A Cooperative Midcourse Guidance Law Design Method Based on Shaping Guidance Law

Abstract

The present invention relates to a collaborative mid-course guidance law design method based on a shaping guidance law, belonging to the field of guidance and control technology. It includes establishing a state space equation by introducing the concept of zero-effect miss distance according to the relative motion relationship between the missile and the target; introducing the remaining flight time to design the missile time collaboration term; designing a shaping guidance law with terminal angle constraints according to the state space equation; and introducing the time collaboration term into the shaping guidance law to achieve the guidance law design with angle and time constraints. The present invention combines methods such as multi-agent consensus theory, shaping mid-course guidance algorithm, and offset proportional guidance law, realizes the design of a multi-missile collaborative mid-course guidance law with time collaboration and angle collaboration, and realizes reaching the target area at a fixed angle and simultaneously, forming a better mid-course to terminal guidance handover situation.

Description

Technical Field

[0001] The present invention relates to the technical field of guidance and control of airborne precision-guided weapons, and specifically to a cooperative mid-course guidance method based on a shaped guidance law, which is applicable to a long-range air-to-air missile for attacking a target that can only obtain situational-level information. Background Art

[0002] With the development of military technology and the deepening of research on combat patterns, multi-missile cooperative attack and defense are attracting more and more attention due to their unique advantages. As a key technology to ensure attack and defense performance, multi-missile cooperative guidance has also developed rapidly. First, in terms of offense, multi-missile cooperative guidance can integrate multiple missiles into a combat group with information sharing, complementary functions, and tactical cooperation through missile group cooperation, and use the group advantage to conduct multi-level and all-round strikes on the enemy's defense system and targets, thereby achieving an overall improvement in penetration ability. Second, multiple missiles can also complete tasks that are difficult for a single missile to complete, such as achieving saturation attacks and "reconnaissance-strike-evaluation" integrated cooperative operations. Third, missiles in the missile group can adopt different guidance systems, thereby achieving tactical stealth, enhancing electronic countermeasures and target recognition capabilities, and improving anti-jamming capabilities in complex battlefield environments. In addition, some missiles in the missile group can be equipped with expensive seeker heads, while other missiles are only equipped with low-cost guidance and control components to reduce combat costs and improve cost-effectiveness. In terms of defense, the effectiveness of the anti-missile system can also be improved through multi-missile cooperation.

[0003] In modern warfare, using long-range precision-guided air-to-ground missiles to carry out air-to-ground strikes has become the main means of attacking the enemy. During the flight of the missile, the over-the-horizon working conditions require it to adopt a composite guidance system of initial guidance + mid-course guidance + terminal guidance. Among them, the main role of the mid-course guidance section is to guide the missile to a predetermined area that can ensure reliable interception of the target by the terminal guidance, and to create good conditions for the seeker head to capture the target, thereby forming a good initial situation for the terminal guidance and greatly improving the strike ability against the target. While guiding the missile to the mid-course / terminal guidance handover point, the mid-course guidance section also needs to make the missile have an ideal flight state at the handover point. Currently, the research work on mid-course guidance laws mainly considers two constraint conditions: the position and the ballistic inclination angle at the end of the mid-course guidance. Summary of the Invention

[0004] To solve the guidance problem in the cooperative operation of long-range air-to-air missiles, in the conventional case, the cooperative mid-course guidance law is designed. In the mid-course phase, due to the long distance between the missile and the target, the cooperative mid-course guidance law based on the missile-follower method is adopted. At the end of the mid-course phase, when approaching the handover area, formation transformation is required to form an encircling attack formation to provide better conditions for the handover between the mid-course and terminal guidance. At this stage, the distance between the missile and the target is close to the detection range of the seeker. At this time, according to the movement trend of the target, an encircling posture should be formed as soon as possible. When the missile seeker is turned on to capture the target, a good handover condition is formed, which is convenient for realizing cooperative encircling attack in the terminal guidance stage. Cooperative mid-course guidance needs to achieve two purposes: First, multiple missiles reach the expected handover position at the same time; Second, according to the requirements of cooperative encirclement, the missiles reach the desired handover position at the desired speed direction.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A design method for a cooperative mid-course guidance law based on a shaping guidance law, characterized in that the steps are as follows:

[0007] Step 1: According to the relative motion relationship between the missile and the target, introduce the concept of zero-efficiency miss distance to establish a state space equation;

[0008] Step 2: Introduce the remaining flight time to design the missile time cooperation term;

[0009] Step 3: Design a shaping guidance law with terminal angle constraints according to the state space equation;

[0010] Step 4: Introduce the time cooperation term into the shaping guidance law to realize the guidance law design with angle and time constraints.

