CN114115307A - Spacecraft back-intersection escape pulse solving method based on deep learning - Google Patents
Spacecraft back-intersection escape pulse solving method based on deep learning Download PDFInfo
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Abstract
The invention discloses a spacecraft back-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; selecting a large number of different initial relative states, solving the size and direction of the corresponding optimal escape pulse by using a numerical optimization technology to form a series of state quantity-control quantity data pairs; carrying out normalization processing on the data pairs to construct a deep learning sample set; constructing a deep neural network and carrying out full training; and solving the short-distance back-intersection 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 quickly generating an approximately optimal escape strategy in real time in an on-orbit mode for the spacecraft in the space countermeasure, and can effectively improve the survival capacity of the spacecraft in the future space countermeasure.
Description
Technical Field
The invention relates to the technical field of spacecraft orbit dynamics and control, in particular to a spacecraft back-intersection escape pulse solving method based on deep learning.
Background
In the future, the in-orbit spacecraft may face non-cooperative intersection of non-own units, and in order to maintain the safety of the spacecraft in the space, a close-range reverse intersection escape technology needs to be developed so as to improve the survival capability of the in-orbit spacecraft when facing the close-range non-cooperative intersection threat. The escape of the spacecraft in the reverse rendezvous mode means that the escaping spacecraft utilizes the self orbital maneuver capability to get rid of the approaching and close-range rendezvous of the tracking spacecraft with the orbital maneuver capability. The current method mainly comprises a pursuit game based on a differential countermeasure and a pulse maneuver evasion based on an optimal index.
In the pursuit escape game based on the differential strategy, the spacecraft is generally assumed to adopt continuous thrust control, the direct method, the indirect method, the semi-direct method and other methods are developed to solve and obtain the pursuit escape strategy with the optimal two parties, and the pursuit escape strategy has strict mathematical theory but has limitations: 1) the theory only solves for the saddle point solution, when the tracking spacecraft does not adopt the saddle point solution, the saddle point solution for the escaping spacecraft is not optimal any more, and the engineering significance is limited; 2) complicated numerical methods are needed for solving the pursuit escape game, the solving speed is low, the result cannot be obtained quickly on track, and the timeliness is poor. The pulse avoidance technology based on the optimal index is developed from research related to space debris collision avoidance, and the escape maneuvering pulse is optimized under the reasonable assumption of state measurement and approach strategy of the tracked spacecraft, so that the established index is optimal. The core of the method is to solve the optimization problem, and currently, global optimization algorithms such as heuristic algorithms and the like are generally used to avoid trapping local extrema, but the method also has the following defects: the numerical optimization algorithm generally has a large calculation amount, is difficult to realize the solution of the escape pulse in real time and quickly in an on-orbit manner, and can cause the consequence that the spacecraft cannot escape in time when the threat of non-cooperative intersection is met. Therefore, new technology with higher solving efficiency and capable of generating the back-intersection escape pulse in real time needs to be developed.
The deep learning technology with the deep neural network as a main representative model has strong representation capability and learning capability, and provides a new idea for efficient and real-time solution of the spacecraft backcross escape.
Disclosure of Invention
The invention provides a spacecraft back-intersection escape pulse solving method based on deep learning, which is used for solving back-intersection escape pulses when a spacecraft faces a non-cooperative intersection threat. The method comprises the steps of solving a double-layer mathematical programming problem describing optimal pulses through numerical values to construct a sample set, constructing a deep neural network and carrying out full training by using samples to obtain the deep neural network capable of fully representing the mapping relation between the relative state of the two pursuing-fleeing spacecraft and the escaping spacecraft back-rendezvous escaping pulses, and directly using the deep neural network for generating the escaping pulses.
In order to achieve the purpose, the invention provides a spacecraft backcross escape pulse solving method based on deep learning, which specifically comprises the following steps:
s1: establishing an orbit dynamics model of the close-range relative motion of the spacecraft, 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, the escape speed pulse size and direction of the escape spacecraft are used as optimization variables, the optimal speed pulse consumption for tracking the spacecraft to complete intersection is used as a target function, and a double-layer mathematical programming model is constructed;
s3: a large number of different initial relative states are selected, the magnitude 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: constructing a deep learning sample set by using the state quantity-control quantity data in the S3, carrying out normalization processing, 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 final deep neural network;
s6: and inputting the relative state of the currently measured tracking spacecraft to the escaping spacecraft into the finally obtained deep neural network S5, and outputting a back-crossing escaping pulse.
In a possible implementation manner, in the method for solving the aircraft backcross escape pulse based on the deep learning provided by the present invention, step S1 specifically includes:
under the complete central gravity field of the earth, the escaping spacecraft flies in a near-circular orbit and tracks the spacecraft in the vicinity of the escaping spacecraft. Selecting a virtual point which does circular orbit motion near the two spacecrafts, subtracting relative motion equations of the tracked spacecraft and the escaping spacecraft relative to the virtual point respectively to obtain a motion equation of the tracked spacecraft relative to the escaping spacecraft, wherein the motion equation can be described as follows by using a Clhessy-Wiltshire equation:
wherein x, y and z represent three components of a position vector of the tracked spacecraft relative to the escaping spacecraft in a virtual point orbit coordinate system, omega represents the circular orbit angular rate of a virtual point, and f represents the circular orbit angular rate of the virtual pointix,fiy,fizFor the control acceleration exerted on the spacecraft, i ═ P, E, P denoting the tracking spacecraft and E denoting the escape spacecraft.
