Multi-agent affine formation control method based on double leaders

Abstract

The invention discloses a multi-agent affine formation control method based on double leaders. The method comprises the following steps: acquiring initial position information of all agents; determining a leader and a follower, and determining a system communication topological structure; all followers initialize an affine transformation matrix estimator; determining an affine transformation matrix A (t) and a translation vector b (t) of the formation, and moving to a target position based on a leader control law; calculating the relative position # imgabs0 # of the target formation and the neighbor, and updating the estimated value of the formation transformation matrix A (t) according to the actual relative position rij of the target formation and the neighbor at the current moment; and the followers update their own positions based on the formation control law to realize formation control. According to the method, only two leaders in the formation need to obtain the formation transformation parameters, the formation of the whole formation can be changed, the complexity of system control is reduced, and the method does not depend on a stress matrix, so that the method is also suitable for the situation that a communication topological graph changes along with time.

Description

Technical Field

[0001] The invention belongs to the field of robot intelligent control, and in particular relates to a multi-agent affine formation control method based on dual leaders. Background Art

[0002] Through reasonable formation layout, the multi-agent system can maintain stable operation of the entire system in a complex environment and reduce the impact of external interference on the system. When carrying out search tasks in complex environments, the formation technology adopted by multi-agents plays an extremely critical role in broadening the search range, improving search efficiency, and improving target recognition accuracy. However, in complex and dangerous environments, such as scenes with complex terrain or potential threats, the formation needs to be able to adjust flexibly to better adapt to environmental changes and ensure the smooth progress of the mission. Therefore, formation transformation research has become a key direction in the field of multi-agent collaborative control research in recent years.

[0003] In order to realize the formation transformation of group robot formation, the following literature proposes affine formation control methods:

[0004] In the literature (Z.Lin, Z.Chen, and M.Fu, “A linear control approach to distributed multi-agent formations in d-dimensional space,” in 52nd IEEE Conference on Decision and Control. IEEE, dec 2013.), a control law is designed using a generalized graph Laplacian matrix with positive or negative weights to make each agent converge to the affine space of the nominal configuration.

[0005] The literature (S. Zhao, "Affine formation maneuver control of multiagent systems," IEEE Transactions on Automatic Control, vol. 63, no. 12, pp. 4140–4155, dec2018.) proposed a stress matrix-based affine formation maneuver control method to make all agents converge to the desired formation.

[0006] In the existing affine formation control method, to realize affine formation control in a two-dimensional plane, at least three agents need to know the affine transformation parameters of the entire formation system. In other words, if the operator wants to change the formation of the formation, he needs to control at least three of the robots. This increases the complexity of formation control in the actual control process. At the same time, conventional affine formation control depends on the stress matrix, which is determined by the nominal formation and the communication topology of the multi-agent system. It can only be calculated centrally, and the calculation process is relatively complicated. When the communication topology changes, it is necessary to collect the communication relationships of all agents and recalculate the stress matrix, which increases the complexity of the entire system algorithm. Summary of the invention

[0007] Purpose of the invention: In order to overcome the deficiencies in the prior art, a multi-agent affine formation control method based on dual leaders is provided. Only the two leaders in the formation need to obtain the formation transformation parameters to change the formation of the entire formation. This not only reduces the complexity of system control, but also does not depend on the stress matrix. Therefore, it is also applicable to the situation where the communication topology changes over time.

[0008] Technical solution: To achieve the above object, the present invention provides a multi-agent affine formation control method based on dual leaders, which includes at least three agents and comprises the following steps:

[0009] S1: Obtain the initial position information of all agents, determine the nominal formation of the formation according to the target task, and ensure that all agents obtain their nominal positions in the nominal formation;

[0010] S2: Determine two agents as leaders and the rest as followers, and determine the system communication topology to ensure that each follower has at least two neighbors and that the positions of followers and neighbors in the nominal formation are not in a straight line;

[0011] S3: All followers initialize the affine transformation matrix estimator

[0012] S4: Affine transformation matrix estimator The leader determines the formation’s affine transformation matrix A(t) and translation vector b(t) based on the mission requirements and environmental information, and moves to the target position based on the leader’s control law;

[0013] S5: The follower obtains the neighbor's nominal position in the nominal formation from the neighbor and calculates the relative position of itself and the neighbor in the target formation And according to the actual relative position r between it and its neighbors at the current moment ij Update the estimated value of the formation transformation matrix A(t);

[0014] S6: The follower updates its own position based on the formation control law to achieve formation control.

