A Cooperative Guidance Method Based on Distributed Multi-Objective Model Predictive Control

Abstract

The present invention discloses a cooperative guidance method based on distributed multi-objective model predictive control. The present invention considers the cooperative guidance problem of the strike time and angle of a multi-agent system with multiple stationary interference zones, and can ensure that the seeker maintains the locked state on the target during the homing phase under the constraint conditions of obstacle avoidance and maneuverability, so as to realize that multiple agents strike the target simultaneously at the desired angle of attack. In addition, the distributed algorithm adopted can meet the online real-time requirements, thereby effectively improving the combat effectiveness.

Description

Technical Field

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

[0002] The suicide attack unmanned aerial vehicle is a precision-guided weapon, and its guidance purpose is mainly to achieve zero miss distance. However, in a strong confrontation environment, conventional guidance methods have limitations when facing key defense targets such as ground radars or sea ships. For example, the close-in weapon system on a sea warship can detect and destroy incoming targets, seriously threatening the ability of conventional anti-ship weapons to complete their combat missions. To improve the survival rate and penetration ability of the unmanned aerial vehicle, an effective strategy is to make multiple unmanned aerial vehicles attack the same target simultaneously, so that the defense system of the enemy target is in a saturated state and cannot interfere with and intercept the unmanned aerial vehicle in time. In addition, increasing the attack angle constraint can enable the unmanned aerial vehicle to avoid the directional defense mechanism of the enemy target and effectively improve the survival ability of the unmanned aerial vehicle. Therefore, it is necessary to study a guidance method that can control the attack time and angle simultaneously.

[0003] In recent years, the research on guidance methods that can achieve a predetermined attack time or angle has attracted extensive attention, but the research on guidance methods that can control the attack time and angle simultaneously is still less. Reference [1] designed a guidance method that can meet the time and angle constraints based on the optimal control method, and its control variable is the jerk of the agent. Reference [2] processed the time and angle control problems in two steps, and obtained a composite guidance scheme that simultaneously meets the time and angle constraints by using two different guidance methods to control the attack time and angle successively, but this scheme cannot guarantee the accuracy of the attack time theoretically. Reference [3] achieved the attack time and angle control by using a nonlinear method to track a predefined desired line-of-sight angle, but the parameters in the desired line-of-sight angle need to be obtained through an offline optimization algorithm, which is essentially an open-loop control method and is prone to error accumulation. The existing guidance methods for a predetermined attack time or angle may lead to highly curved flight trajectories, causing the seeker to lose the target or acceleration saturation, and unable to ensure that the seeker remains locked on the target during the homing stage, that is, it cannot always be within the field of view of the seeker during the guidance process. Summary of the Invention

[0004] The objective of the present invention is to provide a cooperative guidance method based on distributed multi-objective model predictive control. Aiming at the deficiencies of existing control methods for attack time and angle guidance, and leveraging the advantages of distributed model predictive control methods, the present invention designs a multi-agent cooperative guidance method based on distributed multi-objective model predictive control. Under the constraint conditions of obstacle avoidance and maneuverability, it can ensure that the seeker maintains a locked state on the target during the homing stage, enabling multiple agents to strike the target simultaneously at the desired attack angle. In addition, the distributed algorithm adopted effectively improves the decision-making speed of the multi-agent system, thereby enhancing the combat effectiveness.

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

[0006] The present invention includes a multi-agent system containing multiple agents. At the initial moment, all agents start from the given starting positions, and a desired safe distance is always maintained between the agents. Eventually, they cooperatively strike a stationary target in terms of time and angle. The specific steps are as follows:

[0007] S1: Define the dynamic model of the agent, which includes defining the state vector and control vector of the agent.

[0008] S2: Set the constraint condition that the agent needs to avoid entering the radar interference area under the condition of meeting the flight constraint conditions.

[0009] S3: Set the constraint condition that needs to be met to avoid mutual collision when multiple agents cooperate to execute the strike mission.