Order state variable
Control quantity u ═ fPx-fEx,fPy-fEy,fPz-fEz]TT represents transposition; the above equation of relative motion can be written as:
wherein
Is a constant matrix.
According to the ordinary differential equation theory, the relative motion state transition equation can be obtained by solving the differential equation:
wherein t is0Is an initial time, X0Is an initial relative state, phi (t, t)0) As a state transition matrix, let υ ω (t-t)0) The state transition matrix is expressed as:
in a possible implementation manner, in the method for solving the anti-intersection escape pulse of the spacecraft based on the deep learning provided by the invention, the step S2 includes two sub-steps:
s201, performing mathematical modeling on a mode of tracking spacecraft multi-pulse approaching and intersecting, and constructing a bottom layer mathematical programming model, wherein an objective function is the total speed pulse size of the multi-pulse intersection, and optimization variables are each speed pulse time, each speed pulse size and each speed pulse direction.
S202, performing mathematical modeling on an escape mode of the escape spacecraft, and constructing an upper layer mathematical programming model, wherein an objective function is an optimal value of a bottom layer mathematical programming model, and optimization variables are the direction and the size of an escape pulse.
The step S201 specifically includes:
writing a relative motion state transition equation when the tracking spacecraft carries out orbital maneuver in a pulse control mode and the escape spacecraft does not have the orbital maneuver according to the formula (3):
wherein t isiTo track the time of a spacecraft impulse maneuver, i is 1, …, M is the total number of times the spacecraft impulse maneuver is tracked, Δ vPiThe velocity pulse vector for tracking the ith maneuver of the spacecraft comprises three components:
ΔvPi＝[ΔvPicosβcosα,ΔvPicosβsinα,ΔvPisinβ]T (6)
wherein Δ vPiThe magnitude of the ith speed pulse is, and alpha and beta are respectively an azimuth angle and a height angle of the ith speed pulse vector under a virtual point orbit coordinate system.
For convenience of representation, the subscript P of the velocity pulse is omitted, and the vector of M pulse times and the previous M-2 velocity pulses is taken as an optimization variable and is represented as [ t [ [ t ]1,…,tM,Δv1,…,ΔvM-2]TThe total number of 4M-6 optimization variables is calculated, the total speed increment of M pulses is taken as an optimization target, and the expression is as follows:
the constraint that the positions and the speeds of the tracked spacecraft and the escaping spacecraft are the same after the last pulse is considered, and the constraint is naturally established by introducing the specific relation between the last two pulses and the optimized variable, specifically:
considering the natural flight of the tracked spacecraft from the M-1 th pulse to the Mth pulse, the state transition can be expressed as:
X(tM)＝Φ(tM,tM-1)X(tM-1) (8)
writing is in the form of block matrix multiplication:
wherein R isM-1And RMThe position V of the tracked spacecraft relative to the escaping spacecraft is respectively the M-1 th pulse and the Mth pulseM-1 +And VM -The velocity of the tracked spacecraft relative to the escaping spacecraft after the M-1 th pulse and before the Mth pulse respectively, and the symbols "-" and "+" respectively represent before and after the pulse.
V can be solved reversely according to the formula (9)M -And VM-1 +：
In the formula (10), RM-1Can be calculated by the formula (5) according to the optimization variable, and if the positions of the two spacecrafts at the terminal moment are the same, the relative position vector R at the last pulseMIs a zero vector and a relative velocity vector v after the last pulseM +Is also zero vector, so V can be solvedM-1 +And VM -Further, the pulse velocity increments at the M-1 st and M-th times can be found:
v in formula (11)M-1 -And the aforementioned RM-1Again, the optimization variables are given by equation (5).
The last two pulses obtained according to the formula (11) imply that the position vector and the speed vector of the tracking spacecraft relative to the escaping spacecraft after the last pulse are zero, so that the constraint that the positions and the speeds of the tracking spacecraft and the escaping spacecraft are the same is ensured.
Therefore, the underlying mathematical programming model is built as:
s.t.
wherein T islimFor the set upper time limit for tracking spacecraft rendezvous, RLP (-) expression (10) (11) describes the process of solving for the last two pulses.
Wherein, the step S202 specifically includes:
escape pulse vector delta v of escape spacecraftEIn order to optimize the variables, a variable is composed of three components,
ΔvE＝[ΔvEcosβEcosαE,ΔvEcosβEsinαE,ΔvEsinβE]T (13)
wherein Δ vEFor escape velocity pulse size, αE,βEThe azimuth angle and the elevation angle of the escaping velocity pulse vector are respectively.
The optimized optimal value of the model (12) is taken as an objective function and is marked as JE＝f(ΔvE,αE,βE) Here, it is required to maximize the mathematical model, and the upper layer mathematical planning model can be constructed as follows:
max JE＝f(ΔvE,αE,βE)
s.t.
wherein Δ vmaxThe allowable upper limit of the escape pulse size.
In a possible implementation manner, in the method for solving the aircraft backcross escape pulse based on the deep learning provided by the present invention, the step S3 specifically includes:
after the orbit altitude of the given spacecraft and the meeting time upper limit of the tracking spacecraft are given, the model is numerically solved by the double-layer mathematical programming model provided in the step S2 by using a numerical optimization technology, namely 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 for the SQP algorithm to accurately search, and the relative states [ x, y, z, v ] of the two spacecrafts can be determinedx vy vz]TUniquely determining optimal escape pulse [ delta v ] of escape spacecraftEx ΔvEy ΔvEz]TAnd T denotes transposition. Therefore, different relative states are largely selected in the state space, and then the corresponding optimal escape pulses are solved respectively to form a series ofAnd a data pair formed by the 6-dimensional state vector and the 3-dimensional escape pulse vector, namely a state quantity-control quantity data pair.