[0015] Furthermore, the communication topology of the system in step S2 is determined as follows: the multi-agent system is composed of n (n>2) agents moving on a two-dimensional plane, and the information transmission relationship between the agents is represented by a directed communication topology graph. Represents that the node set is Each node corresponds to an agent. The edge in the figure is represented by ε, which corresponds to the communication or perception relationship between the agents. The edge (i, j)∈ε means that agent i receives information from agent j in the system. In this case, agent j is called a neighbor of agent i. The neighbor set of point i is represented by To express.

[0016] Furthermore, in step S2, for the multi-agent system, the overall target position of the formation is p * (t), where p * (t) is composed of the expected position of each agent in the target formation:

[0017]

[0018] The target position of affine formation control is

[0019]

[0020] in, is a nominal configuration, i.e., the desired initial formation set in advance for the system. is the affine transformation matrix of the system, which determines the shape change of the system formation, is a translation vector that is continuous with respect to time t.

[0021] Furthermore, in step S2, for the multi-agent system, the target position of agent i in the target formation is Calculated as follows:

[0022]

[0023] Furthermore, the formation transformation matrix estimator of follower i in step S3 is

[0024]

[0025] in, k1 is a gain greater than zero, and s is the number of neighbors of agent i.

[0026] Furthermore, the Mat(x) operation is referenced in step S3, where Mat(x) indicates that after applying the operation to the d-dimensional vector x, a d×d 2 The matrix of ; Mat(x) is operated according to the following rules:

[0027]

[0028] Furthermore, the leader control law in step S4 is

[0029]

[0030] Here, k2 is a constant greater than zero.

[0031] Furthermore, in step S5, for agents i, r ij is the actual position deviation between agent i and neighbor j, is the position deviation between agent i and neighbor j in the nominal formation, that is,

[0032] r ij =p i -p j ,

[0033]

[0034] Furthermore, in step S6, the follower control law is applied to all followers of the multi-agent system, that is,

[0035]

[0036] in, is the positive feedback gain coefficient, μ is a The scaling function that changes with time is expressed as:

[0037]

[0038] in, And h>0 is a parameter that needs to be selected during the operation;

[0039] The expression is as follows:

[0040]

[0041] By continuously repeating the above information acquisition, calculation and update process, the follower can adapt to the leader's movement and the dynamic changes of the formation in real time, ensuring that the entire formation maintains good coordination and stability in a complex environment, and continuously adjusts and optimizes towards the desired formation. The control algorithm enables the system follower to achieve the desired formation movement through proportional integral control of the position error.

[0042] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0043] 1. The present invention proposes a multi-agent affine formation control method moving in a two-dimensional plane. Only two leaders are needed to obtain the information of the system's formation target formation. Compared with the existing affine formation control method in a two-dimensional plane, there is at least one less leader, which reduces the complexity of system operation.

[0044] 2. The existing affine formation control method needs to rely on the stress matrix, which is jointly determined by the nominal formation and the communication topology of the multi-agent system. It can only be calculated centrally, and the calculation process is relatively complicated. When the communication topology changes, it is necessary to collect the communication relationships of all agents and recalculate the stress matrix. In the implementation process of the method of the present invention, the follower directly estimates the affine transformation matrix A(t), so it can realize the constraint on the relative position of the agent without relying on the stress matrix. It is also applicable to the situation where the communication topology changes over time. There is no need to use centralized calculation, which reduces the complexity of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 is the nominal formation configured in this embodiment;

[0047] Figure 3 This is a diagram of the communication topology configured in this embodiment. DETAILED DESCRIPTION

[0048] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0049] like Figure 1 As shown, the present invention provides a multi-agent affine formation control method based on dual leaders, comprising the following steps:

[0050] S1: Obtain the initial position information of all agents, determine the nominal formation of the formation according to the target task, and ensure that all agents obtain their nominal positions in the nominal formation;

[0051] The nominal formation set in this embodiment is as follows Figure 2 As shown, each point in the figure represents the nominal position of an agent, and the number of agents in the multi-agent system is 8. At the same time, all agents can obtain their nominal positions in the nominal formation, that is, the coordinates in the figure.

