A method to improve the calculation speed of space rendezvous and docking model predictive control

Abstract

The present invention discloses a method for improving the speed of space rendezvous and docking model predictive control calculation. During the close-range rendezvous and docking process of spacecraft, the relative motion dynamics between the tracking spacecraft and the target spacecraft are given by the C-W equation. The targets at this location include rotating targets and stationary targets. Then, the space cone constraint, velocity constraint and control saturation constraint are modeled respectively. Then, the tracking spacecraft is given a control implementation method for following the target rotation or approaching a point near the stationary target by the model predictive control method. After the control method is given, an initial disturbance is added to the nominal trajectory, and the data set required for the training of the machine learning method is collected. For the training of the neural network, behavioral cloning or inverse reinforcement learning can be used. The above two methods belong to imitation learning methods. The approximate initial value of the quadratic programming problem in the corresponding model predictive control solution process can be obtained by the trained neural network, thereby improving the solution speed of the model predictive control.

Description

Technical Field

[0001] The invention relates to the field of aerospace technology, and in particular to a method for improving the calculation speed of space rendezvous and docking model prediction control. Background Art

[0002] For future space missions, small spacecraft that can autonomously reach non-cooperative targets are the focus of many scholars. Such spacecraft usually do not have strong maneuvering capabilities, and their onboard computers have limited computing power. The process of tracking a spacecraft approaching a target in a complex environment requires consideration of multiple constraints, and the solution of multi-constraint problems often has a large computational overhead. Model predictive control technology is a powerful method for dealing with constrained systems under the framework of optimization theory, reflecting the development of constraint control research from feedback stabilization to system optimization. The greatest attraction of model predictive control lies in its ability to effectively handle explicit constraints, which comes from the model's prediction of the future dynamic behavior of the system and the addition of constraints to future inputs, outputs or state variables. At the same time, the rise of machine learning algorithms has provided new ideas for solving optimal control problems. Through deep neural networks, the control input at each moment can directly map the current control output to achieve relatively good control results. Pre-trained neural networks can have excellent characteristics in generalization performance. In addition, their low computing power consumption and high computing speed for online applications bring broad prospects for their application in space maneuvers.

[0003] But in general, for the problem of close approach and rendezvous and docking in space, the computational overhead of model predictive control is large, and it requires a lot of computing resources; the practical application of machine learning methods is limited by their poor interpretability and difficulty in ensuring robustness. At present, it has not been widely and deeply studied to propose a joint algorithm of model predictive control and machine learning for the problem of close approach and rendezvous and docking of spacecraft. Summary of the invention

[0004] The purpose of the present invention is to provide a method for improving the calculation speed of model predictive control of space rendezvous and docking, so as to overcome the lack of extensive and in-depth research on close approach and rendezvous and docking of spacecraft in the prior art, and the large overhead of model predictive control. The present invention provides initial values ​​for the quadratic programming problem of model predictive control through a machine learning method, and the initial values ​​are closer to the true solution than random initial values ​​or zero initial values, thereby improving calculation efficiency and reducing overhead.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for improving the prediction control operation speed of a space rendezvous and docking model comprises the following steps:

[0007] S1: Establish the relative dynamic equations of the spacecraft rendezvous and docking process;

[0008] S2: Establish the target posture dynamics model and obtain the position of the intersection point in the local horizontal-local vertical coordinate system;

[0009] S3: Modeling of space cone constraints, velocity constraints, and control saturation constraints;

[0010] S4: Based on the S1 relative dynamics equation and the S2 target attitude dynamics model, a model predictive control performance index function is established. Then, the S3 space cone constraint model, velocity constraint model, control saturation constraint model and the model predictive control performance index function are combined. Through the model predictive control method, a control implementation method for the spacecraft to follow the target rotation or approach a stationary target is given.

