CN117891259A - Multi-agent formation control method with multi-graph configuration and related product - Google Patents
Multi-agent formation control method with multi-graph configuration and related product Download PDFInfo
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Abstract
The invention discloses a multi-agent formation control method with a multi-graph configuration and related products. The method comprises the following steps: determining a desired formation map, a plurality of gray maps corresponding to the desired formation map and tasks allocated to the intelligent agent; according to the understanding values of the intelligent agents and the neighbor intelligent agents on the positions of the expected formation diagrams in the physical space, the understanding values of the intelligent agents on the positions of the expected formation diagrams in the physical space are updated, so that the understanding values of all the intelligent agents on the positions of the expected formation diagrams in the physical space tend to be consistent; and controlling the motion state of the intelligent body according to the graph entering speed command, the graph exploring speed command and the interaction speed command. The multi-agent formation efficiently and quickly realizes the formation task, and the coverage area is a plurality of communication graphs separated from each other.
Description
Technical Field
The invention relates to a multi-agent formation control method with a multi-graph configuration and a related product.
Background
Multi-agent formation control refers to control techniques that work cooperatively between multiple autonomous agents to achieve a particular task or maintain a particular formation. The field covers various applications of robots, unmanned aerial vehicles, automatic driving vehicles, internet of things equipment and the like, and aims to enable a plurality of intelligent agents to cooperate and communicate with each other and realize collective behaviors. The research background for multi-agent formation control stems from the need for modern complex systems that typically require multiple agents to perform tasks in concert, e.g., unmanned aerial vehicle formation to perform search and investigation tasks, robotic team collaboration to perform article handling, or search and rescue. Multi-agent formation control plays an important role in both civilian and military scenarios. With the development of modern technology, the unmanned cluster formed by multiple intelligent agents has a larger and larger scale, and the scale and the number of tasks which can be executed by the unmanned cluster have gradually increased. In the face of multi-agent and multi-task scenes, the control method not only needs to complete realization of formation configuration of the agents, but also needs to reasonably distribute tasks of the agents. Therefore, how to design a method for simultaneously realizing the distribution and control of the intelligent agents and the formation tasks under the large-scale multi-intelligent agents and multi-formation tasks becomes a problem to be solved.
The existing multi-agent formation control method can be divided into two modes: centralized and distributed. In the centralized method, one main controller is responsible for controlling the whole intelligent agent cluster, but the method can be difficult to implement in many practical application scenes due to the problems of high communication overhead, high single-point fault risk and the like. On the other hand, the distributed method only requires each agent to obtain local information around the agent and can only communicate with neighbor agents within a certain range. The distributed method greatly reduces the requirement of the cluster on communication capacity, and meanwhile, only the utilization of local information increases the fault tolerance of the cluster, so that the distributed method becomes a mainstream method in practical application. But in the case of large-scale clusters, the distribution may face challenges such as information transfer delays, unequal task allocation, etc. Therefore, in a distributed scenario, it is necessary to improve the performance such as the optimality and convergence rate of the control method as much as possible.
Most of the existing distributed multi-agent formation control methods are used for realizing formation configuration aiming at a single graph, tasks are realized for configuration of a plurality of graphs, and the formation control method aiming at the single graph is difficult to directly implement. The multi-graph formation control problem can be abstracted into a multi-agent multi-task problem. The existing task allocation and track planning method aiming at the multi-agent multi-task problem often considers the task as a particle, and further takes factors such as the moving distance of the agent, the energy consumption and the like as optimization indexes and gives an optimal solution. However, such methods cannot meet the demands of formation tasks, and thus cannot be applied to the problem of multi-graphic formation control. In general, the problem of multi-pattern formation control is currently studied to a small extent, and the problem of multi-pattern formation control can be effectively solved by using fresh technology.
The method proposed by the Chinese patent application CN111259327A (optimization method for multi-agent system consistency problem based on subgraph processing) is as follows: 1) Constructing a graph signal model of the multi-agent system; 2) Adding auxiliary constraint conditions to the problem to be solved; 3) Local inversion in the subgraph; 4) Fusion and averaging among subgraphs; 5) And (5) iteratively eliminating errors.