[0011] A further technical solution of the present invention: The specific state space equation in Step 1 is as follows:

[0012]

[0013] Among them, y is the zero-efficiency miss distance, is the relative velocity, is the relative acceleration, n T is the target normal acceleration, n c is the missile acceleration control command, and the zero-efficiency miss distance y is obtained by satisfying y(t F ) = 0, and minimizing and obtained.

[0014] A further technical solution of the present invention: Step 2 is specifically as follows:

[0015] The variable of the missile cooperative flight time is the remaining flight time t goi(t) needs to be used as a state variable of the system. Through the expected cooperation time, the control quantity that can make the remaining flight times of each missile consistent can be obtained, and it is introduced as a bias control item into the mid-course guidance design.

[0016]

[0017]

[0018] Among them, u ε is the acceleration of the missile in the pitch channel, and u β is the acceleration of the missile in the yaw channel. is the coefficient of the cooperative control item; t goi , t goi_d are respectively the estimated remaining flight time and the expected flight time of the missile.

[0019] The further technical solution of the present invention: Step 3 is specifically as follows:

[0020] By introducing the concept of zero-effect miss distance, the form of the trajectory shaping guidance law can be obtained

[0021]

[0022] Further transformation

[0023]

[0024] Since

[0025] In the formula, T is the target parameter, n is the acceleration command, y is the introduced zero-effect miss distance, λ is the line-of-sight vector between the missile and the target, and t go is the estimated remaining flight time;

[0026] Substituting the above formula, the final form of the trajectory shaping guidance law is obtained:

[0027] Among them, n c is the control acceleration of the missile, V c is the speed of the missile, λ is the line-of-sight angle, λ F is the terminal line-of-sight angle, n T is the target normal acceleration, and t go is the estimated remaining flight time;

[0028] Use the basic shaping guidance law to design the mid-course guidance algorithm in the pitch channel and the yaw channel respectively:

[0029]

[0030]

[0031] where n ε is the acceleration of the missile in the pitch channel, n β is the acceleration of the missile in the yaw channel, K is the proportionality coefficient of the guidance law, V cε is the velocity component of the missile in the pitch channel, V cβ is the velocity component of the missile in the yaw channel, is the line-of-sight angular rate of the pitch channel, is the line-of-sight angle of the yaw channel, n Tε is the acceleration of the target in the pitch channel, n Tβ is the acceleration of the target in the yaw channel, λ is the line-of-sight vector between the missile and the target, t go is the estimated remaining flight time.

[0032] A further technical solution of the present invention: Step 4 is specifically as follows:

[0033] Taking the i-th missile as an example, considering the time coordination consistency of mid-course guidance, according to the multi-agent consensus theory, the remaining time t goi is selected as the system state variable x i , and the desired remaining time is obtained through the consensus protocol According to the requirement that the missiles arrive successively, the final desired arrival time of the i-th missile is obtained

[0034]

[0035]

[0036]

[0037] The rightmost term in the above formula is the coordination term. Through the design of this coordination term, multiple missiles can tend to the target according to the set time difference; where K′ = K·[1 + q·(t go_d -t go )], q is the adjustment parameter of the variable proportionality coefficient for adjusting the proportionality parameter, t go_d = max(t goi ), σ is the velocity lead angle obtained by the cosine theorem, and n is the number of cooperative missiles; n ε is the acceleration of the missile in the pitch channel, n β is the acceleration of the missile in the yaw channel, V cε is the velocity component of the missile in the pitch channel, V cβ is the velocity component of the missile in the yaw channel, λ ε is the line-of-sight angle of the pitch channel, λ β is the line-of-sight angle of the yaw channel, λ Fεis the desired terminal line-of-sight angle for the pitch channel, λ Fβ is the desired terminal line-of-sight angle for the yaw channel is the line-of-sight angle rate for the pitch channel is the line-of-sight angle rate for the yaw channel, n Tε is the target normal overload for the pitch channel, n Tβ is the target normal overload for the yaw channel, n Tβ is the target normal overload for the yaw channel, t goi is the remaining time of missile i, t goi_d is the desired remaining time of missile i

