Cooperative guidance method based on distributed multi-target model predictive control

Abstract

The invention discloses a cooperative guidance method based on distributed multi-target model predictive control, which considers the cooperative guidance problem of strike time and angle of a multi-agent system with a plurality of static interference areas, and can realize the cooperative guidance of strike time and angle of the multi-agent system under the constraint conditions of meeting obstacle avoidance and maneuverability. It is guaranteed that the leading head keeps a target locking state in the target-seeking stage, and the aim that multiple agents hit the target at the same time according to the expected attack angle is achieved. In addition, the adopted distributed algorithm can meet the online real-time requirement, so that the combat effectiveness is effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of military weapon technology, and in particular to a collaborative guidance method based on distributed multi-target model predictive control. Background Art

[0002] Suicide attack drones are precision-guided weapons whose main purpose is to achieve zero misses. However, in a strong confrontation environment, conventional guidance methods have limitations when facing key defense targets such as ground radars or surface ships. For example, the close-combat weapon system on a surface warship can detect and destroy incoming targets, which seriously threatens the ability of conventional anti-ship weapons to complete their combat missions. In order to improve the survivability and penetration capability of drones, an effective strategy is to make multiple drones attack the same target at the same time, so that the defense system of the enemy target is saturated and cannot interfere with and intercept the drone in time. In addition, adding attack angle constraints can enable drones to avoid the directional defense mechanism of enemy targets and effectively improve the survivability of drones. Therefore, it is necessary to study guidance methods that can simultaneously control the attack time and angle.

[0003] In recent years, the research on guidance methods that can achieve a predetermined attack time or angle has attracted widespread attention, but there are still few studies on guidance methods that can simultaneously control the attack time and angle. Reference [1] designed a guidance method that can meet the time and angle constraints based on the optimal control method. Its control variable is the jerk of the intelligent agent. Reference [2] divides the time and angle control problem into two steps. By using two different guidance methods to control the attack time and angle respectively, a composite guidance scheme that simultaneously meets the time and angle constraints is obtained. However, this scheme cannot theoretically guarantee the accuracy of the attack time. Reference [3] uses a nonlinear method to track a predefined expected line of sight angle to achieve attack time and angle control. However, the parameters in the expected line of sight angle need to be obtained through an offline optimization algorithm. It is essentially an open-loop control method and is prone to error accumulation. The existing guidance methods for predetermined attack time or angle may result in highly curved flight paths, causing the seeker to lose the target or acceleration saturation. It is impossible to ensure that the seeker remains locked on the target during the search phase. In other words, it cannot always be within the field of view of the seeker during the guidance process. Summary of the invention

[0004] The purpose of the present invention is to provide a collaborative guidance method based on distributed multi-target model predictive control. In view of the shortcomings of the existing methods for controlling attack time and angle guidance, and taking advantage of the distributed model predictive control method, the present invention designs a multi-agent collaborative guidance method based on distributed multi-target model predictive control, which can ensure that the seeker maintains a locked state on the target during the stage of homing under the constraints of obstacle avoidance and maneuverability, and enables multiple agents to simultaneously strike the target at the desired angle of attack. In addition, the adopted distributed algorithm also effectively improves the decision-making speed of the multi-agent system, thereby improving combat effectiveness.

[0005] To achieve the above object, the present invention is implemented according to the following technical solutions:

[0006] The present invention includes a multi-agent system including multiple agents. At the initial moment, all agents start from a given starting position, and the agents always maintain a desired safe distance between each other, and finally coordinate time and angle to strike a stationary target, specifically including the following steps:

[0007] S1: defining a dynamic model of the intelligent agent, wherein the dynamic model includes defining a state vector and a control vector of the intelligent agent;

[0008] S2: Set the constraints that the agent needs to avoid entering the radar interference area while satisfying the flight constraints;

[0009] S3: Set the constraints that need to be met when multiple agents collaborate to perform strike missions to avoid collisions;

[0010] S4: Define the objective functions of the agent's guidance control, attack time cooperative control, and angle cooperative control respectively;

[0011] S5: The agent solves the optimization problem according to the objective function designed in step S4 based on the state of itself and other missiles, and uses the obtained optimal prediction control sequence as the control input sequence in the rolling time domain;

[0012] S6: Execute the control input sequence, and the agent obtains the state at the next moment; at the same time, other agents execute the optimal control sequence determined by the previous decision;

[0013] S7: Repeat steps S5 and S6 until the strike mission is completed.