The method for specifically taking the relative state comprises the following steps of describing a parameter [ r alpha ] of the relative state in a spherical coordinate systemr βr v αv βv]TCarrying out equal interval value taking, T represents transposition, and then converting to the original state space [ x y z vx vy vz]TWhere r is the distance between the two spacecraft, v is the relative velocity between the two spacecraft, αr，βr，αv，βvThe azimuth angle and the elevation angle of the relative position and the relative speed under the virtual point orbit coordinate system are respectively, and the conversion relationship is as follows:
in a possible implementation manner, in the method for solving the aircraft backcross escape pulse based on the deep learning provided by the present invention, the step S4 specifically includes:
after a large number of state quantity-control quantity data pairs are obtained, the state quantity is used as a sample characteristic, the control quantity is used as a sample label, each data pair forms a sample, and a large number of samples form a sample set. In order to eliminate the training difficulty caused by different data scales, the data in all samples are uniformly normalized, and the normalization formula is as follows:
wherein n is a sample number, xdAnd
denotes the d-th dimension, max (x), of the sample before and after normalization, respectivelyd) And min (x)d) Respectively representing the maximum and minimum values 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 the remaining samples are extracted as a verification set, and the rest samples form a testing set.
In a possible implementation manner, in the method for solving the aircraft backcross escape pulse based on the deep learning provided by the present invention, the step S5 specifically includes:
the type of the deep neural network is selected to be a feedforward neural network, the built neural network is composed of an input layer, a hidden layer and an output layer, and the number of the hidden layers is more than 1. 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 performs linear operation on the input and maps the input 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 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)Represents the output of the layer l neurons,
is a weight matrix from layer l-1 to layer l, where MlThe number of layer I neurons is expressed,
is the offset from layer l-1 to layer l, fl(. 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 (Linear) and a Tanh function.
After the deep neural network is constructed, training the network by using the training set obtained in the step S4, wherein the training of the network depends on an error back propagation mechanism, the network weight is optimized by using an Adam algorithm, and a Mean Square Error (MSE) is used as a loss function. The maximum number of training rounds is set, the networks trained in each round are recorded, the mean square error of each network on the verification set obtained in step S4 is calculated, and the network with the minimum mean square error on the verification set is considered to have the best generalization performance. And finally, reserving the deep neural network with the minimum mean square error on the verification set as a final obtained network, and testing the output effect of the final obtained network by using the samples in the test set.
In a possible implementation manner, in the method for solving the anti-intersection escape pulse of the spacecraft based on the deep learning provided by the invention, the step S6: the deep neural network obtained through final training is directly used for solving the close-range back-intersection escape pulse of the escaping spacecraft, and the measured relative state [ x, y, z, v and v ] of the tracking spacecraft to the escaping spacecraft, which contains 6 dimensions, is measuredx vy vz]TInputting the final deep neural network, and outputting an anti-intersection escape pulse [ delta v ] containing 3 dimensionsEx ΔvEy ΔvEz]T。
Has the advantages that:
1. the spacecraft back-rendezvous escape pulse solving method based on deep learning disclosed by the invention is used for training a deep neural network to fit the generation rule of short-distance back-rendezvous escape pulses, and directly outputting the escape pulses by using the fully-trained neural network, so that 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 back-rendezvous escape strategy.
2. According to the spacecraft back-rendezvous escape pulse solving method based on deep learning, the solved back-rendezvous escape pulse has the characteristic of approximate global optimum, the cost required by tracking the spacecraft to complete rendezvous can be maximized, and the survival capacity of the escape spacecraft is effectively improved.
Drawings
FIG. 1 is a flow chart of a method for solving a spacecraft backcross escape pulse based on deep learning, which is disclosed by the invention;
FIG. 2 is a schematic diagram of a dynamic model for establishing a close-range relative motion orbit;
FIG. 3 is a schematic diagram of the geometrical significance of the azimuth and elevation of the escaping pulse;
FIG. 4 is a flow chart of a two-level mathematical programming problem solving using comprehensive learning particle swarm optimization and sequential quadratic programming values;
FIG. 5 is a flow chart of constructing a sample;
FIG. 6 is a graph of error variation over the validation set during the training of the neural network 1;
FIG. 7 is a graph of error variation over a validation set during training of the neural network 2;
FIG. 8 is a trajectory diagram of the escaping spacecraft in the simulation example, which applies the escaping pulse calculated by the neural network 1, tracks the spacecraft for intersection, and the two parties in a virtual point orbit coordinate system;
FIG. 9 is a trace diagram of the escape spacecraft in the simulation example, which applies the escape pulse calculated by the neural network 2, tracks the spacecraft for intersection, and tracks the spacecraft and the spacecraft in a virtual point orbit coordinate system;
fig. 10 is a graph showing that the azimuth angle of the escape pulse obtained by the fixed neural network 1 is unchanged, and the size of the minimum velocity pulse required by the corresponding tracking spacecraft to complete the intersection changes with the altitude angle;
fig. 11 is a graph showing that the minimum velocity pulse size required for the tracking spacecraft to complete the intersection changes with the azimuth angle while the altitude angle of the escape pulse obtained by the fixed neural network 1 is unchanged; (ii) a
Fig. 12 is a graph showing that the minimum velocity pulse size required for the tracking spacecraft to complete the intersection changes with the altitude angle while the azimuth angle of the escape pulse obtained by the fixed neural network 2 is unchanged;
fig. 13 is a graph showing that the altitude angle of the escape pulse obtained by the fixed neural network 2 is not changed, and the size of the minimum velocity pulse required by the tracking spacecraft to complete the intersection changes with the azimuth angle.