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

[0011] S5: The agent solves the optimization problem according to its own and other missiles' states according to the objective function designed in step S4, and takes the obtained optimal prediction control sequence as the control input sequence within 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 in 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 cooperative guidance method based on distributed multi-objective model predictive control. Compared with the prior art, the present invention considers the cooperative guidance problem of the strike time and angle of a multi-agent system with multiple stationary interference zones, and can ensure that the seeker maintains the locked state on the target during the homing phase under the constraint conditions of obstacle avoidance and maneuverability, so as to enable multiple agents to strike the target simultaneously at the desired attack angle. In addition, the distributed algorithm adopted can meet the online real-time requirements, thereby effectively improving the combat effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0017] Figure 2 is the relative distance between three agents of the present invention and interference zone 1, interference zone 2, and interference zone 3 respectively;

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

[0019] Figure 4 is the trajectory diagram of the cooperative control of the strike angles of three agents of the present invention. DETAILED DESCRIPTION OF THE INVENTION

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

[0021] The multi-agent cooperative guidance problem has non-linear dynamic characteristics and also requires meeting hard constraints such as obstacle avoidance and the maneuverability of agents. Therefore, Distributed Model Predictive Control (DMPC) is widely used in control problems because it can explicitly handle the constraint and non-linear coupling problems existing between subsystems. For example, in reference [4], the DMPC algorithm is designed using the trajectory optimization principle to achieve linear queue control; in reference [5], the cooperative guidance problem under the impact angle constraint of multi-agents is studied, and the leader-follower strike method is adopted to reconstruct the multi-agent cooperative strike problem into a distributed optimization problem that can consider complex constraints, and all subsystems adopt the strategy of rolling horizon update. These references utilize the characteristics of high fault tolerance and strong structural flexibility of the distributed algorithm when solving problems, so as to achieve effective control of the target.

[0022] The present invention includes a multi-agent system with N g agents. At the initial moment, all agents start from the given starting positions, and a desired safe distance is always maintained between agents. Finally, the collaborative time and angle are used to strike stationary targets. In addition, it is assumed that the communication network performance of each 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, course angle, and pitch angle are v i (t), χ i (t), γ i (t) respectively. Thus, the dynamic model of agent i is expressed as

[0024]

[0025] Where denotes the derivative of x i (t) with respect to t, and the other symbols are similar. respectively represent the overloads of agent i in the x-axis, y-axis, and z-axis directions, and g represents the acceleration due to gravity.

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

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

[0028] Define three overloads as the control vector:

[0029]

[0030] The state vector and the 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] Where u i,min and x i,min are the lower bounds of the control quantity and the state quantity respectively, and u i,max ​and x i,max are the upper bounds of the control quantity and the state quantity respectively. For convenience, Equation (1) is simplified as follows:

[0033]

[0034] Where:

[0035]

[0036] Therefore, the updated 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 to be struck may have a strong defense system, when the enemy detects the approach of an agent, a radar jamming area is constructed by launching radar jamming bombs to prevent the threat source from approaching the target. When an agent enters the radar jamming area, it will be unable to locate the target, resulting in the failure of the strike mission. Therefore, all agents need to avoid entering the radar jamming area under the condition of meeting the flight constraint conditions, that is, the following constraint conditions are satisfied:

[0040]

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

[0042] When multiple agents cooperate to execute the strike mission, they also need to avoid colliding with each other, that is, the following constraint conditions are satisfied:

[0043]

[0044] Where, d ik represents the relative distance between agent i and agent k, is the safety distance between agents.

[0045] The communication topology relationship of multi-agent cooperative guidance is described by a directed graph G = {V, E, A}. Among them, V = {1, 2,..., N g} is the point set, is the edge set, is the adjacency matrix. If for any (i, j) ∈ E and i ≠ j, then a ij = 1 represents a directed edge from j to i, that is, agent i can directly receive the information transmitted by agent j; if then aij = 0 indicates 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 objective of the present invention is for a multi-agent system (1) to synchronously optimize the strike performance and cooperation performance of each agent, so that under the premise of meeting system constraints and safety constraints, the multi-agents can strike the target at the expected angle simultaneously. 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, assume that the state of agent i at time t is x i (0|t), and the feasible predictive control sequence is U i (t) = {u i (0|t), u i (1|t),..., u i (N-1|t)}, and the corresponding predicted state response sequence is X i (t) = {x i (1|t), x i (2|t),..., x i (N|t)}.