[0014] The beneficial effects of the present invention are:

[0015] The present invention is a collaborative guidance method based on distributed multi-target model predictive control. Compared with the prior art, the present invention considers the collaborative guidance problem of attack time and angle of a multi-agent system with multiple static interference zones. Under the constraint conditions of obstacle avoidance and maneuverability, the seeker can be ensured to keep the target locked in the stage of homing, so that multiple agents can simultaneously attack the target according to the expected attack angle. In addition, the adopted distributed algorithm can meet the online real-time requirements, thereby effectively improving the combat effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is the trajectory diagram of the three agents of the present invention;

[0017] Figure 2 are the relative distances between the three agents of the present invention and interference area 1, interference area 2, and interference area 3, respectively;

[0018] Figure 3 is the convergence curve of the difference between the actual attack angle and the expected attack angle of the three agents of the present invention;

[0019] Figure 4 It is a trajectory diagram of coordinated control of attack angles of three intelligent agents of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0021] The problem of multi-agent collaborative guidance has nonlinear dynamic characteristics and also requires hard constraints such as obstacle avoidance and the maneuverability of the agent. Therefore, distributed model predictive control (DMPC) is widely used in control problems because it can explicitly handle the nonlinear coupling problems between constraints and subsystems. For example, reference [4] uses trajectory optimization principles to design a DMPC algorithm and implements linear queue control; reference [5] studies the problem of collaborative guidance under the impact angle constraint of multi-agents, adopts the leader-follower attack method, and reconstructs the problem of multi-agent collaborative attack into a distributed optimization problem that can consider complex constraints. All subsystems adopt a rolling time domain update strategy. These references use the high fault tolerance and strong structural flexibility of distributed algorithms to solve problems, thereby achieving effective control of the target.

[0022] The present invention contains N g In a multi-agent system with multiple agents, all agents start from a given starting position at the initial moment, and the agents always maintain the expected safe distance between each other. Finally, the stationary target is hit by coordinated time and angle. In addition, it is assumed that the communication network performance of each intelligent agent is good, without network delay and packet loss.

[0023] At time t, the positions of agent i on the x-axis, y-axis, and z-axis are x i (t),y i (t),z i (t), define z i (t) = (x i (t),y i (t),z i (t)), the speed, track angle and pitch angle are v i (t),χ i (t),γ i (t), the dynamic model of agent i is defined as

[0024]

[0025] in, Represents x i (t) The derivative with respect to t. The rest of the symbols are similar. They represent the overload of agent i in the x-axis, y-axis and z-axis directions respectively, and g represents the gravitational acceleration.

[0026] For each agent, define the state vector x of agent i i It is expressed as follows:

[0027] x i =[x i ,y i ,z i ,v i ,x i ,γ i ] T (2)

[0028] Define three overloads as control vectors:

[0029]

[0030] The state vector and control vector satisfy the following constraints:

[0031] u i,min ≤u i ≤u i,max ,x i,min ≤x i ≤x i,max (4)

[0032] Among them, u i,min and x i,min are the lower bounds of the control quantity and state quantity, respectively, u i,maxand x i,max are the upper bounds of the control quantity and state quantity respectively. For convenience, equation (1) is simplified as:

[0033]

[0034] in:

[0035]

[0036] Therefore, the update system model of each agent can be expressed as follows

[0037]

[0038] Where Δt represents the time step and L represents the set of all agents.

[0039] In actual combat, since the target may have a strong defense system, when the enemy detects that an agent is approaching, it will build a radar interference zone by launching radar jammers to prevent the threat source from approaching the target. If the agent enters the radar interference zone, it will not be able to locate the target, resulting in the failure of the strike mission. Therefore, all agents need to avoid entering the radar interference zone while meeting the flight constraints, that is, meeting the following constraints:

[0040]

[0041] in, represents the center position of the e-th radar interference area, N o Indicates the number of radar interference areas, Indicates the safe distance that needs to be maintained between the agent and the radar interference area.

[0042] When multiple agents cooperate to perform strike missions, they also need to avoid collisions with each other, that is, the following constraints must be met:

[0043]

[0044] Among them, d ik represents the relative distance between agent i and agent k, is the safe distance between agents.