Detailed Description
The technical solutions in 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 obvious that the described embodiments are only illustrative and are not intended to limit the present invention.
The invention provides a spacecraft backcross escape pulse solving method based on deep learning, which comprises the following steps as shown in figure 1:
s1: establishing an orbit dynamics model of the close-range relative motion of the spacecraft, 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 complete central gravity field of the earth, the escaping spacecraft flies in a near-circular orbit and tracks the spacecraft in the vicinity of the escaping spacecraft. As shown in fig. 2, a virtual point O which orbits circularly is selected near two spacecraft, a virtual point orbit coordinate system is established, the relative motion equations of the tracked spacecraft P and the escaped spacecraft E with respect to the virtual point are subtracted from each other, so as to obtain the motion equation of the tracked spacecraft with respect to the escaped spacecraft, which is described as follows by using the Clohessy-Wiltshire equation:
wherein x, y and z represent three components of a position vector of the tracked spacecraft relative to the escaping spacecraft in a virtual point orbit coordinate system, omega represents the circular orbit angular rate of a virtual point, and f represents the circular orbit angular rate of the virtual pointix,fiy,fizFor the control acceleration exerted on the spacecraft, i ═ P, E, P denoting the tracking spacecraft and E denoting the escape spacecraft.
Order state variable
Control quantity u ═ fPx-fEx,fPy-fEy,fPz-fEz]TT represents transposition; the above equation of relative motion can be written as:
wherein
Is a constant matrix.
According to the ordinary differential equation theory, the relative motion state transition equation can be written by the solution of the differential equation:
wherein t is0Is an initial time, X0Is an initial relative state, phi (t, t)0) As a state transition matrix, let υ ω (t-t)0) The state transition matrix is expressed as:
s2: according to the relative motion state transfer equation in the step S1, the escape speed pulse size and direction of the escape spacecraft are used as optimization variables, the optimal speed pulse consumption for tracking the spacecraft to complete intersection is used as a target function, and a double-layer mathematical programming model is constructed;
the step S2 specifically includes two substeps:
s201, performing mathematical modeling on a mode of tracking spacecraft multi-pulse approaching and intersecting, and constructing a bottom layer mathematical programming model, wherein an objective function is the total speed pulse size of the multi-pulse intersection, and optimization variables are each speed pulse time, each speed pulse size and each speed pulse direction.
S202, performing mathematical modeling on an escape mode of the escape spacecraft, and constructing an upper layer mathematical programming model, wherein an objective function is an optimal value of a bottom layer mathematical programming model, and optimization variables are the direction and the size of an escape pulse.
The step S201 specifically includes:
writing a relative motion state transition equation when the tracking spacecraft carries out orbital maneuver in a pulse control mode and the escape spacecraft does not have the orbital maneuver according to the formula (3):
wherein t isiTo track the time of a spacecraft impulse maneuver, i 1.. M, M is the total number of times the spacecraft impulse maneuver is tracked, Δ vPiThe velocity pulse vector for tracking the ith maneuver of the spacecraft comprises three components:
ΔvPi＝[ΔvPicosβcosα,ΔvPicosβsinα,ΔvPisinβ]T (6)
wherein Δ vPiThe magnitude of the ith speed pulse is shown, alpha and beta are respectively an azimuth angle and a high-low angle of the ith speed pulse vector under a virtual point orbit coordinate system, and the geometric meaning of the ith speed pulse vector is the same as the azimuth angle and the high-low angle of the escape pulse of the escape spacecraft, which is shown in figure 3.
For convenience of representation, the subscript P of the velocity pulse is omitted, and the vector of M pulse times and the previous M-2 velocity pulses is taken as an optimization variable and is represented as [ t [ [ t ]1,…,tM,Δv1,…,ΔvM-2]TThe total number of 4M-6 optimization variables is calculated, the total speed increment of M pulses is taken as an optimization target, and the expression is as follows:
the constraint that the positions and the speeds of the tracked spacecraft and the escaping spacecraft are the same after the last pulse is considered, and the constraint is naturally established by introducing the specific relation between the last two pulses and the optimized variable, specifically:
considering the natural flight of the tracked spacecraft from the M-1 th pulse to the Mth pulse, the state transition can be expressed as:
X(tM)＝Φ(tM,tM-1)X(tM-1) (8)
writing is in the form of block matrix multiplication:
wherein R isM-1And RMThe position V of the tracked spacecraft relative to the escaping spacecraft is respectively the M-1 th pulse and the Mth pulseM-1 +And VM -The velocity of the tracked spacecraft relative to the escaping spacecraft after the M-1 th pulse and before the Mth pulse respectively, and the symbols "-" and "+" respectively represent before and after the pulse.
V can be solved reversely according to the formula (9)M -And VM-1 +：
In the formula (10), RM-1Can be calculated by the formula (5) according to the optimization variable, and if the positions of the two spacecrafts at the terminal moment are the same, the relative position vector R at the last pulseMIs a zero vector and a relative velocity vector v after the last pulseM +Is also zero vector, so V can be solvedM-1 +And VM -Further, the pulse velocity increments at the M-1 st and M-th times can be found:
v in formula (11)M-1 -And the aforementioned RM-1Again, the optimization variables are given by equation (5).
