Multi-agent formation surrounding control method based on azimuth information

Abstract

The invention provides a multi-agent formation surrounding control method based on azimuth information. Aiming at the scene that multiple agents cooperatively surround a freely moving escape target, a distributed controller is designed for each agent based on a relative orientation measurement value among the multiple agents, so that the distributed controller can continuously surround and monitor the escape target in a uniformly distributed geometric formation. The method comprises the following steps: firstly, designing two estimation algorithms by utilizing the speed of an intelligent agent and measurable relative azimuth information of a neighbor intelligent agent, so as to estimate the distance between an escape target and the intelligent agent and the escape speed of the escape target; and then, on the basis of the estimation algorithm, a distributed surrounding control algorithm is provided, and multiple agents cooperatively track and surround the escape target under the condition of not depending on position information. In addition, the feasibility of the controller and the stability of the system are proved in combination with an azimuth rigidity theory and a Lyapunov stability criterion from three aspects of formation scale, azimuth error and formation centroid position.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system formation control, and in particular to a multi-agent formation encirclement control method based on orientation information. Background Art

[0002] Through communication, interaction and collaboration between agents, multi-agent systems can complete many tasks that a single agent cannot accomplish. Whether in the civil or military fields, compared with a single agent, multi-agent systems have significant advantages such as good scalability, high implementation efficiency, strong robustness, and better adaptability to complex environments. Existing research results mainly focus on multi-agent consistency control, cluster control, formation control, etc. These types of control methods are widely used in trajectory tracking, path planning, and formation movement of simple formations. However, due to the urgent needs of practical engineering applications such as environmental monitoring, protection patrols, reconnaissance and search and rescue, and satellite formations, research on multi-agent formation encirclement control has gradually increased in recent years. Wang et al. implemented inclusion control for a second-order multi-agent system with communication delay. Liu et al. considered an uncertain multi-agent system and completed fully distributed inclusion control based on an event-triggered mechanism. At present, there is a lot of research on inclusion control based on convex hull theory, but this type of control cannot clearly limit the formation of the formation and is not suitable for encirclement control with clear constraints on the formation.

[0003] According to the type of information that can be measured by the subject, the existing multi-agent system formation control methods can be classified into the following three types: formation control based on position information, based on distance information, and based on orientation information. The acquisition of position information depends on the global or local coordinate system, which requires the agent to carry enough sensor equipment, and the amount of communication information is large, resulting in high actual costs. In addition, limited by the application conditions of navigation systems such as GPS, this method has high environmental requirements. The method based on distance information can rely only on the local coordinate system, but requires that the system interaction topology and the formation of the desired formation are both rigid. The advantage of this type of control method is that the agent must interact with less global information, but this type of controlled system is generally nonlinear, and the gradient descent control rate designed based on distance information can often only guarantee the local stability of the corresponding system.

[0004] In view of the limitations of the above methods, Deghat et al. came up with the idea of ​​using the relative orientation between agents for formation control. Zhao et al. gave a precise definition of "orientation information" and elaborated on a series of concepts such as "orientation function", "infinitesimal orientation rigidity", and "orientation Laplace matrix", forming a systematic orientation rigidity theory. In practical applications, the orientation information between neighbors of agents can be directly obtained through airborne optical cameras at low cost. At present, there have been studies on formation encirclement control based on orientation information, but there are still many open problems to be solved. Yu et al. combined orientation information with circumnavigation control and completed circumnavigation control of static and slow-moving targets. Although the formation meets the encirclement requirements, under the influence of the corresponding controller, the agent must constantly make unnecessary circumnavigation movements around the encircled target, which has the disadvantage of wasting system energy. Summary of the invention

[0005] In order to make up for the deficiencies of the above-mentioned prior art, the present invention proposes a multi-agent formation encirclement control method based on azimuth information. Aiming at the scenario where multiple agents cooperate to encircle a freely moving escape target, the present invention designs a distributed controller for each agent based on the relative azimuth measurement values ​​between the multiple agents so that it can complete the real-time encirclement of the escape target in a uniformly distributed geometric formation. First, two estimation algorithms are designed using the agent's own speed and the measurable relative azimuth information of neighboring agents to estimate the distance between the escape target and the agent and its escape speed. Then, based on the above-mentioned estimation algorithm, a distributed encirclement control algorithm is proposed, which enables multiple agents to collaboratively track and encircle the escape target without relying on position information. In addition, the stability of the system can be proved by combining the azimuth rigidity theory and the Lyapunov stability criterion.

