No-fly zone evasion guidance method and device based on mathematical morphology filtering

Abstract

The invention provides a no-fly zone evasion guidance method and device based on mathematical morphology filtering, and relates to the technical field of aircraft guidance control, and the method comprises the steps: obtaining a violation degree function of a task area containing a no-fly zone, the violation degree function is obtained based on mathematical morphology filtering, and the violation degree function is obtained based on mathematical morphology filtering; the representation module is used for representing association degrees of different aircraft positions and no-fly zones; determining an augmented dynamical model and a target optimal control problem according to the violation degree function and an original dynamical model of the aircraft; wherein the augmented dynamical model is obtained by augmenting an accumulative violation degree state on an original dynamical model, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulative violation degree is 0; and determining a target control quantity sequence according to the augmented dynamical model and the target optimal control problem. The method can cope with any form of no-fly zone constraint through mathematical morphology filtering, is high in solving efficiency, and has good model universality.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft guidance and control, and in particular, to a no-fly zone avoidance guidance method and device based on mathematical morphology filtering. Background Art

[0002] No-fly zones are usually demarcated by factors such as military sensitive areas, air traffic control restrictions, or nature reserves. Any unauthorized intrusion may lead to serious consequences. Therefore, developing effective no-fly zone avoidance methods is crucial for ensuring the safety of aircraft and the successful execution of missions.

[0003] In recent years, many researchers have proposed no-fly zone avoidance methods from different perspectives. These methods can be roughly divided into three categories. The first category is the analytical method, such as the analytical reentry guidance law for no-fly zone avoidance proposed by Yu et al. The second category is the numerical method, such as the no-fly zone avoidance guidance method based on linear pseudo-spectrum model predictive control proposed by Yang et al. The third category is the intelligent method, such as the online path decision for no-fly zone avoidance based on graph attention network proposed by Zhang et al. However, the methods mentioned above can only adapt to circular no-fly zone constraints.

[0004] There is less existing research on the avoidance method for non-circular no-fly zones. In terms of shape, Zhang et al. proposed a trajectory optimization method with general polygon no-fly zone constraints based on convex decomposition technology, but this method takes a long time to solve and is not suitable for online guidance. In terms of dimension, Li et al. extended the no-fly zone constraint from a two-dimensional plane to a three-dimensional space and proposed a spatial convex no-fly zone avoidance guidance method based on reinforcement learning technology, but this method needs to be trained for a specific dynamic model and has insufficient generality.

[0005] In summary, the existing no-fly zone avoidance methods can only handle specific forms of no-fly zone constraints and have technical problems such as low solution efficiency and poor model generality. Summary of the Invention

[0006] The purpose of the present invention is to provide a no-fly zone avoidance guidance method and device based on mathematical morphology filtering to cope with arbitrary forms of no-fly zone constraints and alleviate the technical problems of low solution efficiency and poor model generality of the existing no-fly zone avoidance methods.

[0007] In a first aspect, the present invention provides a no-fly zone avoidance guidance method based on mathematical morphology filtering, including:

[0008] Obtain a violation function of a mission area including a no-fly zone, where the violation function is obtained based on mathematical morphology filtering and is used to characterize the degree of association between different aircraft positions and the no-fly zone;

[0009] According to the violation degree function and the original dynamic model of the aircraft, an augmented dynamic model and an objective optimal control problem are determined; among them, the augmented dynamic model is obtained by augmenting the original dynamic model with an accumulated violation degree state, and the no-fly zone constraint in the objective optimal control problem is that the terminal value of the accumulated violation degree is 0;

[0010] According to the augmented dynamic model and the objective optimal control problem, a sequence of target control quantities is determined.

[0011] In an optional implementation manner, the step of obtaining the violation degree function of the mission area including the no-fly zone includes:

[0012] Discretize the mission area to obtain a marker array; among them, the value of the array cell where the no-fly zone is located in the marker array is 1, and the values of the remaining array cells are 0;

[0013] Initialize the violation degree array;

[0014] Iteratively update the violation degree array by performing mathematical morphology filtering on the marker array to obtain a target violation degree array;

[0015] Perform linear interpolation on the target violation degree array to obtain the target violation degree array.

[0016] In an optional implementation manner, the step of iteratively updating the violation degree array by performing mathematical morphology filtering on the marker array to obtain a target violation degree array includes:

[0017] Perform mathematical morphology filtering on the current marker array to obtain an updated marker array;

[0018] Update the current violation degree array according to the updated marker array to obtain an updated violation degree array;

[0019] Judge whether the updated marker array meets a preset first iteration stop condition;

[0020] If the first iteration stop condition is not met, use the updated marker array as the current marker array, use the updated violation degree array as the current violation degree array, and re-execute the step of performing mathematical morphology filtering on the current marker array to obtain an updated marker array;

[0021] If the first iteration stop condition is met, use the updated violation degree array as the target violation degree array.

[0022] In an optional implementation manner, the step of updating the current violation degree array according to the updated marker array to obtain an updated violation degree array includes:

[0023] Determine the sum array of the current violation degree array and the updated marker array as the updated violation degree array.