[0052] S2: Determine two agents as leaders and the rest as followers, and determine the system communication topology to ensure that each follower has at least two neighbors, and the positions of the follower and the neighbors in the nominal formation are not in a straight line (if the follower and the two neighbors are in a straight line, the formation transformation matrix estimator given in step S3 will not converge);

[0053] The multi-agent system consists of n (n>2) agents moving on a two-dimensional plane. The information transmission relationship between agents is represented by a directed communication topology graph. Represents that the node set is Each node corresponds to an agent. The edge in the figure is represented by ε, which corresponds to the communication or perception relationship between the agents. The edge (i, j)∈ε means that agent i receives information from agent j in the system. In this case, agent j is called a neighbor of agent i. The neighbor set of point i is represented by To express.

[0054] For a multi-agent system, the overall target position of the formation is p * (t), where p * (t) is composed of the expected position of each agent in the target formation:

[0055]

[0056] The target position of affine formation control is

[0057]

[0058] in, is a nominal configuration, i.e., the desired initial formation set in advance for the system. is the affine transformation matrix of the system, which determines the shape change of the system formation, is a translation vector that is continuous with respect to time t.

[0059] The target position of agent i in the target formation is Calculated as follows:

[0060]

[0061] The system communication topology diagram in this embodiment is shown in the attached figure. Figure 3As shown in the figure, l1 and l2 are the two leaders of the system, and the remaining agents are followers of the system. In this communication topology diagram, each follower can receive communications from at least two agents, that is, the number of neighbors is at least 2. In the figure, the neighbors of f1 are two leaders, namely l1 and l2; the number of neighbors of f4 is 3, namely f1, f2 and f3; the number of neighbors of all other followers is 2.

[0062] S3: All followers initialize the affine transformation matrix estimator

[0063] The formation transformation matrix estimator of follower i is

[0064]

[0065] in, k1 is a gain greater than zero, s is the number of neighbors of agent i;

[0066] Refer to the Mat(x) operation. Mat(x) means that after applying this operation to the d-dimensional vector x, a d×d 2 The matrix of ; Mat(x) is operated according to the following rules:

[0067]

[0068] Each follower can calculate the estimated value The affine transformation matrix A(t) of the system is estimated to provide the necessary parameters for applying the follower control law to the follower of the system.

[0069] S4: Affine transformation matrix estimator The leader determines the formation’s affine transformation matrix A(t) and translation vector b(t) based on the mission requirements and environmental information, and moves to the target position based on the leader’s control law;

[0070] In this embodiment, leaders l1 and l2 determine the affine transformation matrix A(t) and translation vector b(t) of the formation based on mission requirements and environmental information through sensor data, such as dot matrix information obtained by a laser radar;

[0071] At the same time, leaders l1 and l2 continuously monitor and obtain their actual positions p at the current moment i , and apply the leader control law to l1 and l2, that is,

[0072]

[0073] Where k2 is a constant greater than zero. is the positive feedback gain coefficient, μ is a The scaling function that changes with time is expressed as:

[0074]

[0075] The expression is as follows:

[0076]

[0077] S5: The follower obtains the neighbor's nominal position in the nominal formation from the neighbor and calculates the relative position of itself and the neighbor in the target formation And according to the actual relative position r between it and its neighbors at the current moment ij Update the estimated value of the formation transformation matrix A(t);

[0078] Through the communication topology of this embodiment, all followers in the system can periodically receive the nominal position information of their neighbors in the nominal formation from their neighbors. Based on the obtained nominal positions of their neighbors and their own nominal positions in the nominal formation, the followers can calculate the relative positions of themselves and their neighbors in the target formation. Calculated as follows:

[0079]

[0080] At the same time, the follower continuously monitors and obtains the actual relative position r between itself and its neighbors at the current moment ij , which is calculated as follows:

[0081]

[0082] Based on the above and r ij , the follower updates the estimated value of the affine change matrix A(t) according to the method of step S3; the formation transformation matrix estimator formula of follower i is is obtained by transforming A(t) through Mat(x), and then by After the inverse Mat(x) transformation, the new affine transformation matrix A(t) can be obtained;

[0083] S6: The follower continuously adjusts its position according to its own control law, continuously exchanges information with its neighbors during the whole process, and updates the estimation of the affine transformation matrix in real time to control its own movement and realize formation control:

[0084] For all followers of the multi-agent system, the follower control law is applied, that is,

[0085]

[0086] in, is the positive feedback gain coefficient, μ is a The scaling function that changes with time is expressed as:

[0087]

[0088] in, And h>0 is a parameter that needs to be selected during the operation;

[0089] The expression is as follows:

[0090]

[0091] By continuously repeating the above information acquisition, calculation and update process, the follower can adapt to the leader's movement and the dynamic changes of the formation in real time, ensuring that the entire formation maintains good coordination and stability in a complex environment, and continuously adjusts and optimizes towards the desired formation. The control algorithm enables the system follower to achieve the desired formation movement through proportional integral control of the position error.