Disclosure of Invention
The invention provides a multi-agent formation control method with a multi-graph configuration and related products.
The technical scheme of the invention is as follows: a multi-agent formation control method of a multi-graphic configuration, comprising:
Determining a desired formation map, a plurality of gray maps corresponding to the desired formation map and tasks allocated to the intelligent agent;
according to the understanding values of the intelligent agents and the neighbor intelligent agents on the positions of the expected formation diagrams in the physical space, the understanding values of the intelligent agents on the positions of the expected formation diagrams in the physical space are updated, so that the understanding values of all the intelligent agents on the positions of the expected formation diagrams in the physical space tend to be consistent;
Controlling the motion state of the intelligent agent according to the graph entering speed command, the graph exploring speed command and the interaction speed command;
The method comprises the steps that a gray maximum value or a gray minimum value in an expected formation graph represents a target area, the target area is connected into a plurality of sub-images separated from each other, the sub-images are communicated with each other, the plurality of gray images are in one-to-one correspondence with the plurality of sub-images, each gray image is divided into a target area, a transition area and a non-target area, the coordinates and the gray values of grids in the target area are the same as those of the grids in the expected formation graph, the transition area is close to the target area and smoothly transits along the direction far away from the target area, the non-target area is close to the boundary of the transition area far away from the target area and the gray value is the gray minimum value or the gray maximum value different from the gray value of the target area, and the shapes and the sizes of the grids in the sub-images are equal to those of the grids in the expected formation graph;
Wherein each task corresponds to a sub-graph;
The graphic entry speed instruction is determined according to the corresponding gray level graph and is used for driving the intelligent agent to move from outside the target area to the target area;
the graphic exploration speed instruction is determined according to the corresponding gray level diagram and is used for driving the intelligent agent to enter the target area from the outer side edge of the target area, and further searching and occupying grids which are not occupied by other intelligent agents in the target area;
Wherein the interaction speed command is used for avoiding collision and driving the speed of the intelligent agent to be consistent with the speed of surrounding intelligent agents.
The technical scheme of the invention is as follows: an agent comprising a memory and a processor, the memory storing a program, the processor running the program to perform the multi-agent formation control method of the aforementioned multi-graphic configuration.
The technical scheme of the invention is as follows: a program product that, at run-time, performs the multi-agent formation control method of the aforementioned multi-graph configuration.
The beneficial effects of the invention include: in the proposed multi-agent formation control method, two parts of task allocation and agent control are innovatively combined, and the multi-graph configuration realization problem in the multi-agent formation problem is reasonably and efficiently solved; the distributed and asynchronous calculation mode is adopted, so that the requirement on the communication capacity of the intelligent agent is effectively reduced, and the engineering feasibility is increased; the convergence of formation targets can be guaranteed to be realized within a limited time, and the local calculation complexity of each intelligent agent is within an acceptable range, so that engineering realization is easy.
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FIG. 1 is a flow chart of a multi-agent formation control method of the multi-graph configuration of the present invention.
Fig. 2 is a block diagram of a controller in an agent of the present invention.
Detailed Description
The present invention will be further described with reference to specific examples, but the scope of the present invention is not limited thereto.
Referring to fig. 1, the flow of the multi-agent formation control method of the multi-graphic configuration proposed by the present invention includes the following steps.