[0024] In an alternative embodiment, the steps of determining the augmented dynamics model and the target optimal control problem according to the violation function and the original dynamics model of the aircraft include:

[0025] Establish an initial optimal control problem according to the mission requirements and the original dynamics model of the aircraft;

[0026] Augment the original dynamics model with an accumulated violation state to obtain an augmented dynamics model; wherein, the derivative of the accumulated violation state is the violation function;

[0027] Augment the initial optimal control problem with a terminal constraint that requires the terminal value of the accumulated violation to be 0;

[0028] Replace the no-fly zone constraint of the initial optimal control problem with a terminal constraint to obtain the target optimal control problem.

[0029] In an alternative embodiment, the steps of determining the target control quantity sequence according to the augmented dynamics model and the target optimal control problem include:

[0030] Perform Euler discretization on the augmented dynamics model and the target optimal control problem to obtain a discrete-time system and a discrete-form optimal control problem;

[0031] Initialize the control quantity sequence according to the discrete-form optimal control problem;

[0032] Iteratively update the control quantity sequence through the state quantity sequence and the terminal output value of the discrete-time system obtained by numerically integrating the augmented dynamics model based on the control quantity sequence to obtain the target control quantity sequence.

[0033] In an alternative embodiment, the steps of iteratively updating the control quantity sequence through the state quantity sequence and the terminal output value of the discrete-time system obtained by numerically integrating the augmented dynamics model based on the control quantity sequence to obtain the target control quantity sequence include:

[0034] Numerically integrate the augmented dynamics model according to the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system;

[0035] Judge whether the current control quantity sequence meets a preset second iteration stop condition according to the terminal output deviation corresponding to the current terminal output value;

[0036] If the second iteration stop condition is not satisfied, perform a Taylor expansion on the discrete-time system based on the current state quantity sequence to obtain a linearized state error equation and a linearized terminal output error equation; calculate the sensitivity matrix according to the linearized state error equation and the linearized terminal output error equation; calculate the updated control quantity sequence according to the sensitivity matrix, the current control quantity sequence, and the terminal output deviation; use the updated control quantity sequence as the current control quantity sequence, and re-execute the step of numerically integrating the augmented dynamics model according to the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system;

[0037] If the second iteration stop condition is satisfied, use the current control quantity sequence as the target control quantity sequence.

[0038] In a second aspect, the present invention provides a no-fly zone avoidance guidance device based on mathematical morphology filtering, including:

[0039] A function acquisition module for acquiring a violation degree function of a mission area including a no-fly zone, where the violation degree function is obtained based on mathematical morphology filtering and is used to characterize the association degree between different aircraft positions and the no-fly zone;

[0040] A first determination module for determining an augmented dynamics model and a target optimal control problem according to the violation degree function and the original dynamics model of the aircraft; wherein, the augmented dynamics model is obtained by augmenting the original dynamics model with an accumulated violation degree state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulated violation degree is 0;

[0041] A second determination module for determining a target control quantity sequence according to the augmented dynamics model and the target optimal control problem.

[0042] In a third aspect, the present invention provides an electronic device, including a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, it implements the no-fly zone avoidance guidance method based on mathematical morphology filtering in any one of the foregoing embodiments.

[0043] In a fourth aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the no-fly zone avoidance guidance method based on mathematical morphology filtering in any one of the foregoing embodiments.

[0044] The no-fly zone avoidance guidance method and device based on mathematical morphology filtering provided by the present invention can obtain a violation function of a mission area including a no-fly zone before performing a mission. The violation function is obtained based on mathematical morphology filtering and is used to characterize the degree of association between the positions of different aircraft and the no-fly zone. When performing a mission, online avoidance guidance is performed in the following manner: according to the violation function and the original dynamic model of the aircraft, an augmented dynamic model and a target optimal control problem are determined, and according to the augmented dynamic model and the target optimal control problem, a sequence of target control quantities is determined. The augmented dynamic model is obtained by augmenting the original dynamic model with an accumulated violation state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulated violation is 0. The violation function obtained through mathematical morphology filtering can handle no-fly zone constraints in any form. When the aircraft performs a mission, it only needs to run the part of online avoidance guidance, which has a small amount of calculation and high solution efficiency. Moreover, this guidance method is not specific to a particular dynamic model and has good model versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0046] Figure 1 It is a schematic flowchart of a no-fly zone avoidance guidance method based on mathematical morphology filtering provided by an embodiment of the present invention;

[0047] Figure 2 It is a schematic diagram of a planar no-fly zone constraint provided by an embodiment of the present invention;

[0048] Figure 3 It is a visualization effect of a violation array provided by an embodiment of the present invention;

[0049] Figure 4 It is a planar projection of a missile flight trajectory provided by an embodiment of the present invention;

[0050] Figure 5 It is a schematic structural diagram of a no-fly zone avoidance guidance device based on mathematical morphology filtering provided by an embodiment of the present invention;

[0051] Figure 6 It is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0053] Currently, existing no-fly zone avoidance methods can only handle no-fly zone constraints in specific forms, and there are technical problems such as low solution efficiency and poor model generality. Based on this, a no-fly zone avoidance guidance method and device based on mathematical morphology filtering provided by the embodiments of the present invention can cope with no-fly zone constraints in any form and alleviate the technical problems of low solution efficiency and poor model generality of existing no-fly zone avoidance methods.

