A missile cascade correction guidance method and system under satellite-missile coordination conditions

Abstract

The present invention discloses a missile cascade correction guidance method and system under the condition of satellite-missile cooperation. Firstly, a judgment is made according to the motion information of the missile body and the target obtained from the space base. Then, the control sequence is updated by using the online replanning or MPSP algorithm module and the neighborhood optimal control algorithm respectively. Finally, according to the terminal change of the target, a suitable threshold is selected to weight the control sequences of the two methods to obtain the instruction sequence after the trajectory correction. According to the simulation verification, the scheme can significantly improve the trajectory speed and has a good guidance effect.

Description

Technical Field

[0001] The invention belongs to the technical field of missile guidance, and in particular relates to a missile cascade correction guidance method and system under the condition of satellite-missile cooperation. Background Art

[0002] Precision guidance of missiles is one of the key technologies for carrying out strike missions. With the development of related technologies, the targets faced by missiles are gradually equipped with more intelligent evasion schemes. When facing high-speed and high-maneuverability targets, missiles mostly fly and strike according to the set guides. Therefore, traditional methods cannot generate new corrected trajectories in a timely and accurate manner. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a missile tiered correction guidance method and system under the conditions of satellite-missile cooperation, so as to solve the problem in the prior art that it is difficult for the missile to generate a new corrected trajectory in a timely and accurate manner when facing a high-speed and high-maneuverability target.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A method and system for cascaded correction guidance of a missile under satellite-missile coordination conditions, comprising the following steps:

[0006] Determine whether the flight trajectory of the missile needs to be corrected, and if no correction is needed, set the flight trajectory; if correction is needed, perform the following steps;

[0007] According to the distance between the missile and the terminal target, the weights of the online replanning algorithm, MPSP algorithm and neighborhood optimal control algorithm are determined through the fuzzy membership function.

[0008] Determine the correction value of each algorithm, merge the three algorithms according to the weight of each algorithm, obtain the instruction sequence after the missile's trajectory is corrected, and correct the missile's flight trajectory according to the instruction sequence.

[0009] A further improvement of the present invention is:

[0010] Preferably, the formula for determining whether the flight trajectory of the missile needs to be corrected is:

[0011] t k+1 ={t>t k |ΔE≥ε} (9)

[0012] Among them, ΔE is the estimated trajectory deviation, ε is the threshold of trajectory deviation, and t k+1 is the time of the k+1th trajectory correction, t k is the time when the kth trajectory correction is performed.

[0013] Preferably, the flight trajectory of the missile is obtained by solving the missile center-of-mass motion equation; the missile center-of-mass motion equation incorporates the Coriolis inertial force.

[0014] Preferably, the attack angle control command and the roll angle control command are input into the missile center of mass motion equation, and the set flight trajectory of the missile is obtained after integral solution.

[0015] Preferably, the calculation formula of the fuzzy membership function is:

[0016]

[0017] Among them, t represents the current time of the system, and t0 represents the time when a certain correction method is selected.

[0018] Preferably, the weight calculation method of a given fusion control instruction sequence at time t is as follows:

[0019]

[0020] Preferably, the calculation formula for the correction method decision is:

[0021]

[0022] Where ξ is the estimated terminal deviation, f NN is the terminal deviation calculation function, M i is the motion information of the i-th interceptor missile, T j is the motion information of the jth target.

[0023]

[0024] Among them, x d represents the decision variable, 1, 2, 3 represent the selection of neighborhood correction module, MPSP correction module, and online replanning module respectively, ξ1, ξ2, ξ3 represent thresholds, and different methods are selected according to different thresholds.

[0025] Preferably, the online replanning algorithm is solved by a particle swarm algorithm;

[0026] The online replanning algorithm introduces a no-fly zone model, thermal constraints, dynamic pressure constraints and overload constraints.

[0027] The MPSP algorithm combines model predictive control and approximate dynamic programming to solve problems with terminal constraints by minimizing control energy.