[0011] S5: Obtain multiple spacecraft nominal trajectories, and add disturbances to the initial state of each spacecraft nominal trajectory, combine the control implementation method obtained in S4, obtain the running trajectory under each disturbance, collect the state and control sequence of each control moment in the trajectory as a training set, perform network training on the training set, and obtain the output value of the neural network;

[0012] S6: Approximate the output value of the neural network and substitute the approximate output value of the neural network into the quadratic programming operation, which reduces the number of iterations of the quadratic programming and thus improves the solution speed of the model predictive control.

[0013] Preferably, the relative kinetic equation in S1 is established based on the CW equation.

[0014] Preferably, the relative kinetic equation in S1 is:

[0015]

[0016]

[0017]

[0018] Where n is the orbital angular velocity m c To track the mass of the spacecraft, f is the thrust, u is the control input, and the subscripts x, y, and z of f and u represent the components in the local horizontal-local vertical coordinate system. is the acceleration of the spacecraft in the x direction, is the acceleration of the spacecraft in the y direction, is the acceleration of the spacecraft in the z direction, is the velocity of the spacecraft in the y direction, is the velocity of the spacecraft in the x direction.

[0019] Preferably, the position of the intersection point in the local horizontal-local vertical coordinate system is obtained as follows:

[0020] Firstly, the attitude transfer matrix of the orbital inertial coordinate system to the target body coordinate system and the attitude transfer matrix of the orbital inertial coordinate system to the local horizontal-local vertical coordinate system are obtained. The intersection point position is initially defined in the target body coordinate system. Then, the expression of the intersection point in the local horizontal-local vertical coordinate system is obtained through the target attitude dynamics equation.

[0021] Preferably, the space cone constraint is satisfied, and the spacecraft is always in the space cone when rendezvousing with the target.

[0022] Preferably, the speed constraint satisfies:

[0023]

[0024] Where V max is the maximum speed at a single moment, X(k) is the state of the spacecraft at moment k, and E 3 is the three-dimensional unit matrix, and H is the coefficient of the quadratic term of the index function.

[0025] Preferably, the control saturation constraint satisfies

[0026]

[0027] Among them, E 3 is a three-dimensional unit matrix, is the average control output of the spacecraft, and U(k) is the control output of the spacecraft at time k.

[0028] Preferably, the S4 model predictive control performance index function is:

[0029]

[0030] (Y(k+i|k) is the output vector of the i-th step after time k, ρ p (k+i|k) is the target position of the i-th step after time k, ρ p is the target position vector, Q i is the position-dependent positive definite matrix, N p is the state prediction step length, N c is the control prediction step length, U(k+i|k) is the control amount of the i-th step after time k, and R i is the control-related positive definite matrix.

[0031] Preferably, the S4 control implementation method is:

[0032]

[0033]

[0034] Among them, G is the left side of the constraint equation, g is the right side of the constraint equation, and Hs is the velocity constraint matrix, B s is the augmented input matrix, A cac is the collision avoidance matrix, C s , is the average control output of the spacecraft, is the average maximum velocity, X(k) is the state of the spacecraft at time k, W is the constant matrix, h is the coefficient of the first-order term of the index function, M is the position vector, and U s (k) The control quantity at time k, H is the coefficient of the quadratic term of the indicator function.

[0035] Preferably, the network training of S5 is performed by selecting one of two methods, namely, performing network training by using a control sequence network and performing network training by using a real-time control network.

[0036] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a method for improving the speed of model predictive control calculation for space rendezvous and docking. During the close-range rendezvous and docking of spacecraft, the relative motion dynamics between the tracking spacecraft and the target spacecraft are given by the CW equation. The targets here include rotating targets and stationary targets. Then, the space cone constraint, velocity constraint and control saturation constraint are modeled respectively. Then, the control implementation method for the tracking spacecraft to follow the target rotation or approach a point near the stationary target is given by the model predictive control method. After the control method is given, an initial disturbance is added to the nominal trajectory, and the data set required for the training of the machine learning method is collected. For the training of the neural network, behavioral cloning or inverse reinforcement learning can be used. The above two methods belong to imitation learning methods. The approximate initial value of the quadratic programming problem in the corresponding model predictive control solution process can be obtained through the trained neural network, which improves the solution speed of the model predictive control. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a work flow chart of a method for improving the calculation speed of the prediction control of the space rendezvous and docking model of the present invention;