[0038] A computer system, characterized in that it includes: one or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method

[0039] A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the above-mentioned method when executed

[0040] For a multi-missile system with time coordination and space coordination requirements, a cooperative mid-course guidance law design method based on the shaping guidance law provided by the present invention combines methods such as multi-agent consensus theory, shaping mid-course guidance algorithm, and offset proportional navigation law, realizes the design of a cooperative mid-course guidance law for multiple missiles with time coordination and angle coordination, and realizes reaching the target area at a fixed angle and simultaneously, forming a better mid-course to terminal guidance handover situation BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings are only for the purpose of showing specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs denote the same components

[0042] Figure 1 : Missile-target relative motion geometric relationship

[0043] Figure 2 : Homing loop model

[0044] Figure 3 : Mid-course guidance kinematic relationship in the pitch channel

[0045] Figure 4 : Missile-target rendezvous trajectory

[0046] Figure 5 : Missile-target distance change diagram

[0047] Figure 6 : Remaining time estimation

[0048] Figure 7 : Pitch channel overload change;

[0049] Figure 8 : Yaw channel overload change;

[0050] Figure 9 : Variation diagram of the longitudinal component of the line-of-sight angle;

[0051] Figure 10 : Variation of the horizontal component of the line-of-sight angle. Specific implementation manner

[0052] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0053] The present invention provides a collaborative mid-course guidance law design method based on a shaping guidance law, including the following steps:

[0054] Step 1: According to the relative motion relationship between the missile and the target, introduce the concept of zero-effective miss distance to establish a state-space equation;

[0055] Step 2: Introduce the remaining flight time to design the missile time coordination term;

[0056] Step 3: Design a shaping guidance law with terminal angle constraints according to the state-space equation;

[0057] Step 4: Introduce the time coordination term in the shaping guidance law to achieve the guidance law design with angle and time constraints.

[0058] Specifically as follows:

[0059] Step 1: According to the relative motion relationship between the missile and the target, introduce the concept of zero-effective miss distance to establish a state-space equation

[0060] The relative motion relationship between the missile and the target is as Figure 1 shown, and the following equations can be established

[0061]

[0062] Here, r is the missile-target distance, q is the line-of-sight angle, θ T is the missile velocity inclination angle, θ M is the missile velocity inclination angle, V M is the missile velocity, V T is the target velocity.

[0063] Establish a system model according to the relative motion relationship as Figure 2As shown, the system model can be described by the following state - space equations:

[0064]

[0065] Here, \(y\) is the zero - effort miss distance, is the relative velocity, is the relative acceleration, \(n\) T is the target normal acceleration, \(n\) c is the missile acceleration control command. The zero - effort miss distance \(y\) is obtained by satisfying \(y(t F ) = 0\), and minimizing and obtained.

[0066] Step 2: Introduce the remaining flight time to design the missile time - coordination term

[0067] The coordination variable required for the missile cooperative flight is the remaining flight time, which needs to be used as the system state variable \(x i \). Through the consensus protocol, the control quantity that can control the remaining flight times of each missile to be consistent can be obtained, and it is introduced as a bias control term into the mid - guidance design,

[0068]

[0069]

[0070] where \(K\) is the coefficient of the cooperative control term, which is a time - varying quantity and will be designed later. \(t goi \), \(t goi_d are respectively the estimated remaining flight time and the desired flight time of the missile.

[0071] Step 3: Design a shaping guidance law with terminal angle constraints according to the state - space equation

[0072] The zero - effort miss distance refers to the minimum relative distance when the guidance thrust of the missile stops and both the target and the missile move freely under the influence of gravity only. When the zero - effort miss distance of the missile at a certain point in space is zero, theoretically, it can be considered that even without control, a direct collision interception of the target can be achieved within a finite time. Compared with the guidance based on line - of - sight rate, the guidance based on zero - effort miss distance is a direct guidance method for the miss distance, with more intuitive effects and the advantage of energy saving. However, due to the limitations of existing equipment, most research focuses on mid - guidance. In the guidance closed - loop, we expect the zero - effort miss distance to be 0, hope that the relative velocity at the end of the flight process is a specified value, and the control energy consumption is minimized. Described in mathematical terms, it is \(y(t F ) = 0\), minimize where \(y\) is the zero - effort miss distance, is the relative velocity.

