrix multiplication:
wherein R is M-1 And R is R M Tracking the position of the spacecraft relative to the escaped spacecraft at the occurrence time of the M-1 th pulse and the M th pulse respectively, V M-1 + And V is equal to M - The relative speeds of the space vehicle escaping from the space vehicle are tracked after the M-1 th pulse and before the M-th pulse, and the symbols "-" and "+" respectively represent the before pulse and the after pulse.
V can be inversely solved according to formula (9) M - And V M-1 + ：
In the formula (10), R M-1 The relative position vector R at the last pulse can be determined from equation (5) based on the optimization variables so that the two spacecraft positions at the terminal time are identical M Zero vector and relative velocity vector v after the last pulse M + Also zero vector, so that V can be solved M-1 + And V is equal to M - Then the pulse speed increment of the M-1 th time and the M th time can be obtained:
V in formula (11) M-1 - With R as described above M-1 As such, the optimization variable is given by equation (5).
The last two pulses obtained according to the formula (11) implies that the position vector and the velocity vector of the tracking spacecraft relative to the escape spacecraft after the last pulse are zero, namely the constraint that the positions and the velocities of the tracking spacecraft and the escape spacecraft are the same is ensured to be established.
Therefore, the established underlying mathematical programming model is expressed as:
s.t.
wherein T is lim For the set upper tracking spacecraft intersection time limit, RLP (·) represents the process described by equation (10) (11) to solve for the last two pulses.
The step S202 specifically includes:
with escape pulse vector Deltav of escape spacecraft E To optimize the variables, the variable, including three components,
Δv E ＝[Δv E cosβ E cosα E ,Δv E cosβ E sinα E ,Δv E sinβ E ] T (13)
wherein Deltav E To escape velocity pulse size, alpha E ,β E The azimuth angle and the elevation angle of the escape velocity pulse vector are respectively.
Taking the optimized optimal value of the model (12) as an objective function, and recording as J E ＝f(Δv E ,α E ,β E ) Where it is desired to maximize it, an upper layer mathematical programming model can be constructed as:
max J E ＝f(Δv E ,α E ,β E )
s.t.
wherein Deltav max Is the upper limit of the allowed escape pulse size.
In one possible implementation manner, in the method for solving the escape pulse of the spacecraft based on deep learning provided by the invention, the step S3 specifically includes:
After the orbit height of the given spacecraft and the intersection time upper limit of the tracking spacecraft, the two-layer mathematical programming model is provided in the step S2, and a numerical optimization technology is used for carrying out numerical solution on the model by using a hybrid algorithm comprising Comprehensive Learning Particle Swarm Optimization (CLPSO) and Sequential Quadratic Programming (SQP), wherein the CLPSO algorithm provides an initial value with global optimality to the SQP algorithm for carrying out accurate search, and the relative states [ x y z v ] of the two spacecrafts can be obtained x v y v z ] T Uniquely determining an optimal escape pulse [ Deltav ] for an escape spacecraft Ex Δv Ey Δv Ez ] T T represents the transpose. Therefore, a large number of different relative states are selected in the state space, corresponding optimal escape pulses are respectively solved, and a series of data pairs formed by 6-dimensional state vectors and 3-dimensional escape pulse vectors, namely state quantity-control quantity data pairs, are formed.
Wherein, the method for concretely taking the relative state is that firstly, the ball is seatedParameter describing relative status [ rα ] under the heading r β r v α v β v ] T Performing equidistant value taking, wherein T represents transposition, and converting into an original state space [ x y z v ] x v y v z ] T Wherein r is the distance between the two spacecrafts, v is the relative velocity between the two spacecrafts, and α r ，β r ，α v ，β v The conversion relation is that the azimuth angle and the high-low angle of the relative position and the relative speed under the virtual point orbit coordinate system are respectively:
In one possible implementation manner, in the method for solving the escape pulse of the spacecraft based on deep learning provided by the invention, the step S4 specifically includes:
after a large number of state quantity-control quantity data pairs are obtained, the state quantity is taken as a sample characteristic, the control quantity is taken as a sample label, each data pair forms a sample, and a large number of samples form a sample set. In order to eliminate training difficulties caused by different data scales, the data in all samples are unified for normalization processing, and the normalization formula is as follows:
wherein n is a sample number, x d Andrepresents the d dimension, max (x d ) And min (x) d ) Representing the maximum and minimum values, respectively, in the d-th dimension before normalization.
After the normalized sample set is obtained, about 80% of samples are randomly extracted from the sample set to form a training set, 10% of samples are extracted from the rest of samples to serve as a verification set, and the rest of samples form a test set.