[0054] To facilitate the understanding of this embodiment, first, a no-fly zone avoidance guidance method based on mathematical morphology filtering disclosed in the embodiments of the present invention will be introduced in detail.

[0055] The embodiments of the present invention provide a no-fly zone avoidance guidance method based on mathematical morphology filtering. This method can be executed by an electronic device with data processing capabilities. The electronic device can be located inside the aircraft or at a ground station communicating with the aircraft. Refer to Figure 1 the schematic flowchart of a no-fly zone avoidance guidance method based on mathematical morphology filtering shown. This method mainly includes the following steps S110 to step S130:

[0056] Step S110, obtain a violation function of the mission area including the no-fly zone. This violation function is obtained based on mathematical morphology filtering and is used to characterize the association degree between different aircraft positions and the no-fly zone.

[0057] In this embodiment, the aircraft can be any type of flying device, such as a drone or a missile, etc. Since the specific information of the no-fly zone is generally known in advance, this part can be completed before the aircraft starts to execute the mission. The violation function can be obtained by the ground station before the aircraft starts to execute the mission, or can be obtained by the aircraft itself before the aircraft starts to execute the mission. The violation function is used to describe the violation values at different aircraft positions. The violation values at all positions within the no-fly zone are greater than 0, and the violation values at all positions outside the no-fly zone are 0.

[0058] In some possible embodiments, the above-mentioned violation degree function can be obtained in the following manner: discretize the task area to obtain a marking array; wherein, the value of the array cell where the no-fly zone is located in the marking array is 1, and the values of the remaining array cells are 0; initialize the violation degree array; through mathematical morphological filtering of the marking array, iteratively update the violation degree array to obtain the target violation degree array; perform linear interpolation on the target violation degree array to obtain the target violation degree array.

[0059] When specifically implemented, the task area including the no-fly zone can be discretized into a boolean array, called the marking array, at a certain resolution. If it is a planar no-fly zone, it is discretized into a two-dimensional array; if it is a spatial no-fly zone, it is discretized into a three-dimensional array. Among them, the values of the array cells where the no-fly zone is located are all set to 1, and the values of the remaining array cells are all set to 0. A boolean array is a special type of array, and its elements can only take one of the two values 0 and 1. When initializing the violation degree array, the violation degree array can be initialized as the marking array. Before mathematical morphological filtering, it is necessary to first determine the filtering kernel. Optionally, the erosion kernel in mathematical morphology can be selected as the filtering kernel; if it is a planar no-fly zone, a two-dimensional erosion kernel is selected; if it is a spatial no-fly zone, a three-dimensional erosion kernel is selected.

[0060] The above-mentioned target violation degree array can be obtained in the following manner: perform mathematical morphological filtering on the current marking array to obtain an updated marking array; update the current violation degree array according to the updated marking array to obtain an updated violation degree array; determine whether the updated marking array satisfies a preset first iteration stop condition; if it does not satisfy the first iteration stop condition, use the updated marking array as the current marking array, use the updated violation degree array as the current violation degree array, and re-execute the step of performing mathematical morphological filtering on the current marking array to obtain an updated marking array; if it satisfies the first iteration stop condition, use the updated violation degree array as the target violation degree array. Among them, the first iteration stop condition may include that there are no array cells with a value of 1 in the marking array (i.e., the updated marking array). When specifically implemented, the sum array of the current violation degree array and the updated marking array can be determined as the updated violation degree array.

[0061] When specifically implemented, the step of performing linear interpolation on the target violation degree array to obtain the target violation degree array can be as follows: taking the aircraft position as the interpolation point and the violation degree array as the interpolation table, establish a multi-dimensional linear interpolation function, called the violation degree function. If it is a planar no-fly zone, a bilinear interpolation function is established; if it is a spatial no-fly zone, a trilinear interpolation function is established.

[0062] Step S120: Determine the augmented dynamics model and the target optimal control problem according to the violation function and the original dynamics model of the aircraft. The augmented dynamics model is obtained by augmenting the original dynamics model with an accumulated violation state. The no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulated violation is 0.

[0063] The above step S120 and the following step S130 belong to online avoidance guidance during mission execution, that is, this part runs online when the aircraft executes the mission.

[0064] In some possible embodiments, the above step S120 may include: establishing an initial optimal control problem according to the mission requirements and the original dynamics model of the aircraft; augmenting the original dynamics model with an accumulated violation state to obtain the augmented dynamics model. The derivative of the accumulated violation state is the violation function; adding a terminal constraint to the initial optimal control problem, and the terminal constraint requires that the terminal value of the accumulated violation is 0; replacing the no-fly zone constraint of the initial optimal control problem with the terminal constraint to obtain the target optimal control problem.

[0065] Step S130: Determine the target control quantity sequence according to the augmented dynamics model and the target optimal control problem.

[0066] In some possible embodiments, the above step S130 may include: performing Euler discretization on the augmented dynamics model and the target optimal control problem to obtain a discrete-time system and a discrete-form optimal control problem; initializing the control quantity sequence according to the discrete-form optimal control problem; iteratively updating the control quantity sequence by numerically integrating the augmented dynamics model based on the control quantity sequence to obtain the state quantity sequence and the terminal output value of the discrete-time system, so as to obtain the target control quantity sequence.