[0006] The technical solution of the present invention is:

[0007] A multi-agent formation encirclement control method based on position information specifically comprises the following steps:

[0008] Step 1: Use graph theory and orientation rigidity theory to mathematically describe the communication topology of the multi-agent system, and build a suitable agent dynamics model according to the requirements of the encirclement task. The specific process includes:

[0009] Step 1.1: Consider a multi-agent system consisting of n homogeneous agents, which is used to track and surround a escaping target that moves freely in a two-dimensional space. Describes the communication connection relationship between intelligent agents, where represents the point set, and the edge set is The edge (i, j) indicates that agent j can receive information from agent i. represents the position of agent i, and Define the position of agent j relative to agent i as g ij =(p j -p i ) / ||p j -p i ‖. According to the theory of orientation rigidity, the following orthogonal projection operator P is introduced: For auxiliary control:

[0010]

[0011] in, is a non-zero vector, and I2 represents the second-order identity matrix. The function of is to project the vector x onto its orthogonal complement direction. Denoted as P x .

[0012] Define a position function By finding the Jacobian matrix of p, we can get the orientation rigidity matrix:

[0013]

[0014] in, m represents the number of edges in the directed graph. H is a matrix that represents the communication relationship between nodes in the directed graph.

[0015] Step 1.2: Construct the agent dynamics model as a single integral model:

[0016]

[0017] in, and represent the position and control input of agent i respectively.

[0018] Step 2: Propose specific control objectives based on task requirements. The specific process is as follows:

[0019] The final control goal is clarified according to the mission requirements, that is, the necessary constraints that the system expects the formation to meet:

[0020] (1) The angles between any two neighboring agents and the target are equal, that is, the agents are evenly distributed around the escape target. The orientations between neighboring agents and between each agent and the escape target must be equal to the expected orientation. Its mathematical description is:

[0021] (2) The center of mass of the formation converges to the position of the escape target, that is, the escape target is always trapped in the center of the formation. Its mathematical description is:

[0022] (3) The distance between each agent and the escape target is consistent, that is, the formation encirclement radius is a fixed value d Z , which is mathematically described as:

[0023] Step 3: Design the corresponding distance estimation algorithm and speed estimation algorithm based on the measurable data. The specific process includes:

[0024] Step 3.1: As attached Figure 2 As shown, d iT and d ij is the distance between agents i and j that can be measured by the onboard sensor. The position of the target relative to agent i and the position of agent i relative to j can be obtained by the onboard optical camera. Based on the above information, the angle θ can be obtained. jT The cosine value of , and then the cosine theorem is used to design an estimation algorithm for the distance of the escape target:

[0025]

[0026] Step 3.2: For any position information g ij The derivative is Therefore, there is

[0027]

[0028] In multi-agent networks Under the premise of , we sum both sides of equation (4) and then transform them equivalently to obtain an estimation algorithm for the escape target speed of agent i:

[0029]

[0030] In the formula, Representation in a multi-agent network The set of neighboring agents of agent i, represents the real-time distance between agent j and the escape target obtained by the above distance estimation algorithm, v j Represents the real-time speed of agent j.

[0031] Step 4: Define the encirclement radius error, design the formation encirclement controller and prove its stability. The specific process includes:

[0032] Step 4.1: Define the distance error between agent i and the escape target, expressed as follows:

[0033] δ i =||p i -p T ||-d Z (6)

[0034] Step 4.2: Based on the two estimation algorithms in step 3 above, design the following wraparound controller for the system:

[0035]

[0036] In order to verify the stability of the controller, a Lyapunov function V = ||δ|| 2 , combining the distance error (6) and the controller (7), taking the derivative of V, we finally get It is proved that the controller (7) is feasible and can ensure the global stability of the system.