[0038] Figure 2 It is a specific flow chart of an embodiment of the present invention;

[0039] Figure 3 It is a schematic diagram of the defined earth inertial coordinate system, orbital inertial coordinate system and local horizontal-local vertical coordinate system and the tracking spacecraft and the target spacecraft;

[0040] Figure 4 It is a schematic diagram of the relationship between the target spacecraft body coordinate system and the orbital inertial system and the target nutation;

[0041] Figure 5 It is a schematic diagram of the space cone in the direction of the target +z axis;

[0042] Figure 6 It is a flow chart of a method for real-time control of a network expansion control sequence;

[0043] Figure 7 is the trajectory of the training data set collected when tracking the spacecraft approaching a fixed target in the yx plane in a specific embodiment;

[0044] Figure 8 is the trajectory of the training data set collected when tracking the spacecraft approaching a fixed target in the yz plane in a specific embodiment;

[0045] Fig. 9 It is a comparison chart of the results of using a high-efficiency model predictive control method for close-range approach and rendezvous and docking in space and a common method in a specific embodiment when a fixed target approaches. DETAILED DESCRIPTION

[0046] The present invention is further described in detail below in conjunction with specific embodiments, which are intended to explain the present invention rather than to limit it.

[0047] like Figure 1-9 As shown, the present invention provides a method for improving the calculation speed of space rendezvous and docking model prediction control, comprising the following steps:

[0048] 1. Based on the CW equation, the relative dynamic equation of the spacecraft close rendezvous and docking process is established:

[0049] Through the geocentric inertial coordinate system and the local horizontal-local vertical coordinate system, the relative dynamic equation of the spacecraft close rendezvous and docking process is established through the CW equation

[0050]

[0051]

[0052]

[0053] Here n is the orbital angular velocity, m c To track the mass of the spacecraft, f is the thrust and u is the control input (i.e., acceleration). The subscripts of f and u indicate their components in the local horizontal-local vertical coordinate system. Rewriting the above formula into state space form

[0054]

[0055] Y=CX

[0056] in is the state vector, is the control vector, is the output vector. For this continuous space equation, assuming the sampling time is Ts, the equation in the discrete state is

[0057] X(k+1)=A d X(k)+B d U(k)

[0058] In the formula

[0059] 2. Establish the target posture dynamics model and obtain the position of the approach point in the local horizontal-local vertical coordinate system:

[0060] First, the attitude transfer matrix of the orbital inertial coordinate system to the target body coordinate system and the attitude transfer matrix of the orbital inertial coordinate system to the local horizontal-local vertical coordinate system are obtained. The approach point position is initially defined in the target body coordinate system, and then the expression of the approach point in the local horizontal-local vertical coordinate system is obtained through the target attitude dynamics equation.

[0061] 3. Establish spatial cone constraint, velocity constraint and control saturation constraint models:

[0062] For the space cone constraint, we only consider the relationship between the position of the tracking spacecraft and the space cone during the transfer process. Define the position vector of the tracking spacecraft in the local horizontal-local vertical coordinate system as r = [x, y, z] T , the semi-cone angle of the cone constraint is β. From the geometric relationship, we can see that the position of the tracking spacecraft satisfies

[0063] Dr≤0 4×1

[0064] For the velocity constraint, the maximum velocity of the tracking spacecraft along the three axes is and The maximum speed at a single moment is For the tracking spacecraft state X(k) at time k, the velocity constraint satisfies

[0065]

[0066] For the control saturation constraint, the maximum control input that the tracking spacecraft can provide along the three axes is u xmax 、u ymax and u zmax , the maximum control input at a single moment is U max =(u xmax ,u ymax ,u zmax ),definition

[0067]

[0068] For the control prediction sequence Us (k) needs to satisfy the following formula

[0069]

[0070] In the formula is a 3-dimensional unit matrix.