[0067] When initializing the control quantity sequence, an initial guess sequence of the control quantity (i.e., the initial value of the control quantity sequence) of the discrete-form optimal control problem can be given. For simplicity, the initial guess sequence can be set to a zero matrix. The numerical integration method can be but is not limited to the fourth-order Runge-Kutta method or the Euler method.

[0068] Optionally, the above target control quantity sequence can be obtained through the following update method: According to the current control quantity sequence, numerically integrate the augmented dynamics model to obtain the current state quantity sequence and the current terminal output value of the discrete-time system; According to the terminal output deviation corresponding to the current terminal output value, determine whether the current control quantity sequence meets the preset second iteration stop condition; If the second iteration stop condition is not met, perform a Taylor expansion on the discrete-time system based on the current state quantity sequence to obtain the linearized state error equation and the linearized terminal output error equation; According to the linearized state error equation and the linearized terminal output error equation, calculate the sensitivity matrix; According to the sensitivity matrix, the current control quantity sequence, and the terminal output deviation, calculate the updated control quantity sequence; Take the updated control quantity sequence as the current control quantity sequence, and re-execute the step of numerically integrating the augmented dynamics model according to the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system; If the second iteration stop condition is met, take the current control quantity sequence as the target control quantity sequence. Among them, the second iteration stop condition may include that the terminal output deviation is less than a preset threshold, and this preset threshold can be set according to actual needs and is not limited here.

[0069] The no-fly zone avoidance guidance method based on mathematical morphology filtering provided by the embodiments of the present invention can, before performing a task, obtain a violation function of a task area including a no-fly zone, and this violation function is obtained based on mathematical morphology filtering and is used to characterize the association degree between different aircraft positions and the no-fly zone; When performing a task, perform online avoidance guidance in the following manner: According to the violation function and the original dynamics model of the aircraft, determine the augmented dynamics model and the target optimal control problem, and according to the augmented dynamics model and the target optimal control problem, determine the target control quantity sequence; Among them, the augmented dynamics model is obtained by augmenting the original dynamics model with an accumulated violation state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulated violation is 0. The violation function obtained through mathematical morphology filtering can handle no-fly zone constraints in any form; When the aircraft performs a task, it only needs to run the online avoidance guidance part, and this part has a small amount of calculation and high solution efficiency; Moreover, this guidance method does not target a specific dynamics model and has good model generality.

[0070] For ease of understanding, the above no-fly zone avoidance guidance method based on mathematical morphology filtering will be introduced exemplarily below.

[0071] In this embodiment, the method is divided into two parts: no-fly zone constraint processing and online avoidance guidance.

[0072] 1. No-fly zone constraint processing:

[0073] The no-fly zone constraint processing is the first part. Since the specific information of the no-fly zone is generally known in advance, this part can be completed before the aircraft starts to execute the mission.

[0074] The no-fly zone constraint processing may include the following steps:

[0075] (1) Discretize the mission area: Discretize the mission area including the no-fly zone into a boolean array at a certain resolution, called the marking array. If it is a planar no-fly zone, it is discretized into a two-dimensional array; if it is a spatial no-fly zone, it is discretized into a three-dimensional array. The values of the array cells where the no-fly zone is located are all set to 1, and the values of the remaining array cells are all set to 0.

[0076] (2) Determine the filtering kernel: Select the erosion kernel in mathematical morphology as the filtering kernel. If it is a planar no-fly zone, select a two-dimensional erosion kernel; if it is a spatial no-fly zone, select a three-dimensional erosion kernel.

[0077] (3) Initialize the violation degree array: Define a new array, called the violation degree array, and initialize the violation degree array to the marking array.

[0078] (4) Mathematical morphology filtering: Perform a mathematical morphology filtering on the marking array using the filtering kernel, and use the filtered marking array as the current marking array.

[0079] (5) Update the violation degree array: Update the violation degree array to the sum array of the current violation degree array and the current marking array.

[0080] (6) Judge the iteration condition: Check whether there are array cells with a value of 1 in the current marking array. If not, go to step (7); if so, return to step (4).

[0081] (7) Establish the violation degree function: Take the aircraft position as the interpolation point and the violation degree array as the interpolation table to establish a multi-dimensional linear interpolation function, called the violation degree function. If it is a planar no-fly zone, establish a bilinear interpolation function; if it is a spatial no-fly zone, establish a trilinear interpolation function.

[0082] 2. Online avoidance guidance:

[0083] The online avoidance guidance is the second part. This part runs online when the aircraft executes the mission.

[0084] The online avoidance guidance includes the following steps:

[0085] (1) Problem establishment: According to the mission requirements and the original dynamic model of the aircraft, establish the optimal control problem to be solved by the online avoidance guidance.

[0086] (2) Model transformation: Augment the original dynamic model with a state called the cumulative violation degree. Let the initial value of this state be 0, and let the derivative of this state be the violation degree function to form an augmented dynamic model. Augment the original optimal control problem with a terminal constraint that requires the terminal value of the cumulative violation degree to be 0, and remove the no-fly zone constraint of the original optimal control problem to form a new optimal control problem.

[0087] (3) Euler discretization: Process the augmented dynamic model into a discrete-time system through the Euler method, and process the new optimal control problem into a discrete-form optimal control problem through the Euler method.

[0088] (4) Initial guess: Give an initial guess sequence of the control quantity for the discrete-form optimal control problem.