Step 101, determining a desired formation map, a plurality of gray maps corresponding to the desired formation map and tasks allocated to the intelligent agent;
102, updating the understanding values of the intelligent agents on the positions of the expected formation diagrams in the physical space according to the understanding values of the intelligent agents and the neighbor intelligent agents on the positions of the expected formation diagrams in the physical space, so that the understanding values of all the intelligent agents on the positions of the expected formation diagrams in the physical space tend to be consistent;
Step 103, controlling the motion state of the intelligent agent according to the graph entering speed command, the graph exploring speed command and the interaction speed command;
The method comprises the steps that a gray maximum value or a gray minimum value in an expected formation graph represents a target area, the target area is connected into a plurality of sub-images separated from each other, the sub-images are communicated with each other, the plurality of gray images are in one-to-one correspondence with the plurality of sub-images, each gray image is divided into a target area, a transition area and a non-target area, the coordinates and the gray values of grids in the target area are the same as those of grids in the expected formation graph, the transition area is close to the target area and smoothly transits along the direction far away from the target area, the non-target area is close to the boundary of the transition area far away from the target area, the gray value is the gray minimum value or the gray maximum value different from the gray value of the target area, and the shapes and the sizes of the grids in the sub-images are equal after the grids in the sub-images are mapped to a physical space;
Wherein each task corresponds to a sub-graph;
The graphic entry speed instruction is determined according to the corresponding gray level graph and is used for driving the intelligent agent to move from outside the target area to the target area;
the graphic exploration speed instruction is determined according to the corresponding gray level diagram and is used for driving the intelligent agent to enter the target area from the outer side edge of the target area, and further searching and occupying grids which are not occupied by other intelligent agents in the target area;
Wherein the interaction speed command is used for avoiding collision and driving the speed of the intelligent agent to be consistent with the speed of surrounding intelligent agents.
In one example, the sum of the above three commands is equal to the expected velocity vector of the agent, which the agent is controlled by the agent's power system to move in accordance with.
The execution subject of the above method is a single agent in a multi-agent formation, which may be a controller in the agent from a hardware perspective, and may be a program running on the agent from a software perspective.
The desired formation map and the plurality of gray maps corresponding to the desired formation map are input to the agent by an external device.
In the expected formation map, the target region is represented by a region formed by the following meshes having a gradation value of 0, and the gradation of the meshes of the remaining regions in the expected formation map is 1.
Illustratively, the shape of the target area of the formation is expected to be the shape of "ABC" three letters, which are separated from each other. The target area occupied by letter a constitutes a sub-image (named sub-image a), the target area occupied by letter B constitutes a sub-image (named sub-image B), and the target area occupied by letter C constitutes a sub-image (named sub-image C).
Illustratively, the resolution of each gray map is the same as the resolution of the desired formation map. In the gray scale map corresponding to the sub-map a, the grids having the gray scale value of 0 are connected in the shape of the letter a, and the positions and the sizes are the same as those of the letter a in the desired formation map. In the gray map corresponding to sub-map B, the grid with gray value 0 is connected in the shape of letter B, and the position and size are the same as those of letter a in the desired formation map. In the gray scale map corresponding to the sub-graph C, the grids having the gray scale value of 0 are connected in the shape of the letter C, and the position and size are the same as those of the letter C in the desired formation map.
Illustratively, in each gray scale map, the gray scale value of each grid smoothly transitions from 0 to 1 in a direction away from the target region. In a region far enough from the target region, the gray value of the grid is 1.
The grid of the gray scale map is a data point on the data storage, and the shape when mapped to the physical space is, for example, square, regular hexagon, rectangle, or the like. In the following example, the grid of the gray map is being square in shape in physical space.
The present invention is not limited to how the gray scale map is generated.
Illustratively, the task of the agent coverage area forming the letter a pattern is referred to as task a, the task of the agent coverage area forming the letter B pattern is referred to as task B, and the task of the agent coverage area forming the letter C pattern is referred to as task C. Which task the agent specifically performs may be preset or specified by an external device inputting instructions to the agent.
It should be noted that, step 102 and step 103 are performed in real time.
Optionally, the intelligibility value of the position of the object shape by the agent itself is calculated according to the following formula:
；
；
wherein is an understanding value of the speed of the entity i to the expected formation map in the physical space,/> is an understanding value of the speed of the entity j to the expected formation map in the physical space,/> and/> , both of which are constant gains,/> is a set of neighbor entities (entities which are located within a communication radius and can perform two-way communication, not limited to executing the same task) of the entity i,/> is a sign function,/> is a 2-norm calculation sign,/> is an understanding value of the entity i to the position of the expected formation map in the physical space, and/> is an understanding value of the entity j to the position of the expected formation map in the physical space;
Where c 2 is a positive constant gain, is the understanding value of agent i to the direction of the desired formation in physical space, and/> is the understanding value of agent j to the direction of the desired formation in physical space.