In one possible implementation manner, in the method for solving the escape pulse of the spacecraft based on deep learning provided by the present invention, the step S5 specifically includes:
The deep neural network is selected as a feedforward neural network, and the built neural network consists of an input layer, a hidden layer and an output layer, wherein the hidden layer number is more than 1 layer. The first layer is an input layer, the last layer is an output layer, and the middle layer is a hidden layer. The input layer inputs 6-dimensional state vectors, each hidden layer carries out linear operation on the input, maps to the next hidden layer through a nonlinear function, and finally, the result of the hidden layer is transmitted to the output layer to output 3-dimensional control vectors. The iterative formula for information propagation in the network is:
wherein z is (l) Representing the net input of layer I neurons, a (l) Representing the output of the layer i neurons,is a weight matrix from layer 1 to layer 1, where M l Representing the number of neurons in layer I, < >>Is the offset from layer 1 to layer 1, f l (. Cndot.) represents an activation function.
The neuron activation function of the hidden layer is selected from a Logistic function, a Tanh function and a ReLU function, and the neuron activation function of the output layer is selected from a Linear function and a Tanh function.
After the deep neural network is constructed, the training set obtained in the step S4 is utilized to train the network, the training of the network depends on an error back propagation mechanism, the Adam algorithm is utilized to optimize the weight of the network, and the Mean Square Error (MSE) is utilized as a loss function. Setting the maximum training round number, recording the trained network of each round, solving the mean square error of each network on the verification set obtained in the step S4, and considering the network with the minimum mean square error on the verification set to have the best generalization performance. Finally, the deep neural network with the minimum mean square error on the verification set is reserved as a final obtained network, and the output effect of the final obtained network is tested by using samples in the test set.
In one possible implementation manner, in the method for solving the deep learning-based spacecraft anti-intersection escape pulse provided by the invention, the step S6 is: the depth neural network obtained by final training is directly used for solving the short-range anti-intersection escape pulse of the escape spacecraft, and the measured relative state [ x y z v ] of the tracking spacecraft for the escape spacecraft, which contains 6 dimensions x v y v z ] T Inputting the finally obtained deep neural network, outputting an anti-intersection escape pulse [ delta ] with 3 dimensions Ex Δv Ey Δv Ez ] T 。
The beneficial effects are that:
1. according to the spacecraft anti-intersection escape pulse solving method based on deep learning, disclosed by the invention, the generation rule of the deep neural network fitting short-distance anti-intersection escape pulse is trained, the escape pulse is directly output by using the fully trained neural network, a complex numerical method is avoided, the solving speed is extremely high, and the method can be used for real-time generation of an on-orbit spacecraft anti-intersection escape strategy.
2. According to the method for solving the escape pulse of the spacecraft anti-intersection based on deep learning, the solved escape pulse of the spacecraft anti-intersection based on deep learning has the characteristic of being approximate to global optimum, so that the cost required for tracking the spacecraft to finish intersection is maximized, and the survivability of the escape spacecraft is effectively improved.
Drawings
FIG. 1 is a flow chart of a method for solving a spacecraft back-crossing escape pulse based on deep learning;
FIG. 2 is a schematic diagram of a dynamic model of establishing a close-range relative motion trajectory;
FIG. 3 is a schematic diagram of the geometrical significance of the azimuth and elevation of the escape pulse;
FIG. 4 is a flow chart of a two-layer mathematical programming problem solving by comprehensive learning particle swarm optimization and sequential quadratic programming numerical values;
FIG. 5 is a flow chart of constructing a sample;
FIG. 6 is a graph of the error variation over the validation set during training of the neural network 1;
FIG. 7 is a graph of the error variation across the validation set during training of the neural network 2;
fig. 8 is a trajectory diagram of an escape spacecraft in a simulation example, wherein the escape spacecraft applies escape pulses obtained by the neural network 1, and the escape spacecraft is tracked to meet, and the two escape spacecraft and the spacecraft are in a virtual point orbit coordinate system;
fig. 9 is a trajectory diagram of the escape spacecraft in the simulation example, wherein the escape pulse is obtained by applying the neural network 2 to the escape spacecraft, tracking the spacecraft to meet, and the two sides are in a virtual point orbit coordinate system;
FIG. 10 is a graph showing the variation of the minimum velocity pulse size with the altitude for the corresponding tracking spacecraft to complete the intersection, with the azimuth of the escape pulse obtained by the fixed neural network 1 unchanged;
FIG. 11 is a graph showing the variation of the minimum velocity pulse size with azimuth angle required for the corresponding tracking spacecraft to complete the intersection, with the constant high and low angles of the escape pulse obtained by the fixed neural network 1; the method comprises the steps of carrying out a first treatment on the surface of the
FIG. 12 is a graph showing the variation of the minimum velocity pulse size with the altitude for a corresponding tracking spacecraft to complete the intersection, with the azimuth of the escape pulse obtained by the fixed neural network 2 unchanged;
fig. 13 is a graph showing the variation of the minimum velocity pulse size with azimuth angle required for the corresponding tracking spacecraft to complete the intersection, with the escape pulse obtained by the fixed neural network 2 being constant in height and angle.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is apparent that the described embodiments are merely examples and are not intended to limit the present invention.