[0045] The communication topology of multi-agent collaborative guidance is described by a directed graph G = {V, E, A}. g} is a point set, is the edge set, is an adjacency matrix. If for any (i, j)∈E, i≠j, then a ij = 1 indicates a directed edge from j to i, that is, agent i can directly receive the information transmitted by agent j; if Then aij = 0 means that there is no communication relationship between agent i and agent j. Define the set of agents that have a direct directed path to agent i as V i .

[0046] The present invention aims to optimize the strike performance and coordination performance of each agent in a multi-agent system (1) so that the multi-agents can strike the target at the same time at a desired angle while satisfying system constraints and safety constraints. The present invention adopts a distributed multi-objective MPC strategy to achieve time and angle control.

[0047] Considering the current time t and the prediction horizon N>0, assuming that agent i is in state x at time t i (0|t), the feasible prediction control sequence is U i (t) = {u i (0|t),u i (1|t),...,u i (N-1|t)}, the corresponding predicted state response sequence is X i (t) = {x i (1|t),x i (2|t),...,x i (N|t)}.

[0048] In order to achieve the coordinated attack of multiple agents at the same time according to the desired angle, the objective functions of the guidance control, attack time coordinated control and angle coordinated control of agent i are defined as follows:

[0049]

[0050]

[0051]

[0052] Among them, the guidance control function is:

[0053] L i,m (x i (l|t),x t )=||x i (l|t)-x t || 2

[0054] represents the relative distance between agent i and the target, which can achieve zero miss distance and ensure the completion of the strike mission. ||·|| represents the distance norm, x t =[x t ,y t ,z t ] represents the three-dimensional coordinates of the target. Attack time coordinated control function:

[0055]

[0056] represents the difference between the remaining time for agent i to reach the target and the remaining time for agent j to reach the target, ensuring that the attack time of multiple agents is the same; a ij is an element in the adjacency matrix. Angle coordination control function

[0057]

[0058]

[0059] represents the actual strike track angle and the expected strike track angle of agent i The difference ensures that the multi-agent can strike at the desired angle.

[0060] Therefore, in order to coordinate the attack time and angle guidance, the overall control objective function J of agent i is i It can be constructed as follows:

[0061] J i =μ i J i,m +β i J i,a +ρ i J i,g (13)

[0062] Among them, J i,m ,J i,a ,J i,g As shown in equations (10), (11) and (12), μ i ,β i ,ρ i Represent the weights of the three items respectively.

[0063] At time t, considering the overall control objective function (13) of agent i, the following finite-time optimal control problem is designed:

[0064]

[0065] stx i (0|t)=x i (t), (14a)

[0066] x i (l+1|t)=x i (l|t)+f(x i (l|t),u i (l|t))Δt, (14b)

[0067] u i,min ≤ui (l|t)≤u i,max ,l∈[0,N-1], (14c)

[0068] x i,min ≤x i (l|t)≤x i,max , (14d)

[0069]

[0070]

[0071] in, is the optimal solution of the optimization problem (14), where (14a) is the initial condition, (14b), (14c) and (14d) are the system constraints, control input constraints and state vector constraints respectively, (14e) is to avoid entering the radar interference area, and (14f) is the collision avoidance constraint between agents.

[0072] Therefore, the operation steps of the collaborative guidance method based on distributed multi-objective model predictive control are summarized as follows:

[0073] 1) Assume t = 0, input parameters A, N, μ i ,β i ,ρ i , x t ,

[0074] 2) At time t, agent i solves the optimization problem (14) according to the designed multi-objective function (13) based on its own state and the states of other missiles, and uses the obtained optimal predicted control sequence as the control input in the rolling time domain [0; N-1]

[0075] 3) Execute the control input sequence The first item in Agent i obtains the next moment state

[0076] 4) At the same time, other agents j(j∈V i ) Execute the optimal control sequence from the last decision:

[0077] 5) Let t=t+1 and repeat the above process until the strike mission is completed.

[0078] Simulation results:

[0079] The present invention considers a multi-agent system consisting of three agents, three static interference zones and an enemy static target in three-dimensional space. By designing the maneuvering strategy of our agents, we can avoid the threat of the interference zone and strike the target in consideration of time coordination and angle coordination.