[0092] This embodiment also provides a multi-agent affine formation control system based on dual leaders, which includes a network interface, a memory and a processor; wherein the network interface is used to realize the reception and transmission of signals during the process of sending and receiving information between other external network elements; the memory is used to store computer program instructions that can be run on the processor; the processor is used to execute the steps of the above-mentioned consensus method when running the computer program instructions.

[0093] The present embodiment also provides a computer storage medium, which stores a computer program, and the method described above can be implemented when the processor executes the computer program. The computer readable medium can be considered to be tangible and non-temporary. Non-limiting examples of non-temporary tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital tapes or hard drives) and optical storage media (such as CDs, DVDs or Blu-ray discs), etc. The computer program includes processor executable instructions stored on at least one non-temporary tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a special-purpose computer, a device driver that interacts with a specific device of a special-purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0094] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

Claims

1. A multi-agent affine formation control method based on dual leaders, characterized in that: The steps include: S1: Obtain the initial position information of all agents, determine the nominal formation of the formation according to the target task, and ensure that all agents obtain their nominal positions in the nominal formation; S2: Determine two agents as leaders and the rest as followers, and determine the system communication topology to ensure that each follower has at least two neighbors and that the positions of followers and neighbors in the nominal formation are not in a straight line; S3: All followers initialize the affine transformation matrix estimator S4: Affine transformation matrix estimator The leader determines the formation’s affine transformation matrix A(t) and translation vector b(t) based on the mission requirements and environmental information, and moves to the target position based on the leader’s control law; S5: The follower obtains the neighbor's nominal position in the nominal formation from the neighbor and calculates the relative position of itself and the neighbor in the target formation And according to the actual relative position r between it and its neighbors at the current moment ij Update the estimated value of the formation transformation matrix A(t); S6: The follower updates its own position based on the formation control law to achieve formation control.

2. A multi-agent affine formation control method based on dual leaders according to claim 1, characterized in that: The communication topology of the system in step S2 is determined as follows: the multi-agent system is composed of n agents moving on a two-dimensional plane, and the information transmission relationship between the agents is represented by a directed communication topology graph. Represents that the node set is Each node corresponds to an agent. The edge in the figure is represented by ε, which corresponds to the communication or perception relationship between the agents. The edge (i, j) ∈ ε means that in this system, agent i receives information from agent j. In this case, agent j is called a neighbor of agent i. The neighbor set of point i is represented by To express.

3. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: In step S2, for the multi-agent system, the overall target position of the formation is p * (t), where p * (t) is composed of the expected position of each agent in the target formation: The target position of affine formation control is in, is a nominal configuration, i.e., the desired initial formation set in advance for the system. is the affine transformation matrix of the system, which determines the shape change of the system formation, is a translation vector that is continuous with respect to time t.

4. A dual-leader multi-agent affine formation control method according to claim 3, characterized in that: In step S2, for the multi-agent system, the target position of agent i in the target formation is Calculated as follows:

5. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: The formation transformation matrix estimator of follower i in step S3 is: in, k1 is a gain greater than zero, and s is the number of neighbors of agent i.

6. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: In step S3, the Mat(x) operation is used. Mat(x) indicates that after applying the operation to the d-dimensional vector x, a d×d 2 The matrix of ; Mat(x) is operated according to the following rules:

7. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: The leader control law in step S4 is: Here, k2 is a constant greater than zero.

8. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: In step S5, for agent i, r ij is the actual position deviation between agent i and neighbor j, is the position deviation between agent i and neighbor j in the nominal formation, that is, r ij =p i -p j , 9. The multi-agent affine formation control method based on dual leaders according to claim 1 is characterized in that: In step S6, the follower control law is applied to all followers of the multi-agent system, that is, in, is the positive feedback gain coefficient, μ is a The scaling function that changes with time is expressed as: in, And h>0 is a parameter that needs to be selected during the operation; The expression is as follows: By continuously repeating the above information acquisition, calculation and updating process, the followers can adapt to the leader's movement and the dynamic changes of the formation in real time, ensuring that the entire formation maintains good coordination and stability in a complex environment, and continuously adjusts and optimizes towards the desired formation.

Images