[0037] Step 5: Further demonstrate the feasibility of the above formation encirclement controller from three aspects: formation size, orientation error and formation centroid. The specific process is as follows:

[0038] Step 5.1: The size of the formation can be determined by the distance between neighboring agents and the distance between the agent and the escape target, that is, ||p i (t)-p T (t)|| and ‖p i (t)-p j (t)|| jointly represents. Combining (6) we can prove that and This shows that the size of the formation always has an upper bound during the entire process of surrounding the escaping target, and the convergence is good, which proves the feasibility of the controller.

[0039] Step 5.2: When the multi-agent system achieves the desired goal, the formation must satisfy the desired orientation constraint. To prove this point, we choose to start from the local coordinate system of the escape target and make further arguments. First, write the complex matrix form of the controller according to equation (7): in Since the reference system is the local coordinate system of the escape target, combined with equation (2), it can be seen that the input of the escape target at any time is zero, that is, Combined with the azimuthal rigidity theory in step 1, further theoretical derivation can be performed to obtain and According to the properties of the orthogonal projection operator, we know Established.

[0040] Step 5.3: If the centroid position of the formation is expected to coincide with the position of the escape target, it means that the formation can not only complete the basic task of encircling the target, but also limit the position of the escape target in the encirclement area and play a monitoring role. To this end, the centroid of the multi-agent formation is defined as The error between the center of mass position and the escape target position is δ Z =Z(t)-p TAfter theoretical derivation, we can get From the conclusions of step 4 and step 5.2 above, we can get ||δ Z || 2 Asymptotically converges to 0.

[0041] The above are all the steps of the technical solution of the present invention. The beneficial effects of adopting the above technical solution are:

[0042] Compared with the existing containment control and circumnavigation control technologies, the present invention provides a multi-agent formation encirclement control method based on azimuth information. Two estimation algorithms are designed using azimuth information and azimuth rigidity theory. The real-time speed of the escape target and the distance between the agent and the escape target are estimated using less measurable information, thereby reducing the communication load of the system and improving communication efficiency. A distributed formation encirclement controller is proposed, which enables the agent to complete the tracking and encirclement of the escape target under the constraint of the desired azimuth, without the need for continuous and redundant circling actions, thereby reducing the energy loss of the system. In addition, this method ensures the geometric characteristics of the formation encirclement formation and can play a role in continuous monitoring of the escape target. Finally, the feasibility and stability of the proposed encirclement controller are demonstrated by three indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic diagram of a multi-agent formation encirclement process in this embodiment;

[0044] Figure 2 Schematic diagram of the system structure of the distance estimation algorithm proposed in this implementation;

[0045] Figure 3 This is a process trajectory diagram of the multi-agent system tracking and surrounding the escaping target in the simulation of this embodiment;

[0046] Figure 4 is a real-time distance error diagram between each agent and the escape target in the simulation of this embodiment;

[0047] Figure 5 is a diagram of the position error between each agent and its neighboring agents in the simulation of this embodiment;

[0048] Figure 6 The position error diagram between each intelligent agent and the escape target in the simulation of this embodiment is DETAILED DESCRIPTION

[0049] In order to more completely and clearly describe the technical solution of the present invention, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings. Obviously, the embodiments described below are part of the embodiments of the present invention, not all of the embodiments. The embodiments described with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0050] It should be noted that in the claims, specification and the above-mentioned drawings of the present invention, the terms "upper", "lower", "left", "right", "center", "inside", "outside" and the like indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of simplifying the description of the present invention, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. The term "several" means one or more, "multiple" means more than two, and "above", "below" and the like are understood to include the number itself. If "first" or "second" is described, it is only used for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0051] The embodiment of the present invention provides a multi-agent formation encirclement control method based on position information, and the specific steps and description are as follows:

[0052] As attached Figure 1 As shown in the figure, consider a multi-agent system consisting of n (only 5 are drawn in the figure for demonstration, the actual number can be n) homogeneous agents, which are used to track and surround a fleeing target that moves freely in a two-dimensional space. The viewing order of the schematic diagram is upper left corner → upper right corner → lower left corner → lower right corner. The red dotted circle in the figure represents the sensor observation range of the first agent that captures the orientation information of the fleeing target. The black dotted line with an arrow represents the communication topology between agents. T The black solid lines between agents and between agents and the escape target in the “Expected Encirclement Formation” diagram are only used to highlight the geometric features of the encirclement formation and have no other real meaning.