[0028] The neighborhood optimal control algorithm is to use the reference optimal trajectory information to generate the adjustment amount of the running trajectory control amount; when ensuring the optimal performance indicators of the missile, the state quantity of the system is adjusted to meet the changed terminal constraint conditions.

[0029] A missile cascade correction guidance system under satellite-missile coordination conditions, comprising:

[0030] The correction event trigger device is used to determine whether the flight trajectory of the missile needs to be corrected. When correction is not required, the flight trajectory is set. When correction is required, the following device is executed;

[0031] A correction method decision device is used to determine the weights of the online replanning algorithm, the MPSP algorithm and the neighborhood optimal control algorithm according to the distance between the missile and the terminal target through a fuzzy membership function;

[0032] The correction value calculation execution device is used to determine the correction value of each algorithm, merge the three algorithms according to the weights of each algorithm, obtain the instruction sequence after the missile's trajectory is corrected, and correct the missile's flight trajectory according to the instruction sequence.

[0033] Preferably, the correction method decision device also includes an online replanning module, an MPSP correction module and a neighborhood correction module.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The invention discloses a missile cascade correction guidance method under the condition of satellite-missile cooperation. The method first establishes a missile and a target missile mathematical model in a ground launch coordinate system. Secondly, the missile performs online replanning, model static prediction planning and trajectory neighborhood correction module control instruction calculation according to the correction decision under the premise of satisfying the constraints of the kinematic model and the no-fly zone, and obtains the attack angle and roll angle control instruction sequence after the initial correction. Then, the online replanning module or the model static prediction planning and trajectory neighborhood correction module method selection is determined by the deviation between the current predicted terminal position and the actual terminal position. Finally, the trajectory correction fusion instruction determines the proportion of instructions according to the membership function; which method is used to update the instructions according to the deviation, and then the proportion is determined according to the membership function. The online trajectory replanning module adopts a particle swarm optimization algorithm to optimize the control sequence, and the model static prediction planning and trajectory neighborhood correction module obtain the control sequence through integral iteration.

[0036] Furthermore, the present invention obtains a tiered trajectory correction fusion method by establishing a model simulation verification, and combines the online replanning, MPSP and neighborhood optimal control fusion methods to solve the problems of long time and high calculation of real-time trajectory replanning when the target is maneuvering, thereby improving the real-time and efficiency of trajectory correction.

[0037] The present invention also discloses a missile cascade correction guidance system under the condition of satellite-missile cooperation, the system comprises a correction event triggering device, a correction method decision device and a correction value calculation execution device; when the missile deviates from the trajectory, the correction device is triggered to perform correction calculation, the decision device determines which method to use, and then obtains new instructions and then performs fusion, and after the fusion is completed, the real instructions are used for correction. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the framework diagram of the missile's cascade correction guidance algorithm;

[0039] Figure 2 It is a method for determining missile trajectory correction;

[0040] Figure 3 This is the flow chart of the online trajectory replanning algorithm;

[0041] Figure 4 It is the flow chart of MPSP algorithm;

[0042] Figure 5 Neighborhood optimal algorithm flow chart;

[0043] Figure 6 Schematic diagram of membership function value calculation. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] The present invention discloses a missile cascade correction guidance method under the condition of satellite-missile cooperation. Firstly, a judgment is made according to the motion information of the missile body and the target obtained from the space base. Then, the control sequence is updated by using the online replanning or MPSP algorithm module and the neighborhood optimal control algorithm respectively. Finally, according to the terminal change of the target, a suitable threshold is selected to weight the control sequences of the two methods to obtain the instruction sequence after the trajectory correction. According to the simulation verification, the scheme can obviously improve the trajectory speed and has a good guidance effect.

[0046] The method specifically comprises the following steps:

[0047] Step 1. Establish a mathematical model of the missile's center of mass motion. Consider the various forces acting on the missile, assume that the earth is a homogeneous rotating ellipsoid, take the Coriolis inertial force into account, so that the center of mass motion equation is closer to the actual trajectory of the missile, and establish the missile's center of mass motion equation in the ground launch coordinate system, which is expressed as follows:

[0048]

[0049] In the formula, there are 6 system state variables, (v x ,v y,v z ) are the velocity information of the missile in the ground launch coordinate system; (x, y, z) are the position information of the missile in the ground launch coordinate system.