[0089] (5) Numerical integration: According to the current control quantity sequence, perform numerical integration on the augmented dynamic model to obtain the current state quantity sequence and the current terminal output value of the discrete-time system.

[0090] (6) Precision judgment: Calculate the deviation between the current terminal output value and the preset expected terminal output value, which is called the terminal output deviation. Judge whether the terminal output deviation is less than the preset threshold. If it is less than the preset threshold, output the current control quantity sequence as the target control quantity sequence required for guidance and stop the iteration; if it is not less than the preset threshold, go to step (7).

[0091] (7) Control update: Perform a Taylor expansion on the discrete-time system based on the current state quantity sequence and ignore the high-order small quantities to obtain the linearized state error equation and the linearized terminal output error equation, and then calculate the sensitivity matrix; update the control quantity sequence according to the sensitivity matrix, the current control quantity sequence, and the terminal output deviation, and then return to step (5).

[0092] For the sake of easy understanding, the following refers to Figures 2 to 4 , taking the planar no-fly zone avoidance guidance problem of a medium-range air-to-ground missile as an example, to further describe in detail the above no-fly zone avoidance guidance method based on mathematical morphology filtering.

[0093] 1. Processing of no-fly zone constraints.

[0094] This part is completed before the missile starts to execute the task.

[0095] (1) Discretize the mission area:

[0096] Discretize the mission area shown in Figure 2 into a 1280×720 two-dimensional label array with a resolution of 100m, where the cell value of the white area (belonging to the no-fly zone) is 1, and the cell value of the black area (belonging to the flyable zone) is 0.

[0097] (2) Determine the filtering kernel:

[0098] The selected two-dimensional erosion kernel (a three-order two-dimensional array) is as follows:

[0099]

[0100] (3) Initialize the violation degree array:

[0101] Initialize the violation degree array as the marking array.

[0102] (4) Mathematical morphology filtering:

[0103] Perform one-time mathematical morphology filtering on the marking array using the filtering kernel, and use the filtered marking array as the current marking array.

[0104] (5) Update the violation degree array:

[0105] Update the violation degree array to the sum array of the current violation degree array and the current marking array.

[0106] (6) Judge the iteration condition:

[0107] Check whether there is an array element with a value of 1 in the current marking array. If not, go to step (7); if so, return to step (4).

[0108] (7) Establish the violation degree function:

[0109] Taking the projection position (x, y) of the missile on the ground as the interpolation point and the violation degree array as the interpolation table, establish a bilinear interpolation function ω(x, y) as the violation degree function.

[0110] After repeated iteration of steps (4) to (7), the finally generated violation degree array is as Figure 3 shown. Figure 3 In it, the values and colors in the height direction reflect the magnitude of the violation degree value.

[0111] 2. Online avoidance guidance.

[0112] This part runs online when the missile executes the mission.

[0113] (1) Problem establishment:

[0114] Under the assumption of a flat earth, ignoring the rotational motion of the medium-range air-to-ground missile around its centroid and regarding it as a controllable particle, considering its motion in three-dimensional space, its dynamic model is expressed as:

[0115]

[0116] Among them, (x, y) is the projection position of the missile on the ground, h is the altitude, V is the speed magnitude, θ is the ballistic inclination angle, ψ is the ballistic deflection angle, α is the angle of attack, β is the sideslip angle, m is the missile mass, T is the engine thrust, D, L, and Y are the drag, lift, and side force of the missile respectively, u 1 and u 2 are control variables.

[0117] Also:

[0118] L = qSC L ;

[0119] D = qSC D ;

[0120] Y = qSC Y ;

[0121]

[0122] Among them, q is the dynamic pressure, S is the reference area of the missile, taking 0.025 m 2 , C L , C D and C Y are the lift coefficient, drag coefficient, and side force coefficient of the missile respectively, and are fitted as polynomials about the angle of attack and sideslip angle according to aerodynamic data. t refers to time, the unit of t is second, the unit of m is kg, and the unit of T is Newton (N). ρ is the local atmospheric density, which is a function of the altitude h, such as ρ = ρ 0 e bh , where ρ 0 is the atmospheric density at sea level, taking 1.225 kg / m 3 , and b is a constant, taking -0.00013889.

[0123] The plane no-fly zone constraint suffered by the missile during mission execution is as Figure 2 shown. The scale of the entire area is 128 km × 72 km. The white part is the no-fly zone, and the black part is the flyable zone. The satisfaction of the no-fly zone constraint is abstracted as C NFZ . If entering the no-fly zone, then C NFZ > 0. If not entering the no-fly zone, then C NFZ ≤ 0.

[0124] Then the optimal control problem to be solved for the plane no-fly zone avoidance guidance of the medium-range air-to-ground missile is expressed as:

[0125]

[0126] φ(χ(t 0 ), t 0 , χ(t f ), tf ) = 0;

[0127] C NFZ ≤ 0;

[0128] where t 0 represents the starting time, and t f represents the terminal time. φ represents the endpoint constraint function with respect to the state vector and time, and χ represents the state vector.

[0129] The specific parameter settings in the endpoint constraint φ(χ(t 0 ), t 0 , χ(t f ), t f ) = 0 are described in Table 1. The subscript 0 of each parameter represents the starting position, and the subscript f represents the terminal position.