The last two pulses obtained according to the formula (11) imply that the position vector and the speed vector of the tracking spacecraft relative to the escaping spacecraft after the last pulse are zero, so that the constraint that the positions and the speeds of the tracking spacecraft and the escaping spacecraft are the same is ensured.
Therefore, the underlying mathematical programming model is built as:
s.t.
wherein T islimFor the set upper time limit for tracking spacecraft rendezvous, RLP (-) expression (10) (11) describes the process of solving for the last two pulses.
Wherein, the step S202 specifically includes:
escape pulse vector delta v of escape spacecraftEIn order to optimize the variables, a variable is composed of three components,
ΔvE＝[ΔvEcosβEcosαE,ΔvE cosβE sinαE,ΔvEsinβE]T (13)
wherein Δ vEFor escape velocity pulse size, αE,βEThe azimuth angle and the elevation angle of the escaping velocity pulse vector are respectively.
The optimized optimal value of the model (12) is taken as an objective function and is marked as JE＝f(ΔvE,αE,βE) Here, it is required to maximize the mathematical model, and the upper layer mathematical planning model can be constructed as follows:
max JE＝f(ΔvE,αE,βE)
s.t.
wherein Δ vmaxThe allowable upper limit of the escape pulse size.
S3: a large number of different initial relative states are selected, the magnitude 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 altitude of the spacecraft is given and the meeting time upper limit of the tracked spacecraft is reached, the model is numerically solved by the double-layer mathematical programming model provided in the step S2 by using a numerical optimization technology, namely 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 for the SQP algorithm to accurately search, the flow diagram is shown in figure 4, and therefore the relative states [ x y z v ] of the two spacecrafts can be obtainedx vy vz]TUniquely determining optimal escape pulse [ delta v ] of escape spacecraftEx ΔvEy ΔvEz]TAnd T denotes transposition. Therefore, different relative states are largely selected in the state space, and then the corresponding optimal escape pulses are solved respectively to form a series of data pairs formed by 6-dimensional state vectors and 3-dimensional escape pulse vectors, namely state quantity-control quantity data pairs.
The method for specifically taking the relative state comprises the following steps of describing a parameter [ r alpha ] of the relative state in a spherical coordinate systemr βr v αv βv]TCarrying out equal interval value taking, T represents transposition, and then converting to the original state space [ x y z vx vy vz]TWhere r is the distance between the two spacecraft, v is the relative velocity between the two spacecraft, αr，βr，αv，βvThe azimuth angle and the elevation angle of the relative position and the relative speed in the virtual point orbit coordinate system are respectively, and the geometrical significance is consistent with that described in the figure 3. The conversion relationship is as follows:
s4: constructing a deep learning sample set by using the state quantity-control quantity data in the S3, carrying out normalization processing, 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 used as a sample characteristic, the control quantity is used as a sample label, each data pair forms a sample, and a flow of generating a sample is shown in fig. 5, wherein a large number of samples form a sample set. In order to eliminate the training difficulty caused by different data scales, the data in all samples are uniformly normalized, and the normalization formula is as follows:
wherein n is a sample number, xdAnd
denotes the d-th dimension, max (x), of the sample before and after normalization, respectivelyd) And min (x)d) Respectively representing the maximum and minimum values 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 the remaining samples are extracted as a verification set, and the rest samples form a testing 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 final deep neural network;
the step S5 specifically includes:
the type of the deep neural network is selected to be a feedforward neural network, the built neural network is composed of an input layer, a hidden layer and an output layer, and the number of the hidden layers is more than 1. 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 performs linear operation on the input and maps the input 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 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)Represents the output of the layer l neurons,
is a weight matrix from layer l-1 to layer l, where MlThe number of layer I neurons is expressed,
is the offset from layer l-1 to layer l, fl(. 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 (Linear) and a Tanh function.
After the deep neural network is constructed, training the network by using the training set obtained in the step S4, wherein the training of the network depends on an error back propagation mechanism, the network weight is optimized by using an Adam algorithm, and a Mean Square Error (MSE) is used as a loss function. The maximum number of training rounds is set, the networks trained in each round are recorded, the mean square error of each network on the verification set obtained in step S4 is calculated, and the network with the minimum mean square error on the verification set is considered to have the best generalization performance. And finally, reserving the deep neural network with the minimum mean square error on the verification set as a final obtained network, and testing the output effect of the final obtained network by using the samples in the test set.
S6: and inputting the relative state of the currently measured tracking spacecraft to the escaping spacecraft into the finally obtained deep neural network S5, and outputting a back-crossing escaping pulse.
The step S6 specifically includes:
the deep neural network obtained by final training is directly used for solving the short-distance back-intersection escape pulse of the escaping spacecraft, and the detected package of the tracking spacecraft on the escaping spacecraft isRelative state [ x y z v ] containing 6 dimensionsx vy vz]TInputting the final deep neural network, and outputting an anti-intersection escape pulse [ delta v ] containing 3 dimensionsEx ΔvE yΔvEz]T。
The effectiveness of the proposed method is illustrated by a simulation example.