[0050] In the formula, there are 8 involved variables, θ is the ballistic inclination, σ is the ballistic deviation, r is the distance from the missile to the center of the earth, φ is the latitude of the center of the earth, λ is the longitude, R is the radius of the earth corresponding to the current longitude and latitude, h is the distance from the missile to the ground, and v represents the flight speed.

[0051] In the formula, the calculation formula of Δλ is as follows:

[0052]

[0053] Among them, A0 is the launch azimuth and B0 is the geographical latitude of the launch point.

[0054] In the formula, a e is the average equatorial radius of the Earth, b e is the mean polar radius of the Earth, ω e is the angular velocity of the earth's rotation, and m is the mass of the missile.

[0055] In the formula, g' r , They represent the components of gravitational acceleration in the direction of the earth's center vector and the direction of the earth's rotation, respectively. The calculation formula is as follows:

[0056]

[0057] Among them, μ M is the gravitational constant, M e is the average mass of the Earth, and J2 = 1.08263 × 10 -3

[0058] In the formula, ω ex ,ω ey ,ω ez Respectively

[0059]

[0060] In the formula, R ox , R oy , R oz Respectively

[0061]

[0062] Among them, μ0 is the difference between the geographical latitude of the launch point and the geocentric latitude, and R0 is the geocentric radius vector of the launch point.

[0063] Where, the component form of centrifugal acceleration in the launch coordinate system is:

[0064]

[0065] Where, the component form of the Coriolis acceleration in the launch coordinate system is:

[0066]

[0067] In the formula, X, Y, and Z are the resistance, lift, and lateral force on the missile, respectively. The calculation formula is as follows:

[0068]

[0069] If the missile side slip is not considered, β = 0, so the lateral force Z = 0. S is the reference area, ρ is the atmospheric density, and Ma is the flight Mach number, which is the ratio of the missile speed to the speed of sound. L ,C D They represent the lift coefficient and the drag coefficient respectively, and can be obtained by inputting the current angle of attack command α and the flight Mach number Ma and querying the interpolation table.

[0070] It can be seen that the state variable of the system is v x ,v y ,v z ,x,y,z, the control input is the angle of attack command α and the roll angle command υ. Set the initial value of the state variable, input the angle of attack control command and the roll angle control command into the missile's center of mass motion equation, integrate the system, and you can get the missile's flight trajectory.

[0071] Step 2: Design and establish the missile cascade correction guidance algorithm framework.

[0072] After the missile obtains the movement information of the missile group and the target from the space base, it predicts the movement trajectory of the target and controls the missile to fly towards the target according to the predicted trajectory, and continuously updates the status information during the flight.

[0073] See also Figure 1, using online replanning algorithm, MPSP algorithm and neighborhood optimal control algorithm; according to the change of the distance between the target and the missile, select the appropriate threshold, weight the algorithm to obtain the final instruction sequence, and correct the trajectory. That is, when the terminal constraint of the trajectory cluster does not change much (the distance value of the trajectory is used as the early flight of the missile), the instruction sequence based on the neighborhood optimal control algorithm is used; when the terminal constraint changes greatly, the instruction sequence based on the MPSP algorithm is used to correct the trajectory. When the terminal constraint is particularly large, the instruction sequence based on the online replanning algorithm is used to correct the trajectory, and the weighted instruction sequence and the corrected trajectory are obtained. According to the predicted relative distance of the terminal, the proportion of the online trajectory replanning module, the MPSP correction algorithm module and the trajectory neighborhood correction module in the trajectory correction is determined. The determination of the proportion value can be determined by the fuzzy membership method, and finally the instruction sequence obtained after the trajectory correction is obtained; the fuzzy membership method is:, different control algorithms are used for fusion at different missile running times.