[0053] Step 1: Use graph theory and orientation rigidity theory to mathematically describe the communication topology of the multi-agent system, and build a suitable agent dynamics model according to the requirements of the encirclement task. The specific process includes:

[0054] Step 1.1: Using a directed graph Describes the communication connection relationship between intelligent agents, where represents the point set, and the edge set is The edge (i, j) indicates that agent j can receive information from agent i. represents the set of neighbor agents j of agent i. represents the global coordinate position of agent i, and Define the position of agent j relative to agent i as g ij =(p j -pi ) / ||p j -p i ||. According to the theory of orientation rigidity, the following orthogonal projection operator P is introduced: For auxiliary control:

[0055]

[0056] in, is a non-zero vector, and I2 represents the second-order identity matrix. The role of is to vector Project it to its orthogonal complement direction. For the convenience of writing, Denoted as P x .

[0057] Define a position function By finding the Jacobian matrix of p, we can get the orientation rigidity matrix:

[0058]

[0059] in, m represents the number of edges in the directed graph. H is a matrix that represents the communication relationship between nodes in the directed graph:

[0060]

[0061] Step 1.2: Construct the agent dynamics model as a single integral model:

[0062]

[0063] in, and represent the position and control input of agent i respectively.

[0064] Step 2: Propose specific control objectives based on task requirements. The specific process is as follows:

[0065] The final control goal is clarified according to the mission requirements, that is, the necessary constraints that the system expects the formation to meet:

[0066] (1) The angles between any two neighboring agents and the target are equal, that is, the agents are evenly distributed around the escape target. The orientations between neighboring agents and between each agent and the escape target must be equal to the expected orientation. Its mathematical description is:

[0067] (2) The center of mass of the formation converges to the position of the escape target, that is, the escape target is always trapped in the center of the formation. Its mathematical description is:

[0068] (3) The distance between each agent and the escape target is consistent, that is, the formation encirclement radius is a fixed value d Z , which is mathematically described as:

[0069] Step 3: Design the corresponding distance estimation algorithm and speed estimation algorithm based on the measurable data. The specific process includes:

[0070] Step 3.1: As attached Figure 2 As shown, the escape target is relative to the agent The distance d jT is the data that needs to be estimated. iT and d ij is the distance between agents i and j that can be measured by the onboard sensor. The position of the target relative to agent i and the position of agent i relative to j can be obtained by the onboard optical camera. Based on the above information, the angle θ can be obtained. jT The cosine value of , and then the cosine theorem is used to design an algorithm for agent j to estimate the distance to the escape target:

[0071]

[0072] Step 3.2: Since the agent j cannot directly measure its speed while tracking and surrounding the escaping target, a speed estimation algorithm needs to be designed. ij The derivative is Therefore, there is

[0073]

[0074] In multi-agent networks Under the premise of , we sum both sides of equation (4) and then transform them equivalently to obtain an estimation algorithm for the escape target speed of agent i:

[0075]

[0076] In the formula, Representing a multi-agent network The set of all agents in , represents the real-time distance between agent j and the escape target obtained by the above distance estimation algorithm, v j Represents the real-time speed of agent j.

[0077] Step 4: Define the encirclement radius error, design the formation encirclement controller and prove its stability. The specific process includes:

[0078] Step 4.1: Define the distance error between agent i and the escape target, expressed as follows:

[0079] δi =‖p i -p T ||-d Z (13)

[0080] Step 4.2: Based on the two estimation algorithms in step 3 above, design the following wraparound controller for the system:

[0081]

[0082] In order to verify the stability of the controller, a Lyapunov function V = ||δ|| 2 , combining the distance error (6) and the controller (7), taking the derivative of V, we finally get and It is proved that the controller (7) is feasible and can ensure the global stability of the system. The specific derivation process is as follows:

[0083]

[0084] Step 5: Further demonstrate the feasibility of the above formation encirclement control rate from three aspects: formation size, azimuth error and formation centroid. The specific process is as follows:

[0085] Step 5.1: The size of the formation can be determined by the distance between neighboring agents and the distance between the agent and the escape target, that is, ||p i (t)-p T (t)|| and||p i (t)-p j (t)|| jointly characterizes. Combining (6) to prove that these two indicators have upper bounds:

[0086]

[0087] This shows that the size of the formation always has an upper bound during the entire process of surrounding the escaping target, and the convergence is good, which proves the feasibility of the controller.