[0073] According to the established final form of the trajectory shaping guidance law

[0074]

[0075] where λ here is the line-of-sight angle, and λ F is the terminal line-of-sight angle, and n T is the target normal acceleration.

[0076] The trajectory shaping guidance law can meet the angle constraints, and at the same time has a simple structure and is widely used in engineering practice. Therefore, the time coordination parameter is introduced into the trajectory shaping mid-course guidance law to obtain the trajectory shaping coordinated mid-course guidance law, so as to realize the time coordination of multiple missiles in formation. The design of the multiple-missile coordinated mid-course guidance law is divided into two parts: the basic shaping mid-course guidance law and the time coordination term.

[0077] Use the basic shaping guidance law to design the mid-course guidance algorithm in the pitch channel and the yaw channel respectively:

[0078]

[0079]

[0080] In the formula, ε is the pitch channel parameter, β is the yaw channel parameter, T is the target parameter, n is the acceleration command, K is the guidance law proportionality coefficient, λ is the line-of-sight vector between the missile and the target, and t go is the estimated remaining flight time.

[0081] Step 4: Introduce the time coordination term in the shaping guidance law to realize the guidance law design with angle and time constraints

[0082] Taking the i-th missile as an example, considering the time coordination consistency of the mid-course guidance, from Step 2, according to the multi-agent consensus theory, select the remaining time t goi as the system state variable x i , and the desired remaining time can be obtained through the consensus protocol According to the requirement that the missiles arrive one after another, the final desired arrival time of the i-th missile is obtained

[0083]

[0084]

[0085]

[0086] The rightmost term in the above formula is the coordination term. Through the design of this coordination term, multiple missiles can be made to tend to the target according to the set time difference. Among them, K′ = K·[1 + q·(tgo_d -t go )], where q is the variable proportionality coefficient to obtain the adjustment parameter for adjusting the proportionality parameter, t go_d = max(t goi ), where σ is the velocity leading angle obtained by the cosine theorem, and n is the number of cooperative missiles. n ε is the acceleration of the missile in the pitch channel, n β is the acceleration of the missile in the yaw channel, V cε is the velocity component of the missile in the pitch channel, V cβ is the velocity component of the missile in the yaw channel, λ ε is the line-of-sight angle of the pitch channel, λ β is the line-of-sight angle of the yaw channel, λ Fε is the expected terminal line-of-sight angle of the pitch channel, λ Fβ is the expected terminal line-of-sight angle of the yaw channel, is the line-of-sight angle rate of the pitch channel, is the line-of-sight angle rate of the yaw channel, n Tε is the normal overload of the target in the pitch channel, n Tβ is the normal overload of the target in the yaw channel, n Tβ is the normal overload of the target in the yaw channel, t goi is the remaining time of missile i, t goi_d is the expected remaining time of missile i.

[0087] Under the guidance of the distributed cooperative mid-course guidance law for three missiles, the model parameters and mathematical simulation experiments are as follows: The target position is (400, 8, 6) km. The proportionality parameter p of the cooperative term 1 = p 2 = p 3 = 4, the initial proportional guidance coefficient K = 4, and the adjustable parameter q of the variable proportionality coefficient = -0.088.

[0088] Table of initial model parameters

[0089]

[0090] Figure 4 Shows the missile-target rendezvous trajectory. The three missiles are at a distance of 400 km from the target and the inter-missile distance is 10 km, fully considering the situation of sequential missile launches. The mid-course part forms a high-trajectory and encircles the target at a predetermined distance. Figure 5 and Figure 6 respectively show the changes in the missile-target relative distance and the estimation of the remaining time. It can be seen that under the action of this guidance law, both the missile-target distance and the estimation of the remaining flight time tend to be consistent, achieving time coordination. Figure 6 The dashed lines of Figure 7 and Figure 8The overload change diagram is shown, and the full-trajectory overload is relatively gentle and reasonable. Figure 9 and Figure 10 The line-of-sight angle is shown. That is, at the moment of reaching the mid-course and terminal guidance handover area, a specific-angle encirclement posture towards the target is achieved, which is conducive to carrying out joint search.

[0091] As mentioned above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art in the technical field disclosed by the present invention can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should all be covered within the protection scope of the present invention.

