A multi-agent affine formation control method based on double leaders

Abstract

The application discloses a kind of multi-agent affine formation control method based on double leaders, comprising: obtaining the initial position information of all agents;Determine leader and follower, and determine system communication topology structure;All followers initialize affine transformation matrix estimator;Determine the affine transformation matrix A (t) of formation and translation vector b (t), and move to target position based on leader control law;Calculate the relative position of oneself and neighbor in target formation and according to the actual relative position r ij Update the estimated value of formation transformation matrix A (t);Followers update their own position based on formation control law, realize the control of formation.The application only needs two leaders in formation to obtain formation transformation parameters, which can change the formation of the entire formation, reduce the complexity of system control, and does not depend on stress matrix, so it is also applicable to the case where communication topology graph changes over time.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of intelligent control of robots, and particularly relates to a multi-agent affine formation control method based on double leaders. BACKGROUND

[0002] Through reasonable formation layout, the multi-agent system can keep stable operation in complex environment and reduce the influence of external interference on the system. When carrying out search tasks in complex environment, the formation technology adopted by the multi-agent plays a very key role in widening the search range, improving search efficiency and improving target recognition accuracy. However, in complex and dangerous environment, such as complex terrain or scenes with potential threats, the formation needs to be flexibly adjusted to better adapt to environmental changes and ensure the smooth progress of the task. Therefore, the formation transformation research has become a key direction in the field of multi-agent cooperative control research in recent years.

[0003] In order to realize the formation transformation of the group robot, the following documents propose an affine formation control method:

[0004] In document (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 by using the generalized Laplacian matrix with positive and negative weights, so that each agent converges to the affine space of the nominal configuration.

[0005] Document (S. Zhao, “Affine formation maneuver control of multiagent systems,” IEEE Transactions on Automatic Control, vol. 63, no. 12, pp. 4140-4155, dec 2018.) proposes an affine formation maneuver control method based on stress matrix, so that all agents converge to the expected formation.

[0006] In the existing affine formation control method, affine formation control is realized in a two-dimensional plane, and at least three agents need to know the affine transformation parameters of the entire formation system. That is, at least three robots need to be controlled by the operator to change the formation of the formation. This increases the complexity of the formation control in the actual control process. At the same time, the conventional affine formation control needs to rely on the stress matrix, which is determined by the nominal formation and the communication topology of the multi-agent system, and can only be calculated centrally, and the calculation process is relatively complex. When the communication topology changes, the communication relationship of all agents needs to be collected, and the stress matrix needs to be recalculated, which increases the complexity of the entire system algorithm. SUMMARY

[0007] The purpose of the application is to overcome the deficiencies in the prior art, and provide a multi-agent affine formation control method based on double leaders, which only needs two leaders in the formation to obtain the formation transformation parameters to change the formation of the entire formation, not only reducing the complexity of the system control, but also not relying on the stress matrix, so it is suitable for the case where the communication topology changes over time.

[0008] Technical scheme: To achieve the above purpose, the application provides a multi-agent affine formation control method based on double leaders, at least containing three agents, including 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 remaining agents as followers, and determine the system communication topology, ensure that each follower has at least two neighbors, and the positions of the follower and the neighbors in the nominal formation are not on a straight line;

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

[0012] S4: Based on the affine transformation matrix estimator The leader determines the affine transformation matrix A(t) and the translation vector b(t) of the formation according to the task requirements and environmental information, and moves to the target position based on the leader control law;

[0013] S5: The follower obtains the nominal position of the neighbor in the nominal formation from the neighbor, calculates the relative position of itself and the neighbor in the target formation And according to the actual relative position r 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 the control of the formation.

[0015] Further, the system communication topology in step S2 is determined in the following manner: 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 , where the node set is Each node corresponds to an agent, and the edge ε in the graph represents the communication or perception relationship between the agents; the edge (i, j) ∈ ε indicates that agent i receives information from agent j in the system; at this time, agent j is called a neighbor of agent i; the neighbor set of point i is represented by .

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

[0017]

[0018] The target position of the affine formation control is

[0019]

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

[0021] Further, for the multi-agent system in step S2, the target position of agent i in the target formation is calculated according to the following formula:

[0022]

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

[0024]

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

[0026] ​Further, the step S3 refers to the operation Mat(x), which means that a dxd matrix is obtained after the operation is used on the d-dimensional vector x; Mat(x) is operated according to the following rules: 2 Further, the step S3 refers to the operation Mat(x), which means that a dxd matrix is obtained after the operation is used on the d-dimensional vector x; Mat(x) is operated according to the following rules:

[0027]

[0028] Further, the step S4 is the leader control law

[0029]

[0030] where k2 is a constant greater than zero.

[0031] Further, the step S5 is the actual position deviation of the agent i and the neighbor j, ij the position deviation of the agent i and the neighbor j in the nominal formation, that is,

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

[0033]

[0034] Further, the step S6 is the follower control law for all followers of the multi-agent system, that is,

[0035]

[0036] where, is a positive feedback gain coefficient, and μ is a scaling function that changes over time within , and its expression is:

[0037]

[0038] where, and h>0 is a parameter that needs to be selected during operation;

[0039] The expression of is as follows:

[0040]

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

[0042] Beneficial effects: compared with the prior art, the present application has the following advantages:

[0043] 1. The present application provides a multi-agent affine formation control method in a two-dimensional plane, which only needs two leaders to obtain the information of the formation target shape of the system, at least one leader less than the existing affine formation control method in a two-dimensional plane, reducing the complexity of system operation.