[0071] 4. The control implementation method of the tracking spacecraft following the target rotation or approaching a point near the stationary target is given through the model predictive control method:

[0072] For the state vector X(k) of the tracking spacecraft, the control prediction step size in the model predictive control is specified as N c step, the state prediction step length is N p step, the state prediction equation at time k is obtained as

[0073] X s (k) = A s X s (k)+B s U s (k)

[0074] Y s (k) = C s X s (k)

[0075] Here X s Taking (k) as an example, X(k+1|k) represents the state quantity at time k+1.

[0076] For a given task, the target position can be obtained directly through observation or indirectly through other algorithms. Let the target position vector be ρ p , then in the state prediction step N p The target position within is

[0077]

[0078] It should be noted that for a fixed target ρ p Remains constant over time.

[0079] We give the performance indicator function as shown in the following formula. The performance indicator function consists of two parts. The first part represents the period from time k+1 to time k+N based on time k. p Track the position of the spacecraft and the position of the target at the corresponding time. The second part represents the output N cThe size of the second norm of the step control sequence. For the first part, it is hoped that the tracking spacecraft can "track" the target as time goes by, so the distance between the two should be gradually reduced, that is, the value of the first part should be reduced. For the second part, it is hoped that the tracking spacecraft consumes the least fuel in the process of approaching the target, so this part should also be reduced.

[0080]

[0081] Here And they are all positive definite matrices.

[0082] Convert the above formula into

[0083]

[0084] After mathematical transformation, we get

[0085] Γ(k)=const+2M(k) T QC s B s U s (k)+U s (k) T WU s (k)

[0086] Where const = M(k) T QM(k),

[0087] For the constraints given in 3, we can obtain the following through transformation:

[0088] Spatial cone constraint: After expanding this constraint to the Np-dimensional state prediction sequence, the following expression is obtained:

[0089] A cac Y s (k)≤O

[0090] Then rewritten as: A cac (C s A s X(k)+C s B s U s (k))≤Ο

[0091] Speed ​​constraint: For N p The state prediction sequence X s (k) Definition

[0092]

[0093] Therefore, the constraints in 3 can be rewritten as

[0094]

[0095] Finally rewritten as

[0096]

[0097] The control saturation constraint uses the formula in 3.

[0098] Then the above problem is transformed into a quadratic programming problem. The optimization problem with quadratic programming can be unified as

[0099]

[0100] stGx≤g

[0101] To this end, the constraints and performance index functions need to be converted into the above form through mathematical transformation.

[0102]

[0103]

[0104] By solving the quadratic programming problem, we can obtain the model predictive control sequence U at the current time t s (k), select the first control U T Substitute (k|k) into the state space equation to obtain the state X(k+1) at the next moment, and repeat the above process until the termination condition.

[0105] 5. Collect training sets and network training:

[0106] For a given trajectory, a disturbance is given to track the increments Δx, Δy, Δz of the initial position of the spacecraft along each axis, and the control information of multiple trajectories is collected after the given disturbance. That is, for state X, the control sequence U under the corresponding state is obtained through model predictive control s (k). Network training can be divided into two types:

[0107] (1) Use machine learning methods to learn the state X and control sequence U s (k) Relationship

[0108] (2) Use machine learning methods to learn the state X and control sequence U s The first term in (k) immediately controls the relationship of U(k|k).

[0109] 6. Bring the initial value provided by the neural network after processing into the quadratic programming operation to improve the speed of model predictive control solution:

[0110] For the control sequence network given in (1) of 5, after the current state is given, the network can directly output the approximate value of the quadratic programming problem. This value is directly used as the initial value to accelerate the iteration of the quadratic programming.

[0111] For the real-time network given in (2) of 5, after the current state is given, the network only gives the current control amount. Then it is necessary to bring this control into the state space equation for N c The control sequence is obtained by expansion in the iterations. The control sequence is then used as the initial value to accelerate the iteration of the quadratic programming.