The invention provides a spacecraft anti-intersection escape pulse solving method based on deep learning, which is shown in fig. 1 and comprises the following steps:
s1: establishing an orbit dynamics model of the spacecraft close-range relative motion, defining the relative position and the relative speed as state variables, and constructing a relative motion state transfer equation;
The step S1 specifically includes:
under the full central gravitational field of the earth, the escaped spacecraft flies in a nearly circular orbit, and the spacecraft is tracked nearby. As shown in fig. 2, a virtual point O that performs circular orbit motion is selected near two spacecraft, a virtual point orbit coordinate system is established, the relative motion equations of the tracking spacecraft P and the escape spacecraft E relative to the virtual point are subtracted, and the motion equation of the tracking spacecraft relative to the escape spacecraft can be obtained, and is described as follows by using the Clohessy-Wiltshire equation:
wherein x, y, z represent three components of a position vector of the tracking spacecraft relative to the escape spacecraft in a virtual point orbit coordinate system, ω represents a circular orbit angular rate of the virtual point, f ix ,f iy ,f iz For a control acceleration applied on the spacecraft, i=p, E, P denotes the tracking spacecraft and E denotes the escape spacecraft.
Let state variablesControl amount u= [ f Px -f Ex ,f Py -f Ey ,f Pz -f Ez ] T T represents a transpose; the above equation of relative motion can be written as:
wherein the method comprises the steps ofIs a constant matrix.
According to the theory of ordinary differential equations, the relative motion state transition equation can be written by the solution of the differential equation:
wherein t is 0 For initial time, X 0 For initial relative state, Φ (t, t 0 ) For the state transition matrix, let v=ω (t-t 0 ) The state transition matrix is expressed as:
s2: according to the relative motion state transfer equation in the step S1, taking the escape speed pulse size and direction of the escape spacecraft as an optimization variable, and tracking the optimal speed pulse consumption of the spacecraft for completing the intersection as an objective function, and constructing a double-layer mathematical programming model;
the step S2 specifically includes two sub-steps:
s201, carrying out mathematical modeling on a mode of tracking the approach and intersection of multiple pulses of a spacecraft, and constructing a bottom mathematical programming model, wherein an objective function is the total speed pulse size of the intersection of the multiple pulses, and optimization variables are the time of each speed pulse, the size of each speed pulse and the direction of each speed pulse.
S202, carrying out mathematical modeling on an escape mode of an escape spacecraft, and constructing an upper-layer mathematical programming model, wherein an objective function is an optimal value of the bottom-layer mathematical programming model, and an optimization variable is the direction and the size of an escape pulse.
The step S201 specifically includes:
writing out a relative motion state transfer equation when the tracking spacecraft orbits in a pulse control mode and the escape spacecraft does not orbit according to the formula (3):
wherein t is i To track the moment of a spacecraft pulse maneuver, i=1..m, M are the total number of tracking spacecraft pulse maneuvers, Δv Pi To track the velocity pulse vector of the ith maneuver of the spacecraft, it contains three components:
Δv Pi ＝[Δv Pi cosβcosα,Δv Pi cosβsinα,Δv Pi sinβ] T (6)
wherein Deltav Pi For the size of the ith speed pulse, α, β are the azimuth angle and the altitude angle of the ith speed pulse vector under the virtual point orbit coordinate system, and the geometric meaning of the ith speed pulse vector is the same as the azimuth angle and the altitude angle of the escape pulse of the escape spacecraft, which is later, see fig. 3.
For convenience of representation, the subscript P of the velocity pulse is omitted here, and the M times of pulse time and the vector of the previous M-2 times of velocity pulse are taken as optimization variables and expressed as [ t ] 1 ,…,t M ,Δv 1 ,…,Δv M-2 ] T 4M-6 optimization variables in total, taking the total speed increment of M pulses as an optimization target, and the expression is as follows:
after the last pulse, the constraint that the positions and the speeds of the tracking spacecraft and the escape spacecraft are the same is considered, and the constraint is naturally established by introducing the specific relation between the last two pulses and the optimization variable, specifically:
considering tracking the natural flight of the segment of the spacecraft after the M-1 th pulse and before the M th pulse, the state transition can be expressed as:
X(t M )＝Φ(t M ,t M-1 )X(t M-1 ) (8)
written as a form of block matrix multiplication:
wherein R is M-1 And R is R M Tracking the position of the spacecraft relative to the escaped spacecraft at the occurrence time of the M-1 th pulse and the M th pulse respectively, V M-1 + And V is equal to M - The relative speeds of the space vehicle escaping from the space vehicle are tracked after the M-1 th pulse and before the M-th pulse, and the symbols "-" and "+" respectively represent the before pulse and the after pulse.
V can be inversely solved according to formula (9) M - And V M-1 + ：
In the formula (10), R M-1 The relative position vector R at the last pulse can be determined from equation (5) based on the optimization variables so that the two spacecraft positions at the terminal time are identical M Zero vector and relative velocity vector v after the last pulse M + Also zero vector, so that V can be solved M-1 + And V is equal to M - Then the pulse speed increment of the M-1 th time and the M th time can be obtained:
v in formula (11) M-1 - With R as described above M-1 As such, the optimization variable is given by equation (5).