The first term in the first formula is used for enabling the understanding value of the object shape position of the object i to be consistent with the understanding value of the object shape position of the object j, and the second term is used for enabling the understanding value of the object shape speed of the object i to be consistent with the understanding value of the object shape speed of the object j.
The first term in the second formula is used for enabling the understanding value of the object shape direction of the object i to be consistent with the understanding value of the object shape direction of the object j, and the second term is used for enabling the understanding value of the object shape angular velocity of the object i to be consistent with the understanding value of the object shape angular velocity of the object j.
At the initial time, the agent understands its own position as the position of the target shape.
At the initial time, the understanding value of the object shape direction by the agent can be random or preset.
In the present invention, communication between agents is bi-directional.
A value of less than 1 allows consistency negotiations about the orientation of the target shape to be achieved in a limited time, which is of great importance for speeding up the negotiation process.
In other embodiments takes a value of 1.
The target shape refers to the formation shape of all agents after being mapped to the physical space by the desired formation map.
Optionally, the calculation formula of the graph entry speed command is:
；
Wherein is a graph entry speed command of the agent i, k 1 is a positive control gain constant,/> is a grid closest to the center of the agent i,/> is a grid/> gray value in a gray scale map corresponding to the agent i,/> is a position in physical space of one grid having a gray scale value closest to a gray scale value of a target area in a set area (for example, in a matrix area of 3*3) centered on the grid/> in the gray scale map corresponding to the agent i, and/> is a position in physical space of the agent i.
For example, the graphics entry speed command causes the agent to move toward the target area in the direction in which the gray value decreases.
Optionally, the calculation formula of the graph exploration speed instruction is:
；
Wherein is a graphic search speed instruction of an agent i,/> is a position of the agent i in a physical space,/> is a position of a grid/> in the physical space,/> is a perceived radius of the agent i,/> is a set of grids representing a target area in a gray scale map corresponding to the agent i,/> is a grid occupied by any agent in the gray scale map corresponding to the agent i,/> is a set of grids representing the target area within the perceived radius of the agent i in the gray scale map corresponding to the agent i,/> is a positive control gain constant,/> is a weight function, and/> is a non-negative function, satisfying: ,/> Is a piecewise continuous function and satisfies/> .
For example, the weight function is calculated as
。
When the intelligent agent is at the edge of the corresponding target area and does not enter the target area, the graphic exploration speed instruction pulls the intelligent agent into the target area; and after the intelligent agent enters the target area, the graph exploration speed instruction can push the intelligent agent to explore the graph area which is not occupied by other intelligent agents, so that the multi-intelligent agent formation uniformly covers the target graph.
Optionally, the calculation formula of the interaction speed instruction is:
；
Wherein is an interaction speed instruction of the entity i,/> is a control gain constant of a positive value,/> is a set of neighbor entities of the entity i, o i is a set of obstacle points within a perception radius of the entity i,/> is a position of the entity i in a physical space,/> is a position of the entity or the obstacle point j in the physical space,/> is a speed of the entity i,/> is a speed of the entity j, is a weight function, and monotonically decreases in a range from 0 to an expected distance of the entity.
The first term of the equation is a repulsive velocity that pushes agent i away from the surrounding environment to avoid collisions. The second term aims at keeping the speed of agent i consistent with the speed of the surrounding agents. The interaction speed instruction is helpful to reduce the probability of collision between agents and helps to realize the final stabilization of multi-agent formation.
When the distance between the agents is desired to be as small as possible, the desired distance may be a collision avoidance distance between the agents. The expected distance may also be greater than the collision avoidance distance.
Optionally, the calculation formula of the weight function is:
；
optionally, the method further comprises the step of task allocation:
Each agent performs policy updates through the following iterative steps to complete task allocation. The information stored by each agent , and also the information that needs to be updated for each iteration, is a 4-metadata set: . Where/> is the task allocation policy currently considered by agent/> , in particular is a mapping from agent set/> to task set/> , in particular/> if agent/> is allocated to perform task/> (in particular/> for empty tasks, i.e. not performing tasks) in allocation policy/> ; the/> is a satisfaction criterion indicating whether the agent/> is satisfied with the allocation policy/> , if satisfied, indicating that the agent/> is not willing to change its selected task in the allocation policy/> , otherwise , indicating that the agent/> is not satisfied with the current allocation; the/> represents the number of iterations of agent/> ; Representing a timestamp, is a uniform random variable that is randomly generated (i.e., a random timestamp) whenever an agent/> updates the policy/> .