[0088] Step 5.2: When the multi-agent system completes the control goal, the formation must satisfy the desired orientation constraint. To prove this point, we choose to start from the local coordinate system of the escape target and make further arguments. First, write the complex matrix form of the controller according to (7): in Since the reference system selects the local coordinate system of the escape target, combined with formula (2), it can be known that the input of the escape target at any time is zero. Combined with the azimuth rigidity theory contained in step 1, further theoretical derivation is performed:

[0089]

[0090] When the system is in a dynamic stable state, and According to the properties of the orthogonal projection operator, we know Established.

[0091] Step 5.3: If the centroid position of the formation is expected to coincide with the position of the escape target, it means that the formation can not only complete the basic task of encircling the target, but also limit the position of the escape target in the encirclement area and play a monitoring role. To this end, the centroid of the multi-agent formation is defined as The error between the center of mass position and the escape target position is δ Z =Z(t)-p T .

[0092]

[0093] After the above derivation, we can get From the conclusions of step 4 and step 5.2 above, we can get ||δ Z || 2 Asymptotically converges to 0.

[0094] The above steps 3 to 5 prove the feasibility of the designed controller and the stability of the system. In order to further demonstrate the performance of the controller, the above embodiment is simulated using MATLAB software. The specific operation details and results are as follows:

[0095] Suppose a multi-agent system is composed of five homogeneous agents responsible for tracking and surrounding the escaping target. Their initial positions are randomly distributed, and they are assumed to be p1 = [-4, -2] T (Agent 1), p2 = [-7, 3] T (Agent 2), p3 = [-1, 5] T (Agent 3), p4 = [5, 4] T (Agent 4), p5 = [6, -1] T (Agent 5), the initial position of the escape target is set to p0 = [0,0] T . Set the constant speed of the escape target to v T =[0.8,0.8] T , the encirclement radius of the formation is d Z =1.7m. The parameters in the controller are set as: k1=5, k2=5, k3=1.

[0096] The present invention is attached Figure 3 It shows that under the action of the formation encirclement controller, the multi-agents with random initial position distribution successfully completed the tracking and encirclement of the escaped target. Figure 4 The formation has completed the control goal of maintaining an encirclement radius of 1.7m. Figure 5 ,6 It shows that the formation finally converges to the desired formation and satisfies the corresponding desired orientation constraints.

[0097] Finally, it should be noted that the technical solutions and preferred implementations of the present invention are described above in conjunction with the embodiments, and the present invention is not limited to the specific details of the above implementations. A person of ordinary skill in the art should understand that after reading the patent application of the present invention, he or she may still make various changes, modifications or equivalent substitutions to the specific implementations of the application, but these changes, modifications or equivalent substitutions do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present invention, and these changes and improvements fall within the scope of the present invention to be protected.

Claims

1. A multi-agent formation encirclement control method based on position information, characterized in that: The method comprises the following steps: Step 1: Use graph theory and orientation rigidity theory to mathematically describe the communication topology of the multi-agent system, and build a suitable agent dynamics model according to the requirements of the encirclement task; Step 2: Clarify the final control goal according to the task requirements, that is, the necessary constraints that the system expects the formation to meet; Step 3: Design corresponding distance estimation algorithms and speed estimation algorithms for the agent based on measurable data; Step 4: Define the formation encirclement radius error, design the formation encirclement controller and prove its stability; Step 5: Further demonstrate the feasibility of the above formation encirclement control rate from three aspects: formation size, azimuth error and formation centroid.