[0080] The adjacency matrix of the three-agent communication topology is:

[0081]

[0082] The obstacle avoidance constraints for the agent are:

[0083]

[0084] The collision avoidance constraints between the agent and our agent are:

[0085] ||x i (l|t)-x k (l∣t)||≥10,l=0,1,…,N-1 (16)

[0086] The initial state of our agent is given as:

[0087]

[0088] The target location is:

[0089] x t =[7000 3000 3000] T (18)

[0090] The three interference areas are spheres with radii of 500, 300 and 500 respectively, and the center positions are:

[0091]

[0092]

[0093]

[0094] The expected attack angles of the three agents are:

[0095] δ t =[0° -90° 90°] T (twenty two)

[0096] The minimum and maximum flight speeds of the agent are v min =100m / s and v max =400m / s. The results of multi-agent coordinated time and angle attack are as follows Figure 1 As shown in the figure, the black triangle marks the starting position of the agent. The black sphere marks the radar interference area.

[0097] Depend on Figure 1 It can be seen that in the process of attacking the target, the three agents can not only ensure the safe distance between the three agents, but also successfully avoid the interference area and finally complete the attack task. In addition, since the time coordinated attack is considered in the optimization problem, the agent 3 closest to the target has a detour trajectory at the initial moment in order to achieve time coordination, so as to maintain the same target remaining distance with the other agents to achieve simultaneous attack. In the end, the three agents attacked the target in 19.3 seconds, indicating that the proposed method can effectively achieve simultaneous attack on the target. If the time coordination term in the objective function is not considered, the three agents attack the target in 16.3 seconds, 15.6 seconds and 10.9 seconds respectively, which shows that the proposed method has good time coordination function.

[0098] from Figure 2 It can be seen that in order to ensure the safety of our agent, we always keep a large distance from the interference zone. In addition, the relative distance curve to the interference zone decreases first and then increases. This is because the positions of the three interference zones are fixed, but they are between the initial position and the target position of our agent. Therefore, in order to get close to the target, our agent initially flies towards the interference zone, and the relative distance drops sharply, but then moves away from the interference zone, and the relative distance gradually increases. In addition, the relative distance between our agent and the interference zone is always greater than the safe distance, thus ensuring that our agent can successfully complete the task.

[0099] from Figure 3 It can be seen that the difference between the actual attack angle and the expected attack angle of the three agents can eventually converge to zero, which means that the three agents can attack the target according to the expected attack angle, indicating that the proposed method has good angle coordination performance. In addition, Figure 4 The plan view of three intelligent agents attacking the target from coordinated angles is shown, which explains the angle coordination more intuitively. It can be seen that our intelligent agents attack the target from three directions, thereby achieving greater lethality.

[0100] The technical solution of the present invention is not limited to the above-mentioned specific embodiments. All technical variations made according to the technical solution of the present invention fall within the protection scope of the present invention.

[0101] References:

[0102] [1]Lee JI,Jeon IS,Tahk M J.Guidance law to control impact time and angle[J].IEEE Transactions on Acrospace and Electronic Systems,2007,43(1):301-310.

[0103] [2] Zhang Yougen, Zhang Youan. Three-dimensional guidance law for controlling impact time and angle: a two-stage control approach[J]. Control Theory and Applications, 2010, 27(10): 1429-1434.

[0104] [3]Harl N,Balakrishann S N.Impact time and angle guidance with sliding mode control[J].IEEE Transactions on Control Systems Technology,2012,20(6):1436-1449.

[0105] [4]Kuwata Y,Richards A,Schouwenaars T,et al.Distributed robustreceding borazon control for multivehicle guidance[J].IEEE Transactions onControl Systems Technology,2007,15(4):627-641.

[0106] [5]Cong MY,Cheng XH,Zhao ZQ,et al.Studies on Multi-ConstraintsCooperative Guidance Method Based on Distributed MPC for Multi-Missiles[J].Applied Sciences,2021,11(22),10857.

Claims

1. A collaborative guidance method based on distributed multi-objective model predictive control, characterized in that: It includes a multi-agent system containing multiple agents. At the initial moment, all agents start from a given starting position, and the agents always maintain the expected safe distance between each other, and finally coordinate time and angle to strike a stationary target. Specifically, it includes the following steps: S1: defining a dynamic model of the intelligent agent, wherein the dynamic model includes defining a state vector and a control vector of the intelligent agent; S2: Set the constraints that the agent needs to avoid entering the radar interference area while satisfying the flight constraints; S3: Set the constraints that need to be met when multiple agents collaborate to perform strike missions to avoid collisions; S4: Define the objective functions of the agent's guidance control, attack time cooperative control, and angle cooperative control respectively; S5: The agent solves the optimization problem according to the objective function designed in step S4 based on the state of itself and other missiles, and uses the obtained optimal prediction control sequence as the control input sequence in the rolling time domain; S6: Execute the control input sequence, and the agent obtains the state at the next moment; at the same time, other agents execute the optimal control sequence determined by the previous decision; S7: Repeat steps S5 and S6 until the strike mission is completed.