[0130] Table 1

[0131]

[0132]

[0133] (2) Model transformation:

[0134] Augment the original dynamics model with a state Ω, called the cumulative violation degree, such that:

[0135]

[0136] Ω(t 0 ) = 0;

[0137] Augment the original optimal control problem with a terminal constraint:

[0138] Ω(t f ) = 0;

[0139] Remove the no - fly zone constraint C NFZ ≤ 0 from the original optimal control problem to form a new optimal control problem:

[0140]

[0141]

[0142] φ(χ(t 0 ), t 0 , χ(t f ), t f ) = 0;

[0143] Ω(t 0 ) = Ω(t f ) = 0.

[0144] (3) Euler discretization:

[0145] The augmented dynamic model and the discrete form of the new optimal control problem are obtained by the Euler method, where the state equation, output equation, and performance index are respectively expressed as follows:

[0146] X k+1 = F k (X k , U k );

[0147] Y = HX N ;

[0148]

[0149] Among them, the state quantity X of the discrete-time system is a 9-dimensional vector, the control quantity U in discrete form is a 2-dimensional vector, the terminal output value Y is a 4-dimensional vector, F is the augmented dynamic equation in discrete form, J is the performance index in discrete form, and k = 1, 2,..., N - 1 are discrete time steps.

[0150] (4) Initial guess:

[0151] A sequence of initial guesses for the control quantity in discrete form is given. Since the method in the embodiments of the present invention is not sensitive to the initial guess, for simplicity, the initial guess sequence can be set as a zero matrix.

[0152] (5) Numerical integration:

[0153] According to the current control quantity sequence, the augmented dynamic model is numerically integrated using the fourth-order Runge-Kutta method to obtain the state quantity sequence of the discrete-time system and the terminal output value.

[0154] (6) Precision judgment:

[0155] Calculate the terminal output deviation and determine whether it is less than 10 -3 . If it is less than, then output the current control quantity sequence as the target control quantity sequence required for guidance and stop the iteration; if it is not less than, then go to step (7).

[0156] (7) Control update:

[0157] Taking the current state quantity sequence as a reference, perform a Taylor expansion on the discrete-time system and ignore high-order small quantities to obtain the linearized state error equation and the linearized terminal output error equation as follows:

[0158]

[0159] dY = HdX N .

[0160] In this way, we can obtain The value of the terminal output deviation dY is used for the subsequent calculation of the sensitivity matrix and the update of the control quantity sequence.

[0161] Furthermore, the sensitivity matrix B is calculated. k As follows:

[0162]

[0163]

[0164] The control quantity sequence is updated according to the sensitivity matrix, the current control quantity sequence, and the terminal output deviation as follows:

[0165]

[0166] Where U k is the updated control quantity sequence, is the current control quantity sequence, and dY is the terminal output deviation. After the control quantity sequence is updated, return to step (5).

[0167] After repeated iterations of steps (5) to (7), the planar projection of the missile flight trajectory formed by the finally output control quantity sequence is as Figure 4 shown, and it can be seen that the missile successfully avoids the no-fly zone and reaches the specified position.

[0168] The advantages of the embodiments of the present invention are as follows: Through mathematical morphology filtering processing, it can cope with no-fly zone constraints in any form; when the aircraft executes tasks, it only needs to run the part of online avoidance guidance, which has a small amount of calculation and high solution efficiency; this guidance method does not target a specific dynamic model and has good model generality.

[0169] Corresponding to the above no-fly zone avoidance guidance method based on mathematical morphology filtering, the embodiments of the present invention also provide a no-fly zone avoidance guidance device based on mathematical morphology filtering. Refer to Figure 5 the structural schematic diagram of a no-fly zone avoidance guidance device based on mathematical morphology filtering shown. The device includes:

[0170] A function acquisition module 501, configured to acquire a violation function of a mission area including a no-fly zone. The violation function is obtained based on mathematical morphology filtering and is used to characterize the association degree between different aircraft positions and the no-fly zone;

[0171] A first determination module 502, configured to determine an augmented dynamic model and an optimal target control problem according to the violation function and the original dynamic model of the aircraft; wherein, the augmented dynamic model is obtained by augmenting the original dynamic model with an accumulated violation state, and the no-fly zone constraint in the optimal target control problem is that the terminal value of the accumulated violation is 0;

[0172] The second determination module 503 is configured to determine a target control quantity sequence according to the augmented dynamics model and the target optimal control problem.

[0173] The no-fly zone avoidance guidance device based on mathematical morphology filtering provided by the present invention can, before performing a task, obtain a violation degree function of a task area including a no-fly zone, where the violation degree function is obtained based on mathematical morphology filtering and is used to characterize the association degree between different aircraft positions and the no-fly zone; when performing the task, perform online avoidance guidance in the following manner: determine an augmented dynamics model and a target optimal control problem according to the violation degree function and the original dynamics model of the aircraft, and determine a target control quantity sequence according to the augmented dynamics model and the target optimal control problem; where the augmented dynamics model is obtained by augmenting the original dynamics model with an accumulated violation degree state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the accumulated violation degree is 0. The violation degree function obtained through mathematical morphology filtering can handle no-fly zone constraints in any form; when the aircraft performs a task, it only needs to run the online avoidance guidance part, which has a small amount of calculation and high solution efficiency; moreover, this guidance method does not target a specific dynamics model and has good model generality.