Some parameters are set as: the gravity constant is taken as mu-398600.5-109m3/s2Radius of the earth is taken as Re6371.11km, current time t0The orbit elements of the escaped spacecraft and the tracked spacecraft, where the escaped spacecraft moves on a circular orbit with an orbit height of 300km, are set to 0, and the virtual points are set to coincide with the escaped spacecraft when no maneuvering has occurred, are shown in table 1. Setting an upper time limit T for rendezvous of a tracked spacecraftlim1800s, the number of pulses is at most 3, the tracking spacecraft does not set the upper limit of the size of the allowable maneuvering pulses, and the upper limit of the size of the allowable maneuvering pulses of the escaping spacecraft is set to be 50 m/s.
The relative position of the tracked spacecraft relative to the escaping spacecraft at the current moment under the virtual point orbit coordinate system can be obtained through calculation as [23.34, -34.99, -15.30 ]]Tkm, relative velocity of [ -8.60,1.41,26.79]Tm/s, the distance between the two parties is 44.76km at the current moment.
TABLE 1
| Track element | Escape spacecraft | Tracking spacecraft |
| Semi-major axis/km | 6671.11 | 6687.20 |
| |
0 | 0.0001 |
| Inclination angle of rail-° | 30 | 30.3 |
| The right |
0 | 0 |
| Argument/degree of |
90 | 80 |
| True angle/degree of approach | 1.8 | 12 |
In step S1, the orbital angular rate ω is 0.0011587S from the height of the virtual point circle orbit-1And (4) solving a state transition matrix by substituting the equation (4) so as to determine a relative motion state transition equation.
According to step S2, models (12) and (14) can be constructed from the above-obtained transition equation of the relative motion state, forming a two-layer mathematical programming problem.
According to step S3, the 6 dimensions of the relative state are discretized. Firstly, a parameter [ r alpha ] describing relative state under spherical coordinatesr βr v αv βv]TCarrying out equal interval value taking, wherein r is taken from 10km to 50km at intervals of 10km and alpharFrom 0 radian spaced by 2 pi/15 radian to 2 pi radian, betarSpaced apart by pi/10 radians from-pi/2 radiansThe value is equal to pi/2 radian, v is equal to 35m/s from 11m/s at intervals of 3m/s, and alpha isvFrom 0 radian spaced by 2 pi/15 radian to 2 pi radian, betavThe radian is changed from-pi/2 radian to pi/2 radian at intervals of pi/10 radians, and then the radian is converted into the original state space [ x y z v ] according to the formula (15)x vy vz]TIn (1). Substituting all the values of the relative states into a double-layer mathematical programming model, and performing numerical solution on the model by using a mixed algorithm containing Comprehensive Learning Particle Swarm Optimization (CLPSO) and Sequential Quadratic Programming (SQP) to obtain the optimal control quantity corresponding to each state quantity, and finally forming 1393920 state quantity-control quantity data pairs.
According to step S4, all data pairs are normalized by equation (16), 80% of the samples (1115136) are randomly selected to form a training set, 10% (139392) of the remaining data pairs are randomly selected 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 and is provided with 8 hidden layers, each hidden layer is provided with 64 neurons, the neuron activation function of the hidden layer is a Tanh function, and the neuron activation function of the output layer is also a Tanh function; the other network is marked as a neural network 2 and is provided with 10 hidden layers, each hidden layer is provided with 256 neurons, the neuron activation function of the hidden layer is a ReLU function, and the neuron activation function of the output layer is a Linear function. And (3) training the two network architectures by using the training set obtained in the previous 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 moment estimation and the second moment estimation are respectively set to be 0.9 and 0.999, the maximum training round number is 50, the network with the minimum mean square error output on the verification set is taken as the network finally finished by training, and the test of the output error 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 validation set and the mean square error of the finally trained network on the test set are shown in table 2, and fig. 6 and 7 are error change graphs on the validation set in the training process of the neural network 1 and the neural network 2, respectively.
TABLE 2
After the deep neural networks which are fully trained are obtained, the state (relative position and relative speed under a virtual point orbit system) of the spacecraft tracked at the current moment relative to the escaping spacecraft is input into the two deep neural networks to obtain escaping pulses of the escaping spacecraft, wherein the output result of the neural network 1 is delta vE1＝50m/s，αE1＝3.3712rad，βE1The output of the neural network 2 is Δ v at-0.7123 radE1＝50m/s，αE1＝3.3493rad，βE1At-0.7266 rad, it can be seen that the escape pulses output by the two trained neural networks 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 velocity pulse consumed by the spacecraft to complete rendezvous becomes large enough after the escape spacecraft applies the escape pulse, so that the rendezvous difficulty is improved, and the survival capacity of the escape spacecraft is improved. After the escape spacecraft applies the escape pulse obtained by the neural network 1, the minimum speed pulse size of the tracked spacecraft for meeting is 124.7342 m/s; after applying the escape pulse obtained by the neural network 2, the minimum velocity pulse size for the tracking spacecraft to complete the intersection is 124.7444 m/s. And when the escaping spacecraft does not apply the escaping pulse, the minimum speed pulse size of the tracking spacecraft for completing the rendezvous is calculated to be 74.7456m/s, and the cost of the tracking spacecraft for completing the rendezvous is obviously increased after the escaping pulse solved by the deep neural network is applied. Fig. 8 and 9 show the trajectories of the escaping spacecraft and the neural network 1 and the neural network 2 in the virtual point orbit coordinate system when the escaping spacecraft applies the escaping pulse calculated by the neural network and the neural network 2 and the tracking spacecraft adopts at most 3 pulses to complete the intersection.