[0044] 2. The existing affine formation control method needs to rely on the stress matrix, which is determined by the nominal formation and the communication topology of the multi-agent system, and can only be calculated centrally, and the calculation process is relatively complex. When the communication topology changes, the communication relationship of all agents needs to be collected and the stress matrix needs to be recalculated. The method of the present application directly estimates the affine transformation matrix A(t) during implementation, so it can realize the constraint of the relative position of the agent without relying on the stress matrix, and is suitable for the case where the communication topology changes over time, without the need for centralized calculation, reducing the complexity of calculation. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0047] Figure 3 is the communication topology diagram configured in the present embodiment. DETAILED DESCRIPTION

[0048] The present application will be further illustrated below in conjunction with the drawings and specific embodiments, it should be understood that these embodiments are only used to illustrate the present application and not to limit the scope of the present application, after reading the present application, the modification of various equivalent forms of the present application by those skilled in the art falls within the scope defined by the claims attached hereto.

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

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

[0051] The nominal formation configured in the present embodiment is shown in Figure 2 , in which each point 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, i.e. the coordinates in the figure.

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

[0053] The multi-agent system is composed of n (n>2) agents moving in a two-dimensional plane, and the information transmission relationship between the agents is represented by a directed communication topology graph , where the node set is Each node corresponds to an agent, and the edge in the graph is ε, which represents the communication or perception relationship between the agents; the edge (i, j) ∈ ε indicates that in the system, agent i receives information from agent j; at this time, agent j is called a neighbor of agent i; the neighbor set of point i is represented by .

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

[0055]

[0056] The target position of the affine formation control is

[0057]

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

[0059] The target position of agent i in the target formation is calculated according to the following formula:

[0060]

[0061] The system communication topology structure diagram in this embodiment is shown in FIG. 1. Figure 3As shown in Figure 1, l1 and l2 are the two leaders of the system, and the remaining agents are followers. In this communication topology, each follower can receive communications from at least two agents, meaning it has at least two neighbors. For example, f1's neighbors are the two leaders, l1 and l2; f4 has three neighbors, namely f1, f2, and f3; and all other followers have two neighbors.

[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 required parameters for subsequently 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 formation's affine transformation matrix A(t) and translation vector b(t) based on mission requirements and environmental information using sensor data, such as dot matrix information acquired 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 forward feedback gain coefficient, μ is a An inner time-varying scaling function, whose expression is:

[0074]

[0075] The expression of is as follows:

[0076]

[0077] S5: The follower obtains the nominal position of the neighbor in the nominal formation from the neighbor, and calculates the relative position of the follower and the neighbor in the target formation and the actual relative position r ij of the follower and the neighbor at the current time, updates the estimated value of the formation transformation matrix A(t);

[0078] Through the communication topology of the embodiment, all followers in the system can periodically receive the nominal position information of the neighbor in the nominal formation from the neighbor. Based on the obtained nominal position of the neighbor and the nominal position of the follower in the nominal formation, the follower can calculate the relative position of the follower and the neighbor in the target formation is calculated according to the following formula:

[0079]

[0080] At the same time, the follower continuously monitors and obtains the actual relative position r ij of the follower and the neighbor at the current time, which is calculated according to the following formula:

[0081]

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

[0083] S6: The follower continuously adjusts the position according to the control law of the follower, continuously interacts with the neighbor in the whole process, and updates the estimation of the affine transformation matrix in real time to control the motion of the follower and realize the control of the formation:

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

[0085]

[0086] wherein, is a positive feedback gain coefficient, and μ is a positive constant. a time-varying scaling function expressed as:

[0087]

[0088] wherein, and h>0 is a parameter to be selected during operation;

[0089] The expression of is as follows:

[0090]

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

[0092] The embodiment also provides a multi-agent affine formation control system based on a double leader, which comprises a network interface, a memory and a processor; wherein the network interface is used for realizing the receiving and sending of signals in the process of transceiving information with other external network elements; the memory is used for storing computer program instructions capable of running on the processor; and the processor is used for executing the steps of the consensus method when running the computer program instructions.

[0093] The embodiment also provides a computer storage medium storing a computer program, which can realize the above-described method when the processor executes the computer program. The computer readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory 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 magnetic tapes or hard disk 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-transitory tangible computer readable medium. The computer program can also include or depend on stored data. The computer program can 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 application programs, background services, background application programs, etc.

[0094] Those skilled in the art will appreciate that embodiments of the present application can be devised for a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer-readable program code thereon for use by or in connection with an instruction execution system.

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 The formation transformation matrix estimator of follower i is in, k1 is a gain greater than zero, s is the number of neighbors of agent i; 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: 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; The leader control law is Where k2 is a constant greater than zero; 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 of the current moment and its neighbor ij Update the estimated value of the affine transformation matrix A(t); 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, i.e. r ij =p i -p j , S6: Followers update their own positions based on the formation control law to achieve formation control; Apply the follower control law to all followers of the multi-agent system, that is, in, is the forward feedback gain coefficient, μ is a The time-varying scaling function 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 complex environments, and continuously adjusts and optimizes towards the desired formation.

2. A dual-leader multi-agent affine formation control method according to claim 1, characterized in that: The system communication topology structure 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 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.

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 continuous translation vector about time t.

4. The 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:

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