The last two pulses obtained according to the formula (11) implies that the position vector and the velocity vector of the tracking spacecraft relative to the escape spacecraft after the last pulse are zero, namely the constraint that the positions and the velocities of the tracking spacecraft and the escape spacecraft are the same is ensured to be established.
Therefore, the established underlying mathematical programming model is expressed as:
s.t.
wherein T is lim For the set upper tracking spacecraft intersection time limit, RLP (·) represents the process described by equation (10) (11) to solve for the last two pulses.
The step S202 specifically includes:
with escape pulse vector Deltav of escape spacecraft E To optimize the variables, the variable, including three components,
Δv E ＝[Δv E cosβ E cosα E ,Δv E cosβ E sinα E ,Δv E sinβ E ] T (13)
wherein Deltav E To escape velocity pulse size, alpha E ,β E The azimuth angle and the elevation angle of the escape velocity pulse vector are respectively.
Taking the optimized optimal value of the model (12) as an objective function, and recording as J E ＝f(Δv E ,α E ,β E ) Where it is desired to maximize it, an upper layer mathematical programming model can be constructed as:
max J E ＝f(Δv E ,α E ,β E )
s.t.
wherein Deltav max Is the upper limit of the allowed escape pulse size.
S3: a large number of different initial relative states are selected, the size and the direction of the corresponding optimal escape speed pulse of the escape spacecraft are solved by using a numerical optimization technology according to the double-layer mathematical programming model in the step S2, and a series of state quantity-control quantity data pairs are formed;
the step S3 specifically includes:
after the orbit height of a given spacecraft meets the upper limit of the time for tracking the spacecraftFrom the two-layer mathematical programming model proposed in step S2, the model is numerically solved by a numerical optimization technique, i.e. a hybrid algorithm comprising Comprehensive Learning Particle Swarm Optimization (CLPSO) and Sequential Quadratic Programming (SQP), wherein the CLPSO algorithm provides initial values with global optimality to the SQP algorithm for accurate search, the flow diagram is shown in fig. 4, whereby the relative states of two spacecraft [ x y z v ] can be determined by x v y v z ] T Uniquely determining an optimal escape pulse [ Deltav ] for an escape spacecraft Ex Δv Ey Δv Ez ] T T represents the transpose. Therefore, a large number of different relative states are selected in the state space, corresponding optimal escape pulses are respectively solved, and a series of data pairs formed by 6-dimensional state vectors and 3-dimensional escape pulse vectors, namely state quantity-control quantity data pairs, are formed.
The method for concretely taking the relative state comprises the steps of firstly describing parameters [ ralpha ] of the relative state under a spherical coordinate system r β r v α v β v ] T Performing equidistant value taking, wherein T represents transposition, and converting into an original state space [ x y z v ] x v y v z ] T Wherein r is the distance between the two spacecrafts, v is the relative velocity between the two spacecrafts, and α r ，β r ，α v ，β v The azimuth and elevation angles of the relative position and relative velocity, respectively, in the virtual point orbital coordinate system are consistent with the geometric meaning described in fig. 3. The conversion relation is as follows:
s4: carrying out normalization processing on a sample set for constructing deep learning by using the state quantity-control quantity data in the S3, and dividing the sample set into a training set, a verification set and a test set;
the step S4 specifically includes:
after a large number of state quantity-control quantity data pairs are obtained, the state quantity is taken as a sample characteristic, the control quantity is taken as a sample label, each data pair forms a sample, the flow of generating one sample is shown in fig. 5, and a large number of samples form a sample set. In order to eliminate training difficulties caused by different data scales, the data in all samples are unified for normalization processing, and the normalization formula is as follows:
wherein n is a sample number, x d Andrepresents the d dimension, max (x d ) And min (x) d ) Representing the maximum and minimum values, respectively, in the d-th dimension before normalization.
After the normalized sample set is obtained, about 80% of samples are randomly extracted from the sample set to form a training set, 10% of samples are extracted from the rest of samples to serve as a verification set, and the rest of samples form a test set.
S5: constructing a deep neural network comprising a plurality of hidden layers, training the deep neural network by using the training set in the step S4, and taking the network with the minimum mean square error on the verification set as the finally obtained deep neural network;
the step S5 specifically includes:
the deep neural network is selected as a feedforward neural network, and the built neural network consists of an input layer, a hidden layer and an output layer, wherein the hidden layer number is more than 1 layer. The first layer is an input layer, the last layer is an output layer, and the middle layer is a hidden layer. The input layer inputs 6-dimensional state vectors, each hidden layer carries out linear operation on the input, maps to the next hidden layer through a nonlinear function, and finally, the result of the hidden layer is transmitted to the output layer to output 3-dimensional control vectors. The iterative formula for information propagation in the network is:
wherein z is (l) Representing the net input of layer I neurons, a (l) Representing the output of the layer i neurons,is a weight matrix from layer 1 to layer 1, where M l Representing the number of neurons in layer I, < >>Is the offset from layer 1 to layer 1, f l (. Cndot.) represents an activation function.