Claims

1. A collaborative mid-course guidance law design method based on a shaping guidance law, characterized in that, the steps are as follows: Step 1: According to the relative motion relationship between the missile and the target, introduce the concept of zero-efficiency miss distance to establish a state space equation; Step 2: Introduce the remaining flight time to design the missile time coordination term; Step 3: Design a shaping guidance law with terminal angle constraints according to the state space equation; Step 4: Introduce the time coordination term into the shaping guidance law to achieve the guidance law design with angle and time constraints; specifically as follows: Taking the i-th missile as an example, considering the time coordination consistency of mid-course guidance, according to the multi-agent consensus theory, the remaining time t goi is selected as the system state variable x i , and the desired remaining time is obtained through the consensus protocol According to the requirement that the missiles arrive one after another, the final desired arrival time of the i-th missile is obtained The rightmost term in the above equation is the cooperation term. Through the design of this cooperation term, multiple missiles can tend to the target according to the set time difference; where K′ = K·[1 + q·(t go_d -t go ), q is the adjustment parameter of the variable proportionality coefficient, used to adjust the proportionality coefficient, t go_d = max(t goi ), σ is the velocity lead angle, obtained from the cosine theorem, n is the number of cooperative missiles; n ε is the acceleration of the missile in the pitch channel, n β is the acceleration of the missile in the yaw channel, V cε is the velocity component of the missile in the pitch channel, V cβ is the velocity component of the missile in the yaw channel, λ ε is the line-of-sight angle of the pitch channel, λ β is the line-of-sight angle of the yaw channel, λ Fε is the expected terminal line-of-sight angle of the pitch channel, λ Fβ is the expected terminal line-of-sight angle of the yaw channel, is the line-of-sight angle rate of the pitch channel, is the line-of-sight angle rate of the yaw channel, n Tε is the normal overload of the target in the pitch channel, n Tβ is the normal overload of the target in the yaw channel, n Tβ is the normal overload of the target in the yaw channel, t goi is the remaining time of missile i, t goi_d is the expected remaining time of missile i.

2. The collaborative mid-course guidance law design method based on the shaping guidance law according to claim 1, characterized in that, the state space equation in Step 1 is specifically as follows: where y is the zero-effect miss distance, is the relative velocity, is the relative acceleration, n T is the target normal acceleration, n c is the missile acceleration control command, and the zero-effect miss distance y is obtained by satisfying y(t F ) = 0, and minimizing thereby.

3. The collaborative mid-course guidance law design method based on the shaping guidance law according to claim 1, characterized in that, Step 2 is specifically as follows: The variable of the missile cooperative flight time is the remaining flight time t goi (t), which needs to be used as the state variable of the system. Through the expected cooperative time, the control quantity that can make the remaining flight times of each missile consistent can be obtained, and it is introduced as a bias control item into the mid-course guidance design: where, u ε is the acceleration of the missile in the pitch channel, and u β is the acceleration of the missile in the yaw channel, is the coefficient of the cooperative control term; t goi , t goi_d are the estimated remaining flight time and the desired flight time of the missile, respectively.

4. The collaborative mid-course guidance law design method based on the shaping guidance law according to claim 1, characterized in that, Step 3 is specifically as follows: By introducing the concept of zero-efficiency miss distance, the form of the trajectory shaping guidance law can be obtained Further transformation Due to Where T is the target parameter, n is the acceleration command, y is the introduced zero-effect miss distance, λ is the line-of-sight vector between the missile and the target, and t go is the estimated remaining flight time; Substitute the above formula to obtain the final form of the trajectory shaping guidance law: where n c is the missile control acceleration, V c is the missile velocity, λ is the line-of-sight angle, λ F is the terminal line-of-sight angle, n T is the target normal acceleration, t go is the estimated remaining flight time; Use the basic shaping guidance law to design the mid-course guidance algorithms in the pitch channel and the yaw channel respectively: Where, n ε is the acceleration of the missile in the pitch channel, n β is the acceleration of the missile in the yaw channel, K is the proportionality coefficient of the guidance law, V cε is the velocity component of the missile in the pitch channel, V cβ is the velocity component of the missile in the yaw channel, is the line-of-sight angular rate of the pitch channel, is the line-of-sight angle of the yaw channel, n Tε is the acceleration of the target in the pitch channel, n Tβ is the acceleration of the target in the yaw channel, λ is the line-of-sight vector between the missile and the target, t go is the estimated remaining flight time.

5. A computer system, characterized in that it includes: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to claim 1.

6. A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the method according to claim 1 when executed.

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