[0112] Example:

[0113] The present invention provides a method for improving the calculation speed of space rendezvous and docking model prediction control, comprising the following steps:

[0114] 1. Based on the CW equation, the relative dynamic equation of the spacecraft close rendezvous and docking process is established:

[0115] Through the geocentric inertial coordinate system and the local horizontal-local vertical coordinate system, the relative dynamic equation of the spacecraft close rendezvous and docking process is established through the CW equation

[0116]

[0117] Here n is the orbital angular velocity, m c To track the mass of the spacecraft, f is the thrust and u is the control input (i.e., acceleration). The subscripts of f and u indicate their components in the local horizontal-local vertical coordinate system. Rewriting the above formula into state space form

[0118]

[0119] in is the state vector, is the control vector, is the output vector. The specific expressions of each parameter are:

[0120]

[0121] The form of the equation is a continuous space equation. Assuming the sampling time is Ts, the equation in the discrete state is

[0122] X(k+1)=A d X(k)+B d U(k) (4)

[0123] In the formula

[0124] 2. Establish the target posture dynamics model and obtain the position of the intersection point in the local horizontal-local vertical coordinate system:

[0125] First, we obtain the attitude transfer matrix of the orbital inertial coordinate system to the target body coordinate system and the attitude transfer matrix of the orbital inertial coordinate system to the local horizontal-local vertical coordinate system. The intersection point position is initially defined in the target body coordinate system, and then the expression of the intersection point in the local horizontal-local vertical coordinate system is obtained through the target attitude dynamics equation. Figure 3 , Figure 4 and Figure 5 As shown, definition.

[0126] (1) Geocentric inertial coordinate system O I -X I Y I Z I

[0127] The origin of the geocentric inertial coordinate system is O I Located at the center of mass of the Earth, O I X I The axis points from the center of the earth to the vernal equinox, O I Z I The axis points from the center of the earth to the North Pole, I Y I The axis and the other two axes form a right-handed rectangular coordinate system.

[0128] (2) Local horizontal-local vertical coordinate system Ox O y O z O

[0129] The origin O of the local horizontal-local vertical coordinate system is located at the center of mass of the target spacecraft, Ox O The axis is along the line connecting the center of the earth and the center of mass of the target spacecraft O I O points to the outside of the track, Oz O The axis points in the direction of orbital angular momentum, Oy O The axis and the other two axes form a right-handed rectangular coordinate system.

[0130] (3) Target center inertial coordinate system Ox TI y TI z TI

[0131] The origin O of the target center inertial coordinate system is located at the center of mass of the target spacecraft. The three axes are aligned with the geocentric inertial coordinate system O I -X I Y I Z I Pointing to the same direction.

[0132] (4) Target body coordinate system Ox T y T z T

[0133] The origin O of the target body coordinate system is located at the center of mass of the target spacecraft, and the three axes are considered to coincide with the main rotation inertia axes of the target spacecraft.

[0134] Then the coordinates are rotated to get Ox O y O z O Ox T y T z T Rotation matrix for system transformation

[0135]

[0136] 3. Establish spatial cone constraint, velocity constraint and control saturation constraint models:

[0137] For the space cone constraint, we only consider the relationship between the position of the tracking spacecraft and the space cone during the transfer process. Define the position vector of the tracking spacecraft in the local horizontal-local vertical coordinate system as r = [x, y, z] T , from the geometric relationship, we can see that the tracking spacecraft position satisfies

[0138] Dr≤0 4×1 (6)

[0139] For the velocity constraint, the maximum velocity of the tracking spacecraft along the three axes is and The maximum speed at a single moment is For the tracking spacecraft state X(k) at time k, the velocity constraint satisfies

[0140]

[0141] The matrix H is expressed as follows

[0142]

[0143] For the control saturation constraint, the maximum control input that the tracking spacecraft can provide along the three axes is u xmax 、u ymax and u zmax , the maximum control input at a single moment is U max =(u xmax ,u ymax ,u zmax ),definition

[0144]

[0145] For the control prediction sequence U s (k) needs to satisfy the following formula

[0146]

[0147] In the formula is a 3-dimensional unit matrix.