Specifically, each agent performs policy updates by iterating the steps of:
(1) Initially, the agent considers that all agents perform an empty task, i.e./> , is an agent set; the initial number of iterations per agent/> /> ; the initial timestamp s i for each agent/> is randomly generated, i.e. > , where/> represents the random number in the generation [0,1] interval; initial satisfaction criteria per agent/> /> ; and (2) rotating.
(2) For agent , if satisfy criterion/> , go to (3); otherwise, turning to (4).
(3) The agent selects, based on the currently considered allocation policy/> , a task/> that maximizes the current individual benefit of the agent/> itself, i.e., task/> satisfies/> =/>, where/> represents the set of all agents that are considered to perform task/> by policy/> , and/> represents the number of elements in set/> ; agent/> updates its own considered allocation policy/> so that/> ; the number of iterations of agent/> /> ; satisfaction criteria of agent/> /> ; and (4) rotating.
(4) The agent interacts with neighbor agent/> , where/> represents the neighbor set of agent/> , i.e., other set of agents that can communicate bi-directionally within/> communication range. Specifically, agent/> broadcasts its current information to all neighbor agents/> , and M i=/> receives current information from neighbor/> , thereby obtaining information of allocation policy, iteration number, time stamp, satisfaction status, etc. considered by neighbor agents; after receiving the information of all neighbor agents, the agent/> selects the agent corresponding to the information with the largest iteration number/> from the set formed by all the information as the authoritative agent, and if a plurality of agents with the largest iteration number are provided, the agent with the largest iteration number s k is selected as the authoritative agent by comparing the time stamp, and the selected authoritative agent is/> ; if agent/> is not itself an authoritative agent, i.e. > , replacing all information of agent/> , i.e. > , with all information of authoritative agent, and then updating satisfactory state , proceeding to (2); if agent/> is itself exactly an authoritative agent, i.e. > , then the information of agent/> is unchanged, proceeding to (5).
(5) If the satisfaction status/> of the agent and the satisfaction status information of all neighbors/> received by the agent are all 1, the agent/> terminates the iteration, outputs the allocation policy/> , and the agent/> executes according to the currently considered allocation policy/> ; otherwise, go to (2).
The method can realize stability after finite step iteration, namely, the allocation strategy considered by each agent can be agreed, and each agent is satisfied with the current state under the allocation strategy. Thus, the task allocation policy can be obtained by the above algorithm.
The timestamp initial value is not or can be set by default, so long as all agents are ensured to be inconsistent with each other. When the timestamp initial values are randomly generated, the timestamp initial values of the two agents are the same as each other and are small probability events which can be ignored.
Wherein the benefit of an allocation policy may be defined by the sum of the individual benefits of all agents under the allocation policy.
And if agents and/ tasks are arranged, task allocation is carried out by adopting a reasonable algorithm rule. The notation represents a global set of agents, where/> represents agent i,/> ; represents a global set of tasks, where/> represents task j,/> ,/> represents an empty task, i.e., agent is currently not executing a task.
Individual benefit/> of agent is defined, which is a function of the task that agent i is assigned to and the total agent number/> to perform that task. The/> represents the individual benefit of agent/> in performing task t j with p-1 peers. Further, for a formation task of a multi-graph configuration, defining individual benefits as:
；
Wherein is an agent,/> is a task selected by/> , and/> represents the number of peers (including themselves) that perform task t j together with/> ; the position of agent/> is denoted by/> , and the position of task t j is denoted by/> ;
Representing the maximum distance between the agent performing task t j and task t j; the weight parameter is/(), and is generally 0.1-0.5; n tj represents the minimum number of agents required for task t j calculated as/> , where/> represents the area covered by task t j in physical space and/> represents the take-off integer.