To further illustrate the approximate optimality of the escape pulse solved by the method of the present invention, especially when the allowed escape pulse size is fixedIn the case of (1), the approximate optimality of the escape direction is found, we fix the size of the escape pulse, change the azimuth angle and elevation angle of the escape pulse vector, construct different escape pulses, compare the minimum velocity pulse size required for the tracking spacecraft to complete the rendezvous after they are applied by the escape spacecraft, and the results are presented in fig. 10 to 13, where fig. 10 is the azimuth angle α of the escape pulse found by the fixed neural network 1E1Constant, but high and low angle betaE1Taking the value from-pi/2 radian to pi/2 radian, and correspondingly tracking the minimum speed pulse size required by the spacecraft to finish the intersection; FIG. 11 shows the elevation angle β of the escape pulse obtained by the fixed neural network 1E1Constant, but the azimuth angle αE1Taking the value from 0 radian to 2 pi radian, and correspondingly tracking the minimum speed pulse size required by the spacecraft to finish intersection; fig. 12 and 13 are representations of the results corresponding to the neural network 2. It can be seen from the figure that, in both the neural network 1 and the neural network 2, the azimuth angle and the elevation angle of the solved escape pulse are close to the optimal values, which is an approximate solution for maximizing the pulse consumed by the tracking spacecraft to complete the intersection, and the approximate optimality of the escape pulse solved by the method provided by the invention is verified.
Table 3 reflects the time length required for solving escape pulses once by using the neural network trained by the genetic algorithm, the particle swarm optimization algorithm and the method provided by the invention, and the cpu model of the used computer is i 7-8700.
TABLE 3
As can be seen from the above table, the method provided by the invention also has the characteristic of extremely high calculation speed, and can be used for generating an approximately optimal escape pulse in real time by the in-orbit spacecraft, thereby greatly shortening the reaction time when the in-orbit spacecraft encounters a threat and effectively improving the survival capability of the in-orbit spacecraft.
In conclusion, the method provided by the invention has the characteristics of good effect, approximate optimization, extremely high speed and the like in the aspect of solving the short-distance back-intersection escape pulse of the spacecraft, has good engineering application value and has popularization prospect.
The basic principle and implementation steps of the invention are shown above, and the validity and practicability of the method provided by the invention are verified by using examples. It will be apparent to those skilled in the art that various changes and modifications may be made in the invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (7)
1. A spacecraft back-intersection escape pulse solving method based on deep learning is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing an orbit dynamics model of the close-range relative motion of the spacecraft, 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, the escape speed pulse size and direction of the escape spacecraft are used as optimization variables, the optimal speed pulse consumption for tracking the spacecraft to complete intersection is used as a target function, and a double-layer mathematical programming model is constructed;
s3: a large number of different initial relative states are selected, the magnitude 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: constructing a deep learning sample set by using the state quantity-control quantity data in the S3, carrying out normalization processing, 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 final deep neural network;
s6: and inputting the relative state of the currently measured tracking spacecraft to the escaping spacecraft into the finally obtained deep neural network S5, and outputting a back-crossing escaping pulse.
2. The method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: the step S1 specifically includes:
under the complete gravity field of the earth, selecting a virtual point moving on a circular orbit near a tracking spacecraft and an escaping spacecraft which move in a close range, subtracting a relative motion equation of the tracking spacecraft and the escaping spacecraft relative to the point, and obtaining a relative motion orbit dynamics model of the tracking spacecraft relative to the escaping spacecraft, which is described by Clohessy-Wiltshire equation; defining the relative position and the relative speed as state variables, and writing a relative motion state transition equation according to an ordinary differential equation theory:
wherein t is0Is an initial time, X0Is an initial relative state, phi (t, t)0) A state transition matrix, B a constant matrix,
let υ be ω (t-t)0) The state transition matrix is expressed as:
3. the method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: in the step S2, a two-layer mathematical programming model is constructed, which specifically includes two sub-steps:
s201, performing mathematical modeling on a mode of tracking spacecraft multi-pulse approaching and rendezvous, and constructing a bottom-layer mathematical programming model, wherein an objective function is the total speed pulse size of the multi-pulse rendezvous, and optimization variables are each speed pulse time, each speed pulse size and each speed pulse direction;
s202, performing mathematical modeling on an escape mode of the escape spacecraft, and constructing an upper layer mathematical programming model, wherein an objective function is an optimal value of a bottom layer mathematical programming model, and optimization variables are the direction and the size of an escape pulse;
the step S201 specifically includes:
writing a relative motion state transition equation when the tracking spacecraft carries out orbital maneuver in a pulse control mode and the escape spacecraft does not have the orbital maneuver according to the formula (1):
wherein t isiTo track the time of a spacecraft impulse maneuver, i is 1, …, M is the total number of times the spacecraft impulse maneuver is tracked, Δ vPiThe velocity pulse vector for tracking the ith maneuver of the spacecraft comprises three components:
ΔvPi＝[ΔvPicosβcosα,ΔvPicosβsinα,ΔvPisinβ]T (4)
wherein Δ vPiThe magnitude of the ith speed pulse is, and alpha and beta are respectively an azimuth angle and a height angle of the ith speed pulse vector under a virtual point orbit coordinate system;
for convenience of representation, the subscript P of the velocity pulse is omitted, and the vector of M pulse times and the previous M-2 velocity pulses is taken as an optimization variable and is represented as [ t [ [ t ]1,...,tM,Δv1,...,ΔvM-2]TTaking the total speed increment of the M pulses as an optimization target, the expression is as follows:
adding constraint to limit the positions and the speeds of the tracked spacecraft and the escaped spacecraft after the last pulse to be the same, specifically:
writing the state transition of natural flight after the M-1 th pulse of the tracking spacecraft to before the M-th pulse:
X(tM)＝Φ(tM,tM-1)X(tM-1) (6)
expressed in the form of block matrix multiplication:
wherein R isM-1And RMThe position V of the tracked spacecraft relative to the escaping spacecraft is respectively the M-1 th pulse and the Mth pulseM-1 +And VM -The speed of the tracked spacecraft relative to the escaping spacecraft after the M-1 th pulse and before the Mth pulse respectively, and the symbols "-" and "+" respectively represent before and after the pulse;
reverse decomposition of V according to formula (7)M -And VM-1 +：
In the formula (8), RM-1According to the optimized variable, the relative position vector R of the last pulse is determined by the formula (3) according to the condition that the relative positions and the speeds of the two spacecrafts at the terminal moment are the sameMIs a zero vector and a relative velocity vector v after the last pulseM +For zero vector, solve for VM-1 +And VM -Then, the pulse velocity increment of the M-1 th and M-th times is obtained:
v in formula (9)M-1 -The same applies to the optimization variables, which are determined by equation (3);
the established underlying mathematical programming model is expressed as:
s.t.