[0048] To enable the multi-agents to cooperate and strike the target at the same time at the expected angle, the guidance control, attack time cooperation control, and angle cooperation control objective functions of agent i are defined respectively as follows:

[0049]

[0050]

[0051]

[0052] Among them, the guidance control function:

[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, and x t = [x t , y t , z t represents the three-dimensional coordinates of the target. The attack time cooperation 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 multi-agent strike times can be the same; a ij is an element in the adjacency matrix. The angular coordination control function

[0057]

[0058]

[0059] represents the difference between the actual strike path angle of agent i and the desired strike path angle , ensuring that the multi-agent can strike according to the desired angle.

[0060] Therefore, to coordinate the attack time and angle guidance, the total control objective function J of agent i i can be constructed in the following form:

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

[0062] where, J i,m , J i,a , J i,g are shown in Eqs. (10), (11) and (12) respectively, and μ i , β i , ρ i represent the weights of the corresponding three terms respectively.

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

[0064]

[0065] s.t. x 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] where is the optimal solution to the optimization problem (14), equation (14a) is the initial condition, equations (14b), (14c) and (14d) are the system constraint, control input constraint and state vector constraint respectively, equation (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 cooperative guidance method based on distributed multi - objective model predictive control are summarized as follows:

[0073] 1) Let 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 its own and other missiles' states, in accordance with the designed multi - objective function (13), and takes the obtained optimal predictive control sequence as the control input within the rolling time domain [0; N - 1]

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

[0076] 4) Meanwhile, other agents j (j ∈ V i ) execute the optimal control sequence obtained from the previous decision:

[0077] 5) Let t = t + 1, 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 stationary interference zones, and an enemy stationary target in a three-dimensional space. By designing the maneuvering strategies of our agents, the threats of the interference zones can be avoided, and time coordination and angle coordination for attacking the target are considered simultaneously.

[0080] The adjacency matrix of the communication topology of the three agents is as follows:

[0081]

[0082] The obstacle avoidance constraints for the agents are as follows:

[0083]

[0084] The collision avoidance constraints between the agents and our agents are as follows:

[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 position is:

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

[0090] All three interference zones are spheres, and their radii are 500, 300, and 500 respectively. The center positions are:

[0091]

[0092]

[0093]

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

[0095] δ t =[0° -90° 90°] T (22)

[0096] The minimum and maximum flight speeds of the agents are v min =100m / s and v max =400m / s respectively. The results of multi-agent collaborative time and angle attacks are as Figure 1 shown. The starting positions of the agents are marked by black triangles. The radar interference zones are marked by black spheres.

[0097] It can be seen from Figure 1 that during the process of the three agents attacking the target, not only can the safety distance between the three agents be guaranteed, but also the interference area can be successfully avoided and the attack mission can be finally completed. In addition, due to the consideration of time-coordinated attack in the optimization problem, Agent 3, which is the closest to the target, has a detour trajectory at the initial moment in order to achieve time coordination, so as to keep the same remaining distance to the target as the other agents to achieve simultaneous attack. Finally, the attack time of the three agents on the target is 19.3 seconds, indicating that the proposed method can effectively achieve simultaneous attack on the target. If the time-coordinated term in the objective function is not considered, the attack times of the three agents on the target are 16.3 seconds, 15.6 seconds, and 10.9 seconds respectively, which shows that the proposed method has good time-coordination function.

[0098] It can be seen from Figure 2 that in order to ensure the safety of our agents, our side always keeps a large distance from the interference area. In addition, the relative distance curve to the interference area first decreases and then increases. This is because the positions of the three interference areas are fixed, but they are between the initial position and the target position of our agents. Therefore, initially in order to approach the target, our agents fly towards the interference area and the relative distance drops sharply, but then move away from the interference area and the relative distance gradually increases. In addition, the relative distance between our agents and the interference area is always greater than the safety distance, thus ensuring that our agents can successfully complete the mission.

[0099] It can be seen from Figure 3 that the difference between the actual attack angles and the desired attack angles of the three agents can finally converge to zero, which means that the three agents can strike the target according to the desired attack angles, indicating that the proposed method has good angle-coordination performance. In addition, Figure 4 shows a plan view of the three agents coordinating the angle to attack the target, which more intuitively illustrates the angle coordination. It can be seen that our agents attack the target from three directions, thus achieving greater lethality.

[0100] The technical solution of the present invention is not limited to the restrictions of the above specific embodiments. Any technical deformation made according to the technical solution of the present invention falls within the protection scope of the present invention.