2. According to the multi-agent formation encirclement control method based on position information of claim 1, it is characterized in that: The step 1 further comprises: Consider a multi-agent system consisting of n homogeneous agents, which is used to track and surround a fleeing target that moves freely in a two-dimensional space. Describes the communication connection relationship between intelligent agents, where represents the point set, and the edge set is The edge (i, j) indicates that agent j can receive information from agent i. represents the position of agent i, and Define the position of agent j relative to agent i as g ij =(p j -p i ) / ‖p j -p i ||. According to the theory of orientation rigidity, the orthogonal projection operator P is introduced: Used for auxiliary control. Define a position function By finding the Jacobian matrix of p, we can get the orientation rigidity matrix: in, Represents the number of edges in a directed graph. H is a matrix that represents the communication relationship between nodes in a directed graph. Construct the agent dynamics model as a single integral model: in, and represent the position and control input of agent i respectively.

3. According to claim 1, a multi-agent formation encirclement control method based on position information is characterized in that: The step 2 further comprises: The final control goal is clarified according to the mission requirements, that is, the necessary constraints that the system expects the formation to meet: (1) The angles between any two neighboring agents and the target are equal, that is, the agents are evenly distributed around the escape target, and the orientations between neighboring agents and between each agent and the escape target must be equal to the expected orientation. Its mathematical description is: (2) The center of mass of the formation converges to the position of the escape target, that is, the escape target is always trapped in the center of the formation. Its mathematical description is: (3) The distance between each agent and the escape target is consistent, that is, the formation encirclement radius is a fixed value d Z , which is mathematically described as:

4. According to the multi-agent formation encirclement control method based on position information of claim 1, it is characterized in that: The step 3 further comprises: As shown in Figure 2 of the present invention, d iT and d ij is the distance between agents i and j that can be measured by the onboard sensor. The position of the target relative to agent i and the position of agent i relative to j can be obtained by the onboard optical camera. Based on the above information, the angle θ can be obtained. jT The cosine value of , and then the cosine theorem is used to design an estimation algorithm for the distance of the escape target: According to the theory of positional rigidity, in multi-agent networks Under the premise of , the speed estimation algorithm (5) is designed: In the formula, Representation in a multi-agent network The set of neighboring agents of agent i, represents the real-time distance between agent j and the escape target obtained by the above distance estimation algorithm, v j Represents the real-time speed of agent j.

5. According to claim 1, a multi-agent formation encirclement control method based on position information is characterized in that: The step 4 further comprises: Define the distance error between agent i and the escape target, the expression is as follows: d i =||p i -p T ||-d Z (6) Based on the two estimation algorithms in step 3 above, the following wraparound controller is designed for the system: In order to verify the stability of the controller, a Lyapunov function V = ||δ|| 2 , combining the distance error (6) and the controller (7), taking the derivative of V, we finally get and It is proved that the controller (7) is feasible and can ensure the global stability of the system.

6. According to the multi-agent formation encirclement control method based on position information of claim 1, it is characterized in that: The step 5 further comprises: The size of the formation is determined by the distance between neighboring agents and the distance between the agent and the escape target, i.e., ||p i (t)-p T (t)|| and||p i (t)-p j (t)|| jointly represents. Combining with equation (6), we can prove that and This shows that the size of the formation always has an upper bound during the entire process of surrounding the escaping target, and the convergence is good, which proves the feasibility of the controller. When the multi-agent system achieves the desired goal, the formation must satisfy the desired orientation constraint. To prove this point, we choose to start from the local coordinate system of the escape target and make further arguments. First, write the complex matrix form of the controller according to equation (7): in Since the reference system is the local coordinate system of the escape target, combined with equation (2), it can be seen that the input of the escape target at any time is zero, that is, Combined with the azimuthal rigidity theory in step 1, further theoretical derivation can be performed to obtain and According to the properties of the orthogonal projection operator, we know Established. If the centroid position of the formation is expected to coincide with the position of the escape target, it means that the formation can not only complete the basic task of encircling the target, but also limit the position of the escape target in the encirclement area and play a monitoring role. To this end, the centroid of the multi-agent formation is defined as The error between the center of mass position and the escape target position is δ Z =Z(t)-p T After theoretical derivation, we can get From the conclusions of step 4 and step 5 in the above claims, we can get: Z || 2 converges asymptotically to 0.

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