wherein T islimFor the set upper time limit of the spacecraft tracking meeting, RLP (-) expression (8) (9) describes the process of solving the last two pulses;
wherein, the step S202 specifically includes:
escape pulse vector delta v of escape spacecraftEIn order to optimize the variables, a variable is composed of three components,
ΔvE＝[ΔvEcosβEcosαE,ΔvEcosβEsinαE,ΔvEsinβE]T (11)
wherein Δ vEFor escape velocity pulse size, αE,βERespectively an azimuth angle and a high-low angle of the escape velocity pulse vector;
the optimal value optimized in the model (10) is taken as an objective function and is marked as JE＝f(ΔvE,αE,βE) And constructing a top layer mathematical programming model as follows:
max JE＝f(ΔvE,αE,βE)
s.t.
wherein Δ vmaxThe allowable upper limit of the escape pulse size.
4. The method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: the step S3 specifically includes:
after the orbit height of the spacecraft is given and the meeting time upper limit of the tracked spacecraft is set, the model is numerically solved by the double-layer mathematical programming model provided in the step S2 through a numerical optimization technology, and the relative state [ x, y, z and v ] of the two spacecraftsx vy vz]TUniquely determining optimal escape pulse [ delta v ] of escape spacecraftEx ΔvEy ΔvEz]TT represents transposition; selecting a large number of different relative states in a state space, and then respectively solving out 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 specific method for acquiring the relative state is to describe the parameter [ r alpha ] of the relative state in a spherical coordinate systemr βr v αv βv]TCarrying out equal interval value taking, and then converting to the original state space [ x y z vx vy vz]TWhere r is the distance between the two spacecraft, v is the relative velocity between the two spacecraft, αr，βr，αv，βvThe azimuth angle and the elevation angle of the relative position and the relative speed under the virtual point orbit coordinate system are respectively, and the conversion relationship is as follows:
5. the method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: the step S4 specifically includes:
after a large number of state quantity-control quantity data pairs are obtained, the state quantity in the state quantity-control quantity data pairs is used as sample characteristics, the control quantity is used as a sample label, each data pair forms a sample, and a sample set containing a large number of samples is formed; and uniformly normalizing the data in all the samples, wherein the normalization formula is as follows:
wherein n is a sample number, xdAnd
denotes the d-th dimension, max (x), of the sample before and after normalization, respectivelyd) And min (x)d) Respectively representing the maximum value and the minimum value on 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 the remaining samples are extracted as a verification set, and the rest samples form a testing set.
6. The method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: the step S5 specifically includes:
selecting a deep neural network type as a feedforward neural network, wherein the built neural network consists of an input layer, a hidden layer and an output layer, and the number of the hidden layers is more than 1; the first layer is an input layer, the last layer is an output layer, and the middle layer is a hidden layer; inputting a 6-dimensional state vector by an input layer, performing linear operation on the input by each hidden layer, mapping the input to the next hidden layer through a nonlinear function, transmitting the result of the hidden layer to an output layer, and outputting 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)Represents the output of the layer l neurons,
is a weight matrix from layer l-1 to layer l, where MlThe number of layer I neurons is expressed,
is the offset from layer l-1 to layer l, fl(. -) represents an activation function;
training the constructed deep neural network by using the training set obtained in the step S4, wherein the training of the network depends on an error back propagation mechanism, the network weight is optimized by using an Adam algorithm, and the mean square error is used as a loss function; setting the maximum training turn number, recording the networks trained in each turn, 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 network, and testing the output effect of the final network by using the samples in the test set.
7. The method for solving the spacecraft backcross escape pulse based on the deep learning as claimed in claim 1, wherein: the step S6: the deep neural network obtained through final training is directly used for solving the close-range back-intersection escape pulse of the escaping spacecraft, and the measured relative state [ x, y, z, v and v ] of the tracking spacecraft to the escaping spacecraft, which contains 6 dimensions, is measuredx vy vz]TInputting the final deep neural network, and outputting an anti-intersection escape pulse [ delta v ] containing 3 dimensionsEx ΔvEyΔvEz]T。
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