[0074] The whole method mainly includes a correction event trigger device, a correction method decision device, and a correction value calculation device. The correction value calculation device includes an online replanning module, an MPSP correction module, and a neighborhood correction module. The control sequence calculated by the online replanning module and the MPSP correction module is the body value, and the control sequence calculated by the neighborhood correction module is the deviation value. The decision device mainly refers to judging whether the instruction needs to be updated according to the deviation between the ballistic terminal and the target obtained by the current instruction, which method to use for updating, and after the update, it is merged according to the weight calculated subsequently. The correction value calculation device calculates the operation of updating the instruction for three methods.

[0075] Step 3. Modify the design of the method decision device.

[0076] After obtaining the motion information of the missile group and the target from the space, the calculation method of the corrected trajectory control sequence will be selected according to the change of the target terminal deviation. Finally, the fuzzy membership method is used to obtain the weight calculation to obtain the new control sequence during fusion.

[0077] See also Figure 3 ,The correction method based on online replanning is more likely to be selected in the early stage of flight, because the flight time to reach the target is long, and a simple change of the target may have a significant impact on the terminal deviation.,However, the online replanning module takes a long time to calculate, and is inefficient.

[0078] The online replanning module uses the particle swarm optimization algorithm to solve the problem. In order to obtain a control sequence that is more in line with the actual situation, a no-fly zone model is introduced:

[0079]

[0080] Where S grepresents the g-th no-fly zone, R g represents the no-fly radius of the g-th no-fly zone, x g ,y g Indicates the center coordinates of the no-fly zone.

[0081] Since the missile's reentry process is very complicated, it is necessary to consider the impact of factors such as heat flow, dynamic pressure and overload on the missile and the constraints on the flight trajectory.

[0082] Thermal constraints:

[0083]

[0084] Where Q represents the heat flux in kilowatts per square meter, and k is a constant coefficient related to the shape and appearance of the stagnation point.

[0085] Dynamic pressure constraint:

[0086] q=0.5ρv 2 ≤q max (14)

[0087] Overload constraints:

[0088] n y =(Lcosα+Dsinα) / mg≤n ymax (15)

[0089] See also Figure 4 The trajectory correction method based on MPSP can accurately and quickly correct the trajectory, and can take into account the control quantity and process constraints. Its high solution efficiency and online correction potential will play a key role in intercepting high-speed targets. The MPSP guidance method combines the predictive control MPC (model predictive control) and ADP (approximate dynamic programming) methods to solve the optimal control problem with terminal constraints by minimizing the control energy. The calculation rate of this method is faster than the online replanning but slower than the neighborhood optimization module.

[0090] MPSP algorithm formula:

[0091] The state equation and output equation in discrete form are as follows:

[0092] X k+1 =F k (X k ,U k ) (16)

[0093] Y k =h(X k ) (17)

[0094] The output deviation at the end moment is ΔY N =Y N-Y * N ,Y N Relative Y * N Carry out Taylor series expansion, and we get:

[0095]

[0096] Where HOT is a high-order term. Ignoring the influence of high-order terms, the output deviation at the end moment is:

[0097]

[0098] Discretize the above equation at each node and get:

[0099] dY N =AdX1+BdU1+…+B N-1 Ud N-1 (20)

[0100] Due to random disturbances and system errors, the actual flight trajectory of the missile is inconsistent with the optimal reference trajectory. To solve this problem, the optimal trajectory is generally re-planned, but this method is computationally intensive, time-consuming, and difficult to implement; therefore, the neighborhood optimal control theory is used to obtain the corrected value of the control quantity through calculation. Specifically:

[0101] Firstly, the optimal reference trajectory is obtained based on the piecewise Radau pseudospectral method. Based on the reference trajectory, the optimal control problem is transformed into a two-point boundary value problem of state quantity deviation and co-state quantity deviation. Then, the optimal feedback control law on the LGR (Legendre-Gauss-Radau) collocation point is solved. It has good robustness to a large range of deviations of the initial state quantity and can meet the real-time requirements.

[0102] By performing second-order variation on the first-order optimality necessary conditions satisfied by the trajectory, a corrected trajectory that satisfies the second-order optimality is obtained in the neighborhood of the nominal trajectory to ensure the optimality of the correction algorithm.