[0148] 4. The control implementation method of the tracking spacecraft following the target rotation or approaching a point near the stationary target is given through the model predictive control method:

[0149] For the state vector X(k) of the tracking spacecraft, the control prediction step size in the model predictive control is specified as N c step, the state prediction step length is N p step, the state prediction equation at time k is obtained as

[0150]

[0151] Here In the formula

[0152]

[0153] X s (k) as an example, X(k+1|k) represents the state quantity at time k+1. For the above parameters,

[0154]

[0155]

[0156] In the formula is the Kronecker product, Table N p dimensional identity matrix.

[0157] For a given task, the target position can be obtained directly through observation or indirectly through other algorithms. Let the target position vector be ρ p , then in the state prediction step N p The target position within is

[0158]

[0159] It should be noted that for a fixed target ρ p Remains constant over time.

[0160] We give the performance indicator function as shown in the following formula. The performance indicator function consists of two parts. The first part represents the period from time k+1 to time k+N based on time k. p Track the position of the spacecraft and the position of the target at the corresponding time. The second part represents the output N cThe size of the second norm of the step control sequence. For the first part, it is hoped that the tracking spacecraft can "track" the target as time goes by, so the distance between the two should be gradually reduced, that is, the value of the first part should be reduced. For the second part, it is hoped that the tracking spacecraft consumes the least fuel in the process of approaching the target, so this part should also be reduced.

[0161]

[0162] Here And they are all positive definite matrices.

[0163] Convert the above formula into

[0164]

[0165] The right-hand side is transformed again into

[0166]

[0167] Where Q = diag (Q 1 ,Q 2 ,…,Q Np ), R = diag(R 1 ,R 2 ,…,R Nc-1 ). We further define

[0168]

[0169] After splitting and combining similar terms, we get

[0170] Γ(k)=const+2M(k) T QC s B s U s (k)+U s (k) T WU s (k) (19)

[0171] Where const = M(k) T QM(k),

[0172] For the constraints given in 3, we can obtain the following through transformation:

[0173] Spatial cone constraint: After expanding this constraint to the Np-dimensional state prediction sequence, the following expression is obtained:

[0174] A cac Y s (k)≤O (20)

[0175] Where O is a column vector whose elements are all 0, and the matrix Acac The expression is

[0176]

[0177] Finally rewritten as:

[0178] A cac (C s A s X(k)+C s B s U s (k))≤Ο (22)

[0179] Speed ​​constraint: For N p The state prediction sequence X s (k) Definition

[0180]

[0181] Therefore, the constraints in 3 can be rewritten as

[0182]

[0183] Here It is defined as

[0184]

[0185] The expression of T is T=(E 3 ;-E 3 ). Finally rewritten as

[0186]

[0187] The control saturation constraint follows the formula (9) in 3.

[0188] Then the above problem is transformed into a quadratic programming problem. The optimization problem with quadratic programming can be unified as

[0189]

[0190] stGx≤g

[0191] To this end, the constraints and performance index functions need to be converted into the above form through mathematical transformation.

[0192]

[0193]

[0194] By solving the quadratic programming problem, we can obtain the model predictive control sequence U at the current time t s (k), select the first control UT Substitute (k|k) into the state space equation to obtain the state X(k+1) at the next moment, and repeat the above process until the termination condition.

[0195] 5. Collect training sets and network training:

[0196] For a given trajectory, a disturbance is given to track the increments Δx, Δy, Δz of the initial position of the spacecraft along each axis, and the control information of multiple trajectories is collected after the given disturbance. That is, for state X, the control sequence U under the corresponding state is obtained through model predictive control s (k). Network training can be divided into two types:

[0197] (1) Use machine learning methods to learn the state X and control sequence U s (k) relationship. Control sequence U s (k) is directly given by the quadratic programming algorithm, and its vector length is related to the control prediction step length N c It is related to the length of control U and is the product of the two. In the present invention, the length of each control is 3, that is, the three-axis control component in the local horizontal-local vertical coordinate system at that moment. Therefore, the control sequence U s (k) length is 3N c The network input is a 6-dimensional state vector X(k), and the output is 3N c Dimension Control Sequence U s (k).