2. The collaborative guidance method based on distributed multi-objective model predictive control according to claim 1 is characterized in that: The number of agents is N g , the expected safe distance between agents is At time t, the positions of agent i on the x-axis, y-axis, and z-axis are x i (t),y i (t),z i (t), define z i (t) = (x i (t),y i (t),z i (t)), the speed, track angle and pitch angle are v i (t),χ i (t),γ i (t), and the dynamic model of agent i is defined as: in, and Respectively represent x i (t), y i (t), z i (t), v i (t), χ i (t) and γ i (t) Derivative with respect to t; They represent the overload of agent i in the x-axis, y-axis and z-axis directions respectively, and g represents the gravitational acceleration; Define the state vector x of agent i i It is expressed as follows: x i =[x i ,y i ,z i ,v i ,χ i ,γ i ] T (2) Define three overloads as control vectors: The state vector and control vector satisfy the following constraints: u i,min ≤u i ≤u i,max ,x i,min ≤x i ≤x i,max (4) Among them, u i,min and x i,min are the lower bounds of the control quantity and state quantity, respectively, u i,max and x i,max are the upper bounds of the control quantity and the state quantity respectively; Formula (1) is simplified as: in Therefore, the update system model of each agent is expressed as follows: Where Δt represents the time step and L represents the set of all agents.

3. The collaborative guidance method based on distributed multi-objective model predictive control according to claim 2 is characterized in that: The step S2 satisfies the following constraints: in, represents the center position of the e-th radar interference area, N o Indicates the number of radar interference areas, Indicates the safe distance that needs to be maintained between the agent and the radar interference area.

4. The collaborative guidance method based on distributed multi-objective model predictive control according to claim 3 is characterized in that: The step S3 satisfies the following constraints: Among them, d ik represents the relative distance between agent i and agent k, is the safe distance between agents; The communication topology of multi-agent collaborative guidance is described by a directed graph G = {V, E, A}. g } is a point set, is the edge set, is an adjacency matrix. If for any (i, j)∈E, i≠j, then a ij = 1 indicates a directed edge from j to i, that is, agent i can directly receive the information transmitted by agent j; if Then a ij = 0 means that there is no communication relationship between agent i and agent j. Define the set of agents that have a direct directed path to agent i as V i .

5. The collaborative guidance method based on distributed multi-objective model predictive control according to claim 4 is characterized in that: The step S4 is specifically as follows: considering the current time t and the prediction time domain N>0, assume that the state of agent i at time t is x i (0t), the feasible prediction control sequence is U i (t) = {u i (0|t),u i (1|t),...,u i (N-1|t)}, the corresponding predicted state response sequence is X i (t) = {x i (1|t),x i (2|t),...,x i (N|t)}; The objective functions of the guidance control, attack time cooperative control and angle cooperative control of agent i are defined as follows: Among them, the guidance control function: L i,m (x i (l|t),x t )=||x i (l|t)-x t || 2 represents the relative distance between agent i and the target, which can achieve zero miss distance and ensure the completion of the strike mission. ||f(x)|| represents the distance norm of f(x), x t =[x t ,y t ,z t ] represents the three-dimensional coordinates of the target; attack time coordinated control function: represents the difference between the remaining time for agent i to reach the target and the remaining time for agent j to reach the target, a ij is an element in the adjacency matrix; Angle coordination control function: represents the actual strike track angle and the expected strike track angle of agent i The difference between the total control objective function J of agent i i It can be constructed as follows: Among them, J i,m ,J i,a ,J i,g As shown in equations (10), (11) and (12), μ i ,β i ,ρ i Respectively represent the weights of the corresponding three items; At time t, considering the overall control objective function (13) of agent i, the following finite-time optimal control problem is designed: in, is the optimal solution of the optimization problem (14), where (14a) is the initial condition, (14b), (14c) and (14d) are the system constraints, control input constraints and state vector constraints respectively, (14e) is to avoid entering the radar interference area, and (14f) is the collision avoidance constraint between agents.

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