[0174] Further, the function acquisition module 501 is specifically configured to: discretize the task area to obtain a marker array; where the value of the array cell where the no-fly zone is located in the marker array is 1, and the values of the remaining array cells are 0; initialize a violation degree array; iteratively update the violation degree array by performing mathematical morphology filtering on the marker array to obtain a target violation degree array; perform linear interpolation on the target violation degree array to obtain a target violation degree array.

[0175] Further, the function acquisition module 501 is further configured to: perform mathematical morphology filtering on the current marker array to obtain an updated marker array; update the current violation degree array according to the updated marker array to obtain an updated violation degree array; determine whether the updated marker array satisfies a preset first iteration stop condition; if it does not satisfy the first iteration stop condition, use the updated marker array as the current marker array, use the updated violation degree array as the current violation degree array, and re-perform the step of performing mathematical morphology filtering on the current marker array to obtain an updated marker array; if it satisfies the first iteration stop condition, use the updated violation degree array as the target violation degree array.

[0176] Further, the function acquisition module 501 is further configured to: determine the sum array of the current violation degree array and the updated marker array as the updated violation degree array.

[0177] Further, the first determination module 502 is specifically configured to: establish an initial optimal control problem according to the task requirements and the original dynamic model of the aircraft; augment the original dynamic model with an accumulated violation degree state to obtain an augmented dynamic model, where the derivative of the accumulated violation degree state is the violation degree function; augment the initial optimal control problem with a terminal constraint, and the terminal constraint requires that the terminal value of the accumulated violation degree is 0; replace the no-fly zone constraint of the initial optimal control problem with the terminal constraint to obtain the target optimal control problem.

[0178] Further, the second determination module 503 is specifically configured to: perform Euler discretization on the augmented dynamic model and the target optimal control problem to obtain a discrete-time system and a discrete-form optimal control problem; initialize a control quantity sequence according to the discrete-form optimal control problem; perform numerical integration on the augmented dynamic model based on the control quantity sequence, and iterate and update the control quantity sequence according to the state quantity sequence and the terminal output value of the obtained discrete-time system to obtain the target control quantity sequence.

[0179] Further, the second determination module 503 is further configured to: perform numerical integration on the augmented dynamic model according to the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system; determine whether the current control quantity sequence meets a preset second iteration stop condition according to the terminal output deviation corresponding to the current terminal output value; if the second iteration stop condition is not met, perform Taylor expansion on the discrete-time system based on the current state quantity sequence to obtain a linearized state error equation and a linearized terminal output error equation; calculate a sensitivity matrix according to the linearized state error equation and the linearized terminal output error equation; calculate an updated control quantity sequence according to the sensitivity matrix, the current control quantity sequence, and the terminal output deviation; use the updated control quantity sequence as the current control quantity sequence, and re-execute the step of performing numerical integration on the augmented dynamic model according to the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system; if the second iteration stop condition is met, use the current control quantity sequence as the target control quantity sequence.

[0180] The no-fly zone avoidance guidance device based on mathematical morphology filtering provided in this embodiment has the same implementation principle and technical effects as those of the foregoing no-fly zone avoidance guidance method embodiment based on mathematical morphology filtering. For the sake of brief description, for the parts not mentioned in the no-fly zone avoidance guidance device embodiment based on mathematical morphology filtering, reference may be made to the corresponding content in the foregoing no-fly zone avoidance guidance method embodiment based on mathematical morphology filtering.

[0181] Such as Figure 6As shown, an electronic device 600 provided by an embodiment of the present invention includes: a processor 601, a memory 602, and a bus. The memory 602 stores a computer program that can run on the processor 601. When the electronic device 600 runs, the processor 601 communicates with the memory 602 through the bus, and the processor 601 executes the computer program to implement the above-mentioned no-fly zone avoidance guidance method based on mathematical morphology filtering.

[0182] Specifically, the above-mentioned memory 602 and processor 601 can be general-purpose memory and processor, and no specific limitation is made here.

[0183] An embodiment of the present invention also provides a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is run by a processor, it executes the no-fly zone avoidance guidance method based on mathematical morphology filtering in the foregoing method embodiment. The computer-readable storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM), RAMs, magnetic disks, or optical discs that can store program codes.

[0184] The term "and / or" in this article is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the term "at least one" in this article means any one of multiple or any combination of at least two of multiple. For example, including at least one of A, B, and C can represent selecting any one or more elements from the set composed of A, B, and C.

[0185] In all the examples shown and described here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments can have different values.

[0186] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of apparatuses, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that, in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as combinations of blocks in the block diagram and / or flowchart, may be implemented by a dedicated hardware-based system that performs the specified functions or actions, or may be implemented by a combination of dedicated hardware and computer instructions.

[0187] In several embodiments provided in this application, it should be understood that the disclosed apparatuses and methods may be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of modules is only a logical function division, and there may be other division methods in actual implementation. For another example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the couplings or direct couplings or communication connections shown or discussed among each other may be through some communication interfaces. The indirect couplings or communication connections of apparatuses or modules may be in electrical, mechanical, or other forms.