[0198] (2) Use machine learning methods to learn the state X and control sequence U s (k) is the first immediate control U(k|k). In the present invention, the length of each control is 3, that is, the three-axis control component in the local horizontal-local vertical coordinate system at that moment. Therefore, the control sequence U s (k) The length of the first term U(k|k) is 3. The network inputs a 6-dimensional state vector X(k) and outputs a 3-dimensional immediate control U(k|k).

[0199] 6. Bring the initial value provided by the neural network after processing into the quadratic programming operation to improve the speed of model predictive control solution:

[0200] For the control sequence network given in (1) of 5, after the current state is given, the network can directly output the approximate value of the quadratic programming problem. This value is directly used as the initial value to accelerate the iteration of the quadratic programming.

[0201] For the real-time control network given in (2) of 5, Figure 6 As shown, given the current state, the network only gives the current control amount. Then this control needs to be brought into the state space equation for N cThe control sequence is obtained by expansion in the iterations. The control sequence is then used as the initial value to accelerate the iteration of the quadratic programming.

[0202] The following is a description of the efficient model predictive control method for close-range approach and rendezvous and docking in space based on a neural network according to the present invention in conjunction with an embodiment.

[0203] For this example, we discuss tracking a spacecraft approaching a target from the +y direction. The following explanation is given for the space cone constraints in steps 3 and 4: The D matrix in equation 20 is

[0204]

[0205] For this example, a simplified analysis is done. The target is a stationary target, and the tracking spacecraft approaches a fixed point. The fixed point position information and the initial information of the tracking spacecraft are shown below: the spacecraft is in a circular orbit with a radius of 500km, the initial position coordinates of the tracking spacecraft in the local horizontal-local vertical coordinate system are (140m,-140m,0m), the fixed coordinates of the intersection point on the target spacecraft are (0m,-10m,0m), and the simulation time step is T s =0.5s, the semi-cone angle of the cone constraint β=50°.

[0206] For the data set in step 5, Figure 7 and Figure 8 As shown in Figure 2. The dataset is generated by giving perturbations to track the initial position of the spacecraft along each axis increment Δx, Δy, Δz∈[-3m,+3m], which contains a total of 1000 trajectories. Based on this dataset, the network is trained using the behavioral cloning method to obtain the network used later.

[0207] As mentioned in step 6, the initial value provided by the neural network after processing is brought into the quadratic programming operation to improve the solution speed of the model predictive control. The result is as follows Fig. 9 As shown. The zero vector initial value is to set the initial value of the iteration to zero and then directly bring it into the quadratic programming algorithm for solution. This is the most common way to provide initial values ​​for the quadratic programming algorithm. As shown in the figure, the quadratic programming iterative algorithm using a neural network to provide initial values ​​can effectively reduce the number of iterations compared to the conventional quadratic programming algorithm that provides zero initial values. For the two neural network initial value providing methods, the network that directly fits the control sequence is more effective than the sequence expansion network.

[0208] In summary, the present invention provides an efficient model predictive control method for close approach and rendezvous and docking in space based on a neural network, thereby combining the rapidity of machine learning methods represented by neural networks and the robustness of model predictive control to provide a highly robust and low computing power demand algorithm for on-orbit maneuvers of spacecraft. The method performs machine learning on the trajectory set given by the original model predictive control, explores the relationship between the state and the control sequence or real-time control through a neural network, and provides an approximate initial value for the quadratic programming before solving the quadratic programming. The method provides modeling methods for both rotating targets and fixed (stationary) targets. The present invention is practical and has the advantages of high robustness and speed, and can provide a highly robust, low computing demand solution for the problem of autonomous approach and rendezvous and docking of small spacecraft.

[0209] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive. Under the guidance of the specification, a person skilled in the art can also make many forms without departing from the scope of protection of the claims of the present invention, all of which belong to the scope of protection of the present invention.