The neuron activation function of the hidden layer is selected from a Logistic function, a Tanh function and a ReLU function, and the neuron activation function of the output layer is selected from a Linear function and a Tanh function.
After the deep neural network is constructed, the training set obtained in the step S4 is utilized to train the network, the training of the network depends on an error back propagation mechanism, the Adam algorithm is utilized to optimize the weight of the network, and the Mean Square Error (MSE) is utilized as a loss function. Setting the maximum training round number, recording the trained network of each round, solving the mean square error of each network on the verification set obtained in the step S4, and considering the network with the minimum mean square error on the verification set to have the best generalization performance. Finally, the deep neural network with the minimum mean square error on the verification set is reserved as a final obtained network, and the output effect of the final obtained network is tested by using samples in the test set.
S6: and inputting the relative state of the currently measured tracking spacecraft to the escape spacecraft into the depth neural network finally obtained in S5, and outputting the back-intersection escape pulse.
The step S6 specifically includes:
the depth neural network obtained by final training is directly used for solving the short-range anti-intersection escape pulse of the escape spacecraft, and the measured relative state [ x y z v ] of the tracking spacecraft for the escape spacecraft, which contains 6 dimensions x v y v z ] T Inputting the finally obtained deep neural network, outputting an anti-intersection escape pulse [ delta ] with 3 dimensions Ex Δv E y Δv Ez ] T 。
The effectiveness of the proposed method is illustrated below by a simulation example.
Some parameters were set as: the gravitational constant is μ= 398600.5.10 9 m 3 /s 2 The radius of the earth takes R e = 6371.11km, current time t 0 The orbit elements of the escape spacecraft and the tracking spacecraft are shown in table 1, wherein the escape spacecraft moves on a circular orbit with the orbit height of 300km, and the virtual point is set to coincide with the escape spacecraft when maneuver does not occur. Setting the upper limit T of the intersection time of the tracking spacecraft lim =1800 s, the number of pulses is at most 3, the tracking spacecraft does not set the upper limit of allowable maneuver pulse size, and the upper limit of allowable maneuver pulse size of the escape spacecraft is set to be 50m/s.
The relative position of the tracking spacecraft relative to the escape spacecraft at the current moment under the virtual point orbit coordinate system can be calculated to be [ 23.34-34.99-15.30 ] ] T km, relative speed of [ -8.60,1.41,26.79 [] T m/s, and the distance between the two parties at the current moment is 44.76km.
TABLE 1
| Track element | Escape spacecraft | Tracking spacecraft |
| Semi-long axis/km | 6671.11 | 6687.20 |
| Eccentricity ratio | 0 | 0.0001 |
| Track inclination- ° | 30 | 30.3 |
| The ascending intersection is barefoot- ° | 0 | 0 |
| Near-site argument/° | 90 | 80 |
| True near point angle/° | 1.8 | 12 |
According to step S1, the track angular velocity ω= 0.0011587S can be obtained from the virtual point circle track height -1 The substitution formula (4) can find a state transition matrix to determine a relative motion state transition equation.
According to step S2, models (12) and (14) can be constructed from the relative motion state transfer equation obtained in the previous step, and a double-layer mathematical programming problem is formed.
According to step S3, the 6 dimensions of the relative state are discretized. First, the parameter [ rα ] describing the relative state in the spherical coordinates r β r v α v β v ] T Performing equidistant value taking, wherein r is from 10km to 50km, alpha r Take the value from 0 radian interval 2 pi/15 radian to 2 pi radian, beta r From-pi/2 radian interval pi/10 radian to pi/2 radian, v from 11m/s interval 3m/s to 35m/s, alpha v Take the value from 0 radian interval 2 pi/15 radian to 2 pi radian, beta v Take values from-pi/2 radian interval pi/10 radian toPi/2 radians, which are then converted into the original state space [ x y z v ] according to equation (15) x v y v z ] T Is a kind of medium. Substituting all the valued relative states into a double-layer mathematical programming model, carrying out numerical solution on the model by using a mixed algorithm comprising Comprehensive Learning Particle Swarm Optimization (CLPSO) and Sequential Quadratic Programming (SQP), obtaining the optimal control quantity corresponding to each state quantity, and finally forming 1393920 state quantity-control quantity data pairs in total.
According to step S4, all data pairs are normalized by formula (16), 80% of samples (1115136) are randomly extracted to form a training set, 10% (139392) of the remaining data pairs are randomly extracted to form a verification set, and the remaining 10% (139392) of the data pairs form a test set.
According to step S5, two deep neural networks are constructed for training and testing to verify the effectiveness of the proposed method. The first network is marked as a neural network 1, which is provided with 8 hidden layers, each hidden layer is provided with 64 neurons, the activation function of the hidden layer neurons is a Tanh function, and the activation function of the output layer neurons is also a Tanh function; the other network is denoted as neural network 2, having 10 hidden layers, each having 256 neurons, with a hidden layer neuron activation function as a ReLU function and an output layer neuron activation function as a Linear function. Training the two network architectures by using the training set obtained in the last step, wherein the training is realized by adopting an Adam algorithm, the learning rate is 0.005, the exponential decay rates of the gradient first-order moment estimation and the second-order moment estimation are respectively set to be 0.9 and 0.999, the maximum round number of the training is 50, the network with the minimum mean square error output on the verification set is taken as the network with the final training completion, and the output error test is carried out on the test set.