[0188] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place, or may be distributed to multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0189] In addition, the functional modules in various embodiments of the present invention may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A no-fly zone avoidance guidance method based on mathematical morphology filtering, characterized in that: include: Obtaining a violation function of a mission area including a no-fly zone, wherein the violation function is obtained based on mathematical morphology filtering and is used to characterize the degree of association between different aircraft positions and the no-fly zone; Determine an augmented dynamics model and a target optimal control problem according to the violation function and the original dynamics model of the aircraft; wherein the augmented dynamics model is obtained by augmenting the original dynamics model with a cumulative violation state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the cumulative violation is 0; According to the augmented dynamics model and the target optimal control problem, a target control quantity sequence is determined.

2. The method according to claim 1, characterized in that The steps of obtaining the violation function of the mission area including the no-fly zone include: Discretizing the mission area to obtain a marking array; wherein the value of the array unit where the no-fly zone is located in the marking array is 1, and the values ​​of the other array units are 0; Initialize the violation degree array; By performing mathematical morphological filtering on the marker array, the violation degree array is iteratively updated to obtain a target violation degree array; Linear interpolation is performed on the target violation degree array to obtain the target violation degree array.

3. The method according to claim 2, characterized in that The step of performing mathematical morphological filtering on the marker array and iteratively updating the violation degree array to obtain a target violation degree array comprises: Perform mathematical morphological filtering on the current marker array to obtain an updated marker array; Update the current violation degree array according to the updated mark array to obtain an updated violation degree array; Determining whether the updated marker array satisfies a preset first iteration stop condition; If the first iteration stop condition is not met, the updated mark array is used as the current mark array, the updated violation degree array is used as the current violation degree array, and the step of performing mathematical morphological filtering on the current mark array to obtain an updated mark array is re-executed; If the first iteration stop condition is met, the updated violation degree array is used as the target violation degree array.

4. The method according to claim 3, characterized in that The step of updating the current violation degree array according to the updated mark array to obtain the updated violation degree array comprises: The sum array of the current violation degree array and the updated mark array is determined as the updated violation degree array.

5. The method according to claim 1, characterized in that The step of determining the augmented dynamics model and the target optimal control problem according to the violation function and the original dynamics model of the aircraft comprises: Establishing an initial optimal control problem based on mission requirements and the original dynamics model of the aircraft; Augmenting the original dynamic model with a cumulative violation state to obtain the augmented dynamic model; wherein the derivative of the cumulative violation state is the violation function; Adding a terminal constraint to the initial optimal control problem, wherein the terminal constraint requires that the terminal value of the cumulative violation degree is 0; The no-fly zone constraint of the initial optimal control problem is replaced by the terminal constraint to obtain the target optimal control problem.

6. The method according to claim 1, characterized in that The step of determining a target control quantity sequence according to the augmented dynamics model and the target optimal control problem comprises: Performing Euler discretization on the augmented dynamics model and the target optimal control problem to obtain a discrete-time system and a discrete form optimal control problem; Initializing a control quantity sequence according to the discrete form optimal control problem; The state quantity sequence and terminal output value of the discrete-time system are obtained by numerically integrating the augmented dynamics model based on the control quantity sequence, and the control quantity sequence is iteratively updated to obtain the target control quantity sequence.

7. The method according to claim 6, characterized in that The step of numerically integrating the augmented dynamics model based on the control quantity sequence to obtain the state quantity sequence and terminal output value of the discrete-time system, iteratively updating the control quantity sequence to obtain the target control quantity sequence comprises: According to the current control quantity sequence, the augmented dynamics model is numerically integrated to obtain the current state quantity sequence and the current terminal output value of the discrete time system; According to the terminal output deviation corresponding to the current terminal output value, judging whether the current control amount sequence meets a preset second iteration stop condition; If the second iteration stop condition is not met, the discrete-time system is Taylor expanded based on the current state quantity sequence to obtain a linearized state error equation and a linearized terminal output error equation; a sensitivity matrix is ​​calculated based on the linearized state error equation and the linearized terminal output error equation; an updated control quantity sequence is calculated based on the sensitivity matrix, the current control quantity sequence and the terminal output deviation; the updated control quantity sequence is used as the current control quantity sequence, and the augmented dynamics model is numerically integrated based on the current control quantity sequence to obtain the current state quantity sequence and the current terminal output value of the discrete-time system. If the second iteration stop condition is met, the current control amount sequence is used as the target control amount sequence.

8. A no-fly zone avoidance guidance device based on mathematical morphology filtering, characterized in that: include: A function acquisition module, used to acquire a violation function of a mission area including a no-fly zone, wherein the violation function is obtained based on mathematical morphology filtering and is used to characterize the degree of association between different aircraft positions and the no-fly zone; A first determination module is used to determine an augmented dynamics model and a target optimal control problem according to the violation function and the original dynamics model of the aircraft; wherein the augmented dynamics model is obtained by augmenting the original dynamics model with a cumulative violation state, and the no-fly zone constraint in the target optimal control problem is that the terminal value of the cumulative violation is 0; The second determination module is used to determine the target control quantity sequence according to the augmented dynamics model and the target optimal control problem.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the no-fly zone avoidance guidance method based on mathematical morphological filtering described in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the no-fly zone avoidance guidance method based on mathematical morphological filtering according to any one of claims 1 to 7 is executed.

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