[0103] The direct method discretizes the state variables, converts the continuous optimal control problem into a discrete nonlinear programming problem, and then obtains the optimal solution through the nonlinear programming algorithm. Compared with the indirect method, the convergence domain of the direct method is wider.

[0104] See also Figure 5 The neighborhood optimization algorithm (NOC) was developed on its basis. Compared with the first-order variational optimal control method, this method has second-order accuracy. The most important feature is that within the small neighborhood of the first-order optimal trajectory, it can calculate the optimal trajectory family that satisfies a cluster of initial or terminal constraints at one time, which is very suitable for forming optimized trajectory data.

[0105] When the terminal constraints of the trajectory cluster do not change much, they can be adjusted within the neighborhood of the benchmark optimal trajectory terminal constraints. NOC theory is applied to generate trajectory clusters that meet different terminal constraints to cover the predicted hit area.

[0106] Optimal control theory algorithm formula:

[0107]

[0108]

[0109]

[0110]

[0111] ψ f (x(t f ))=0 (25)

[0112] The idea of ​​this method is to use the information of the benchmark optimal trajectory to generate the adjustment of the control quantity. The information of the benchmark optimal trajectory refers to the trajectory generated by the above two methods as a benchmark, and then use NOC to offset the above trajectory in the subsequent process to adjust the system state x to meet the changed terminal (the last part of the trajectory) constraint conditions, while ensuring that the performance index J still maintains a certain degree of optimality. The neighborhood optimal control theory can use the data of the reference trajectory to quickly calculate the correction value of the control quantity, avoiding the problem of slow solution speed due to re-optimization, and the result has high accuracy and optimality.

[0113] Step 4. Revise the design of the event trigger device.

[0114] See also Figure 2 , the correction event triggering device can be expressed based on the correction time. The time of the k+1th trajectory correction can be expressed as:

[0115] t k+1 ={t>t k |ΔE≥ε} (9)

[0116] Where ΔE is the estimated trajectory deviation, and ε is the threshold of trajectory deviation. If the deviation is higher than this threshold, trajectory correction must be performed.

[0117] The decision device of the correction method mainly relies on the distance judgment between the missile and the target terminal. It is expressed as follows using interval inequality:

[0118]

[0119] Where ξ is the estimated terminal deviation, f NN is the terminal deviation calculation function, Mi is the motion information of the i-th interceptor missile, T j is the motion information of the jth target.

[0120]

[0121] where x d represents the decision variable, 1, 2, 3 represent the selection of neighborhood correction module, MPSP correction module, and online replanning module respectively, ξ1, ξ2, ξ3 represent thresholds, and different methods are selected according to different thresholds.

[0122] Step 5. Revise the design of the instruction fusion device.

[0123] The decision of the correction method is mainly based on the size of the estimated terminal deviation. If the target is a static target, no trajectory correction is required. However, in actual military mission applications, enemy targets often have certain mobility capabilities, and with the development of military level, most intelligent targets have multiple mobility methods to avoid being hit. Online replanning, MPSP correction algorithm and trajectory neighborhood correction have good trajectory correction capabilities under certain environments. However, considering the enemy's variable mobility problem during the entire mission, it is difficult to perform trajectory correction efficiently and quickly by simply applying a specific method to complete precision strikes or reconnaissance missions. Therefore, the method needs to be integrated. In the design of the correction method selection device, the present invention selects three methods by stipulating the values ​​of ξ1, ξ2, and ξ3.

[0124] The design instruction fusion membership function is as follows:

[0125]

[0126] Among them, t represents the current time of the system, and t0 represents the time when a certain correction method is selected. When a new instruction sequence is obtained after the method is selected next time, the current time can be brought into the membership function and then normalized. Determine the weight between the new sequence and the old sequence.