For the two selected deep neural network architectures, the mean square error of the finally trained network on the verification set and the mean square error of the finally trained network on the test set are shown in table 2, and fig. 6 and fig. 7 are graphs of error changes on the verification set in the training process of the neural network 1 and the neural network 2 respectively.
TABLE 2
After obtaining fully trained deep neural networks, inputting the state (relative position and relative speed under a virtual point orbit system) of the tracking spacecraft relative to the escape spacecraft at the current moment into two deep neural networks to obtain escape pulses of the escape spacecraft, wherein the output result of the neural network 1 is Deltav E1 ＝50m/s，α E1 ＝3.3712rad，β E1 The output of neural network 2 is Δv = -0.7123rad E1 ＝50m/s，α E1 ＝3.3493rad，β E1 It can be seen that the escape pulses of the trained two neural network outputs are substantially identical. Under the framework of the method provided by the invention, the index for measuring the escape pulse is to track whether the size of the speed pulse consumed by the spacecraft for completing the intersection becomes large enough after the escape pulse is applied to the escape spacecraft, so that the difficulty of realizing the intersection is improved, and the survivability of the escape spacecraft is improved. After the escape spacecraft is subjected to simulation calculation and the escape pulse obtained by the neural network 1 is applied, the minimum speed pulse size for tracking the spacecraft to finish the intersection is 124.7342m/s; after the escape pulse obtained by the neural network 2 is applied, the minimum speed pulse size for tracking the completion of the intersection of the spacecraft is 124.7444m/s. When the escape spacecraft does not apply escape pulse, the minimum speed pulse size for completing the intersection of the tracking spacecraft is 74.7456m/s, and the cost for completing the intersection of the tracking spacecraft is obviously increased after the escape pulse solved by the deep neural network is applied. Fig. 8 and 9 show the trajectories of the two parties in the virtual point orbit coordinate system when the escape spacecraft applies the escape pulse calculated by the neural network 1 and the neural network 2 and the tracking spacecraft adopts at most 3 pulses to finish the intersection.
In order to further explain the approximate optimality of the escape pulse solved by the method provided by the invention, especially under the condition that the allowed escape pulse is fixed in size, the approximate optimality of the escape direction is solved, the escape pulse is fixed in size, the azimuth angle and the high-low angle of the escape pulse vector are changed, different escape pulses are constructed,comparing the minimum velocity pulse size required by the tracking spacecraft to complete the intersection after they are applied by the escaping spacecraft, the results are shown in fig. 10 to 13, wherein fig. 10 is the azimuth angle α of the escaping pulse obtained by fixing the neural network 1 E1 Unchanged, but high and low angle beta E1 The value is from pi/2 radian to pi/2 radian, and the minimum speed pulse size required by the spacecraft to finish intersection is tracked correspondingly; FIG. 11 shows the escape pulse angle β obtained by the fixed neural network 1 E1 Unchanged, azimuth angle alpha E1 The value is from 0 radian to 2 pi radian, and the minimum speed pulse size required by the spacecraft to finish intersection is correspondingly tracked; fig. 12 and 13 are representations of the results corresponding to the neural network 2. It can be seen from the figure that the azimuth angle and the elevation angle of the escape pulse obtained by the neural network 1 or the neural network 2 are both near the optimal value, and the approximate solution for maximizing the consumed pulse for completing the intersection of the tracking spacecraft proves the approximate optimality of the escape pulse obtained by the method provided by the invention.
Table 3 reflects the length of time required for solving escape pulses for a single time by using a neural network trained by a genetic algorithm, a particle swarm optimization algorithm and the method provided by the invention, and the CPU model of a computer is i7-8700.
TABLE 3 Table 3
From the table, the method provided by the invention has the characteristic of extremely high calculation speed, can be used for generating the near-optimal escape pulse in real time for the on-orbit spacecraft, greatly shortens the reaction time when encountering the threat, and effectively improves the survivability of the on-orbit spacecraft.
In conclusion, the method provided by the invention has the characteristics of good effect, approximate optimum, extremely high speed and the like in solving the short-range cross escape pulse of the spacecraft, has good engineering application value and has popularization prospect.