[0101] References:

[0102] [1]Lee J I,Jeon I S,Tahk M J.Guidance law to control impact time andangle[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 method[J].Control Theory & Applications,2010,27(10):1429-1434.

[0104] [3]Harl N,Balakrishann S N.Impact time and angle guidance withsliding 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 M Y,Cheng X H,Zhao Z Q,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 cooperative 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 the given starting positions, and an expected safe distance is always maintained between the agents. Finally, they cooperate in terms of time and angle to strike a stationary target. The specific steps are as follows: S1: Define the dynamic model of the agent. The dynamic model includes defining the state vector and control vector of the agent. S2: Set the constraint condition that the agent needs to avoid entering the radar interference area under the condition of meeting the flight constraint conditions. S3: Set the constraint condition that needs to be met to avoid mutual collision when multiple agents cooperate to execute the strike mission. S4: Define the guidance control, attack time cooperation control, and angle cooperation control objective functions of the agent respectively. Consider the current time \(t\) and the prediction horizon \(N>0\). Let the state of agent \(i\) at time \(t\) be \(x\) i (0|t), and the feasible predictive control sequence be \(U\) i (t)=\{u i (0|t),u i (1|t),\(\cdots\),u i (N - 1|t)\}, and the corresponding predicted state response sequence be \(X\) i (t)=\{x i (1|t),x i (2|t),\(\cdots\),x i (N|t)\}; Define the guidance control, attack time cooperation control, and angle cooperation control objective functions of agent i as follows: Among them, the guidance and control function: L i,m (x i (l|t), x t ) = ||x i (l|t) - x t || 2 represents the relative distance between the agent i and the target, which can achieve a zero miss distance and ensure the completion of the strike mission; ||f(x)|| represents the distance norm of f(x), and x t = [x t , y t , z t represents the three-dimensional coordinates of the target; the attack time cooperative control function: Denote 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 cooperation control function: Denote the difference between the actual strike track angle and the desired strike track angle of agent i, and the total control objective function J of agent i can be constructed in the following form: i as follows: Among them, J i,m , J i,a , J i,g are respectively shown in formulas (10), (11) and (12), respectively representing the weights corresponding to the three items; At time t, considering the total control objective function of agent i in Equation (13), design the following optimal control problem with a finite time domain: Among them, is the optimal solution to the optimization problem (14), Equation (14a) is the initial condition, Equations (14b), (14c) and (14d) are the system constraint, control input constraint and state vector constraint respectively, Equation (14e) is to avoid entering the radar interference area, and (14f) is the collision avoidance constraint between agents; S5: The agent solves the optimization problem according to its own state and the states of other missiles according to the objective function designed in step S4, and uses the obtained optimal predictive control sequence as the control input sequence within 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 in the previous decision. S7: Repeat steps S5 and S6 until the strike mission is completed.

2. The cooperative guidance method based on distributed multi-objective model predictive control according to claim 1, wherein: Let: The number of agents is N g , and 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), Thus, the dynamic model of agent i is defined as: Among them, and respectively represent x i (t), y i (t), z i (t), v i (t), and are differentiated with respect to t; respectively represent the overload of agent i in the x-axis, y-axis, and z-axis directions, and g represents the acceleration due to gravity; Define the state vector x of agent i i as follows: Define three overloads as the control vector: 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) where, u i,min and x i,min are the lower bounds of the control quantity and the state quantity respectively, and u i,max and x i,max are the upper bounds of the control quantity and the state quantity respectively; Equation (1) is simplified as: where Therefore, the updated 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 cooperative guidance method based on distributed multi-objective model predictive control according to claim 2, characterized in that: The constraint condition satisfied by S2 is: Among them, represents the center position of the e-th radar interference area, and N o represents the number of radar interference areas, represents the safe distance that needs to be maintained between the agent and the radar interference area.

4. The cooperative guidance method based on distributed multi-objective model predictive control according to claim 3, wherein: The constraint condition satisfied by S3 is: where d ik represents the relative distance between agent i and agent k, which is the safety distance between agents; The communication topology relationship of multi-agent cooperative guidance is described by a directed graph G = {V, E, A}; where, V = {1, 2,..., N g} is the set of points, is the set of edges, is the adjacency matrix. If for any (i, j) ∈ E, i ≠ j, then a ij = 1 represents 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 .

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