[0127] like Figure 6 As shown in the figure, when trajectory correction is performed at both t0 and t1, the corresponding control instructions are obtained. The weight calculation method of the given fusion control instruction sequence at the current time t is as follows:

[0128]

[0129] This weight is used to determine the proportion of each algorithm. wn represents the membership function value corresponding to the nth method at the current moment, w n represents the weight of the nth method. For example, f w1is the membership function value of replanning at the current moment, and w1 is the calculated weight of the replanning algorithm when it is integrated.

[0130] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A missile cascade correction guidance method under satellite-missile coordination conditions, characterized in that: The following steps are involved: Determine whether the flight trajectory of the missile needs to be corrected, and if no correction is needed, set the flight trajectory; if correction is needed, perform the following steps; According to the distance between the missile and the terminal target, the weights of the online replanning algorithm, MPSP algorithm and neighborhood optimal control algorithm are determined through the fuzzy membership function. Determine the correction value of each algorithm, fuse the three algorithms according to the weights of each algorithm, obtain the instruction sequence after the missile trajectory is corrected, and correct the missile's flight trajectory according to the instruction sequence; The calculation formula of the fuzzy membership function is: （26） Among them, t represents the current time of the system, Indicates the moment of selecting a correction method; The weight calculation method of a given fusion control instruction sequence at time t is as follows: （27） in, f wn Represents the membership function value corresponding to the nth method at the current moment, w n represents the weight of the nth method; The calculation formula for the revised method decision is: （10） in is the estimated terminal deviation, is the terminal deviation calculation function, is the motion information of the i-th interceptor missile, is the motion information of the jth target; （11） in, represents the decision variable, 1, 2, and 3 represent the selection of the neighborhood correction module, the MPSP correction module, and the online replanning module, respectively. Indicates the threshold. Different methods are selected according to different thresholds.

2. The method for missile cascade correction guidance under satellite-missile coordination conditions according to claim 1 is characterized in that: The formula for judging whether the missile's flight trajectory needs to be corrected is: （9） in, is the estimated trajectory deviation, is the threshold of trajectory deviation, is the time of the k+1th trajectory correction, is the time when the kth trajectory correction is performed.

3. The method for missile cascade correction guidance under satellite-missile coordination conditions according to claim 1 is characterized in that: The flight trajectory of the missile is obtained by solving the missile center-of-mass motion equation; the missile center-of-mass motion equation is combined with the Coriolis inertial force.

4. The method for missile cascade correction guidance under satellite-missile coordination conditions according to claim 1 is characterized in that: Input the angle of attack control command and the roll angle control command into the missile center of mass motion equation, and obtain the set flight trajectory of the missile after integral solution.

5. The method for missile cascade correction guidance under satellite-missile coordination conditions according to claim 1 is characterized in that: The online replanning algorithm is solved by a particle swarm algorithm; The online replanning algorithm introduces a no-fly zone model, thermal constraints, dynamic pressure constraints and overload constraints; The MPSP algorithm combines model predictive control and approximate dynamic programming to solve problems with terminal constraints by minimizing control energy; The neighborhood optimal control algorithm is to use the reference optimal trajectory information to generate the adjustment amount of the running trajectory control amount; when ensuring the optimal performance indicators of the missile, the state quantity of the system is adjusted to meet the changed terminal constraint conditions.

6. A missile cascade correction guidance system under satellite-missile coordination conditions for implementing the method described in claim 1, characterized in that: include: The correction event trigger device is used to determine whether the flight trajectory of the missile needs to be corrected. When correction is not required, the flight trajectory is set. When correction is required, the following device is executed; A correction method decision device is used to determine the weights of the online replanning algorithm, the MPSP algorithm and the neighborhood optimal control algorithm according to the distance between the missile and the terminal target through a fuzzy membership function; The correction value calculation execution device is used to determine the correction value of each algorithm, merge the three algorithms according to the weights of each algorithm, obtain the instruction sequence after the missile's trajectory is corrected, and correct the missile's flight trajectory according to the instruction sequence.

7. The missile cascade correction guidance system under the satellite-missile coordination condition according to claim 6 is characterized in that: The correction method decision device also includes an online re-planning module, an MPSP correction module and a neighborhood correction module.

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