Claims

1. A method for improving the speed of space rendezvous and docking model predictive control operation, characterized in that: The following steps are involved: S1: Establish the relative dynamic equations of the spacecraft rendezvous and docking process; S2: Establish the target posture dynamics model and obtain the position of the intersection point in the local horizontal-local vertical coordinate system; S3: Modeling of space cone constraints, velocity constraints, and control saturation constraints; S4: Based on the S1 relative dynamics equation and the S2 target attitude dynamics model, a model predictive control performance index function is established. Then, the S3 space cone constraint model, velocity constraint model, control saturation constraint model and the model predictive control performance index function are combined. Through the model predictive control method, a control implementation method for the spacecraft to follow the target rotation or approach a stationary target is given. S5: Obtain multiple spacecraft nominal trajectories, and add disturbances to the initial state of each spacecraft nominal trajectory, combine the control implementation method obtained in S4, obtain the running trajectory under each disturbance, collect the state and control sequence of each control moment in the trajectory as a training set, perform network training on the training set, and obtain the output value of the neural network; S6: Approximate the output value of the neural network and substitute the approximate output value of the neural network into the quadratic programming operation, which reduces the number of quadratic programming iterations and thus improves the solution speed of the model predictive control; The space cone constraint is satisfied, and the spacecraft is always in the space cone when rendezvousing with the target; The speed constraints satisfy: in is the maximum speed at a single moment, for The state of the spacecraft at that moment, is a three-dimensional unit matrix, is the coefficient of the quadratic term of the indicator function; Controlling saturation constraints in, is a three-dimensional unit matrix, is the average control output of the spacecraft, for The control output of the spacecraft at the moment; The S4 control implementation method is: Transform the above problem into a quadratic programming problem. The optimization problem of quadratic programming is unified as in, is the left side of the constraint equation, is the right-hand side of the constraint equation, is the velocity constraint matrix, is the augmented input matrix, is the collision avoidance matrix, , is the average control output of the spacecraft, is the average maximum speed, for The state of the spacecraft at that moment, is a constant matrix, is the coefficient of the first-order term of the indicator function, is the position vector, The control quantity at time k, is the coefficient of the quadratic term of the indicator function, where It means that Q(x) needs to satisfy the constraint GX≤g, where x represents an arbitrary parameter.

2. The method for improving the calculation speed of the space rendezvous and docking model predictive control according to claim 1, characterized in that: The relative dynamics equation in S1 is established based on the CW equation.

3. The method for improving the calculation speed of the space rendezvous and docking model predictive control according to claim 1, characterized in that: The relative dynamic equation in S1 is: in, is the orbital angular velocity To track the mass of the spacecraft, f For thrust, u is the control input, f and u Subscript , , represents the component in the local horizontal-local vertical coordinate system, For spacecraft The acceleration in the direction, For spacecraft The acceleration in the direction, For spacecraft The acceleration in the direction, For spacecraft Speed ​​in direction, For spacecraft Speed ​​in direction.

4. The method for improving the calculation speed of the space rendezvous and docking model predictive control according to claim 1, characterized in that: The specific location of the intersection point in the local horizontal-local vertical coordinate system is: Firstly, the attitude transfer matrix of the orbital inertial coordinate system to the target body coordinate system and the attitude transfer matrix of the orbital inertial coordinate system to the local horizontal-local vertical coordinate system are obtained. The intersection point position is initially defined in the target body coordinate system. Then, the expression of the intersection point in the local horizontal-local vertical coordinate system is obtained through the target attitude dynamics equation.

5. The method for improving the calculation speed of the space rendezvous and docking model predictive control according to claim 1, characterized in that: The performance index function of the S4 model predictive control is: is the output vector of the i-th step after k time, is the target position of the i-th step after k time, is the target position vector, is a position-dependent positive definite matrix, is the state prediction step length, To control the prediction step size, is the control amount of the i-th step after time k, is the control-related positive definite matrix.

6. The method for improving the calculation speed of the space rendezvous and docking model predictive control according to claim 1, characterized in that: The network training of S5 is performed in two ways, one of which is performed using a control sequence network and the other is performed using a real-time control network.

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