The foregoing illustrates the basic principles and steps of the invention and uses examples to verify the validity and utility of the methods presented in the invention. It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (6)
1. A spacecraft anti-intersection escape pulse solving method based on deep learning is characterized by comprising the following steps of: the method comprises the following steps:
s1: establishing an orbit dynamics model of the spacecraft close-range relative motion, defining the relative position and the relative speed as state variables, and constructing a relative motion state transfer equation;
s2: according to the relative motion state transfer equation in the step S1, taking the escape speed pulse size and direction of the escape spacecraft as an optimization variable, and tracking the optimal speed pulse consumption of the spacecraft for completing the intersection as an objective function, and constructing a double-layer mathematical programming model;
s3: a large number of different initial relative states are selected, the size and the direction of the corresponding optimal escape speed pulse of the escape spacecraft are solved by using a numerical optimization technology according to the double-layer mathematical programming model in the step S2, and a series of state quantity-control quantity data pairs are formed;
s4: carrying out normalization processing on a sample set for constructing deep learning by using the state quantity-control quantity data in the S3, and dividing the sample set into a training set, a verification set and a test set;
s5: constructing a deep neural network comprising a plurality of hidden layers, training the deep neural network by using the training set in the step S4, and taking the network with the minimum mean square error on the verification set as the finally obtained deep neural network;
S6: inputting the relative state of the currently measured tracking spacecraft to the escape spacecraft into the depth neural network finally obtained in S5, and outputting an anti-intersection escape pulse;
the step S2 is to construct a double-layer mathematical programming model, and specifically comprises two sub-steps:
s201, carrying out mathematical modeling on a mode of tracking the approach and intersection of multiple pulses of a spacecraft, and constructing a bottom mathematical programming model, wherein an objective function is the total speed pulse size of the intersection of the multiple pulses, and optimization variables are the time of each speed pulse, the size of each speed pulse and the direction of each speed pulse;
s202, carrying out mathematical modeling on an escape mode of an escape spacecraft, and constructing an upper-layer mathematical programming model, wherein an objective function is an optimal value of the bottom-layer mathematical programming model, and an optimization variable is the direction and the size of an escape pulse;
the step S201 specifically includes:
writing a relative motion state transfer equation when the tracking spacecraft orbits in a pulse control mode and the escape spacecraft does not orbit according to the formula (1):
wherein t is i To track the moment of a spacecraft pulse maneuver, i=1..m, M are the total number of tracking spacecraft pulse maneuvers, Δv Pi To track the velocity pulse vector of the ith maneuver of the spacecraft, it contains three components:
Δv Pi ＝[Δv Pi cosβcosα,Δv Pi cosβsinα,Δv Pi sinβ] T (2)
Wherein Deltav Pi The size of the ith speed pulse, alpha and beta are the azimuth angle and the high-low angle of the ith speed pulse vector under the virtual point orbit coordinate system respectively;
for convenience of representation, the subscript P of the velocity pulse is omitted, and the M times of pulse time and the vector of the previous M-2 times of velocity pulse are taken as optimization variables and expressed as [ t ] 1 ,...,t M ,Δv 1 ,...,Δv M-2 ] T Taking the total speed increment of M pulses as an optimization target, the expression is as follows:
adding constraint, and limiting the positions and speeds of the tracking spacecraft and the escape spacecraft after the last pulse to be the same, wherein the method specifically comprises the following steps:
writing out the state transition of natural flight after the M-1 th pulse of the tracking spacecraft to before the M-th pulse:
X(t M )＝Φ(t M ,t M-1 )X(t M-1 ) (4)
expressed in terms of a block matrix multiplication:
wherein R is M-1 And R is R M Tracking the position of the spacecraft relative to the escaped spacecraft at the occurrence time of the M-1 th pulse and the M th pulse respectively, V M-1 + And V is equal to M - Tracking the speed of the spacecraft relative to the escaped spacecraft after the M-1 th pulse and before the M th pulse respectively, wherein the symbols "-" and "+" respectively represent the pre-pulse and the post-pulse;
inverse solution of V according to (5) M - And V M-1 + ：
In the formula (6), R M-1 The relative position vector R at the last pulse is obtained according to the optimization variable and the relative position and speed of the two spacecrafts at the terminal moment are the same by the formula (1) M For zero vector and relative velocity vector v after the last pulse M + For zero vector, solve for V M-1 + And V is equal to M - Then, the pulse velocity increment of the M-1 th and M th times is obtained:
v in formula (7) M-1 - And the same is calculated according to the optimized variable by the formula (1);
the established bottom mathematical programming model is expressed as:
s.t.
wherein T is lim For the set upper limit of the cross-over time of the tracking spacecraft, RLP (& gt) represents the process of solving the last two pulses described by the formulas (6) (7);
the step S202 specifically includes:
with escape pulse vector Deltav of escape spacecraft E To optimize the variables, the variable, including three components,
Δv E ＝[Δv E cosβ E cosα E ,Δv E cosβ E sinα E ,Δv E sinβ E ] T (9)
wherein Deltav E To escape velocity pulse size, alpha E ,β E The azimuth angle and the high-low angle of the escape velocity pulse vector are respectively;
taking the optimal value optimized in the model (8) as an objective function, and recording as J E ＝f(Δv E ,α E ,β E ) The upper layer mathematical programming model is constructed as follows:
max J E ＝f(Δv E ,α E ,β E )
s.t.
wherein Deltav max Is the upper limit of the allowed escape pulse size.
2. The spacecraft back-off escape pulse solving method based on deep learning as claimed in claim 1, wherein the method is characterized by comprising the following steps: the step S1 specifically includes:
under the earth full center gravitational field, selecting a virtual point moving on a circular orbit near a tracking spacecraft and an escape spacecraft which move in a short distance, and subtracting a relative motion equation of the tracking spacecraft and the escape spacecraft relative to the point to obtain a relative motion orbit dynamics model of the tracking spacecraft relative to the escape spacecraft, which is described by using a Clohessy-Wiltshire equation; the relative position and the relative speed are defined as state variables, and a relative motion state transition equation is written according to the theory of ordinary differential equations:
Wherein t is 0 For the initial time, ω represents the circular orbit angular rate of the virtual point, X 0 For initial relative state, Φ (t, t 0 ) Is a state transition matrix, B is a constant matrix,let v=ω (t-t) 0 ) The state transition matrix is expressed as:
3. the spacecraft back-off escape pulse solving method based on deep learning as claimed in claim 1, wherein the method is characterized by comprising the following steps: the step S3 specifically includes:
after the orbit height of a given spacecraft and the intersection time upper limit of a tracking spacecraft, carrying out numerical solution on the model by using a numerical optimization technology through the double-layer mathematical programming model proposed in the step S2, and carrying out the relative state [ x y z v ] of the two spacecrafts x v y v z ] T Uniquely determining an optimal escape pulse [ Deltav ] for an escape spacecraft Ex Δv Ey Δv Ez ] T T represents a transpose; selecting a large number of different relative states in a state space, and respectively solving corresponding optimal escape pulses to form a series of state quantity-control quantity data pairs consisting of 6-dimensional state vectors and 3-dimensional escape pulse vectors;
the method for acquiring the relative state comprises the steps of describing parameters [ rα ] of the relative state under a spherical coordinate system r β r v α v β v ] T The values are taken at equal intervals and then converted into the original state space [ x y z v ] x v y v z ] T Wherein r is the distance between the two spacecrafts, v is the relative velocity between the two spacecrafts, and α r ，β r ，α v ，β v The conversion relation is that the azimuth angle and the high-low angle of the relative position and the relative speed under the virtual point orbit coordinate system are respectively:
4. the spacecraft back-off escape pulse solving method based on deep learning as claimed in claim 1, wherein the method is characterized by comprising the following steps: the step S4 specifically includes:
after a large number of state quantity-control quantity data pairs are obtained, the state quantity is taken as a sample characteristic, the control quantity is taken as a sample label, and each data pair forms a sample to form a sample set containing a large number of samples; unifying the data in all the samples, wherein the normalization formula is as follows:
wherein n is a sample number, x d Andrepresents the d dimension, max (x d ) And min (x) d ) Respectively representing the maximum value and the minimum value in the d dimension before normalization;
after the normalized sample set is obtained, about 80% of samples are randomly extracted from the sample set to form a training set, 10% of samples are extracted from the rest of samples to serve as a verification set, and the rest of samples form a test set.
5. The spacecraft back-off escape pulse solving method based on deep learning as claimed in claim 1, wherein the method is characterized by comprising the following steps: the step S5 specifically includes:
The deep neural network type is selected as a feedforward neural network, and the built neural network consists of an input layer, a hidden layer and an output layer, wherein the hidden layer number is more than 1 layer; the first layer is an input layer, the last layer is an output layer, and the middle layer is a hidden layer; the input layer inputs a 6-dimensional state vector, each hidden layer carries out linear operation on the input, maps to the next hidden layer through a nonlinear function, and finally transmits the result of the hidden layer to the output layer to output a 3-dimensional control vector; the iterative formula for information propagation in the network is:
wherein z is (l) Representing the net input of layer I neurons, a (l) Representing the output of the layer i neurons,is a weight matrix from layer 1 to layer 1, where M l Representing the number of neurons in layer I, < >>Is the offset from layer 1 to layer 1, f l (. Cndot.) represents an activation function;
training the constructed deep neural network by using the training set obtained in the step S4, optimizing the network weight by using an Adam algorithm by means of an error back propagation mechanism, and using the mean square error as a loss function; setting the maximum training round number, recording the trained network of each round, solving the mean square error of each network on the verification set obtained in the step S4, reserving the deep neural network with the minimum mean square error on the verification set as the final obtained network, and testing the output effect of the final obtained network by using the sample in the test set.
6. The spacecraft back-off escape pulse solving method based on deep learning as claimed in claim 1, wherein the method is characterized by comprising the following steps: the step S6: the depth neural network obtained by final training is directly used for solving the short-range anti-intersection escape pulse of the escape spacecraft, and the measured relative state [ x y z v ] of the tracking spacecraft for the escape spacecraft, which contains 6 dimensions x v y v z ] T Inputting the finally obtained deep neural network, outputting an anti-intersection escape pulse [ delta ] with 3 dimensions Ex Δv Ey Δv Ez ] T 。
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