The design of this individual utility function enables the population benefit of task t j to be exactly maximized when the number of agents for task t j is chosen to be exactly n tj. Therefore, the task allocation based on the benefit function can make the number of agents allocated to the task t j approach n tj, which also meets the practical requirement. Note that the design of the benefit function is not unique and can be adjusted according to actual scene requirements. For any task , agent/> , for any two positive integers and satisfying/> , there must be/> .
The step of task allocation may be performed before the agent performs the formation task.
Through the distributed asynchronous algorithm, each agent can obtain the same allocation strategy, and the allocation strategy is Nash stable, namely, if any agent changes own task execution selection, the benefit of the agent cannot become larger.
Based on the same inventive concept, the present invention also provides a program product that performs the aforementioned multi-agent formation control method of the multi-graphic configuration at runtime.
Based on the same inventive concept, referring to fig. 2, the present invention also provides an agent including a memory and a processor, the memory storing a program, the processor running the program to perform the aforementioned multi-agent formation control method of the multi-graphic configuration.
The embodiments of the present invention are described in a progressive manner, and the same and similar parts of the embodiments are all referred to each other, and each embodiment is mainly described in the differences from the other embodiments.
The scope of the present invention is not limited to the above-described embodiments, and it is apparent that various modifications and variations can be made to the present invention by those skilled in the art without departing from the scope and spirit of the invention. It is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. A multi-agent formation control method of a multi-graphic configuration, comprising:
Determining a desired formation map, a plurality of gray maps corresponding to the desired formation map and tasks allocated to the intelligent agent;
according to the understanding values of the intelligent agents and the neighbor intelligent agents on the positions of the expected formation diagrams in the physical space, the understanding values of the intelligent agents on the positions of the expected formation diagrams in the physical space are updated, so that the understanding values of all the intelligent agents on the positions of the expected formation diagrams in the physical space tend to be consistent;
Controlling the motion state of the intelligent agent according to the graph entering speed command, the graph exploring speed command and the interaction speed command;
The method comprises the steps that a gray maximum value or a gray minimum value in an expected formation graph represents a target area, the target area is connected into a plurality of sub-images separated from each other, the sub-images are communicated with each other, the plurality of gray images are in one-to-one correspondence with the plurality of sub-images, each gray image is divided into a target area, a transition area and a non-target area, the coordinates and the gray values of grids in the target area are the same as those of the grids in the expected formation graph, the transition area is close to the target area and smoothly transits along the direction far away from the target area, the non-target area is close to the boundary of the transition area far away from the target area and the gray value is the gray minimum value or the gray maximum value different from the gray value of the target area, and the shapes and the sizes of the grids in the sub-images are equal to those of the grids in the expected formation graph;
Wherein each task corresponds to a sub-graph;
The graphic entry speed instruction is determined according to the corresponding gray level graph and is used for driving the intelligent agent to move from outside the target area to the target area;
the graphic exploration speed instruction is determined according to the corresponding gray level diagram and is used for driving the intelligent agent to enter the target area from the outer side edge of the target area, and further searching and occupying grids which are not occupied by other intelligent agents in the target area;
Wherein the interaction speed command is used for avoiding collision and driving the speed of the intelligent agent to be consistent with the speed of surrounding intelligent agents.
2. The method of claim 1, wherein the graphic entry speed command is calculated as:
；
Wherein is a graph entry speed command of the agent i, k 1 is a positive control gain constant,/> is a grid closest to the center of the agent i,/> is a grid/> gray value in a gray scale map corresponding to the agent i,/> is a position in physical space of one grid closest to a gray scale value in a target area in a set area centered on the grid/> in the gray scale map corresponding to the agent i, and/> is a position in physical space of the agent i.
3. The method of claim 1, wherein the graphic exploration rate instruction is calculated by the formula:
；
Wherein is a graph search speed instruction of the entity i,/> is a position of the entity i in the physical space,/> is a position of the grid in the physical space,/> is a perceived radius of the entity i,/> is a set of grids representing the target area in the gray map corresponding to the entity i,/> is a grid occupied by any entity in the gray map corresponding to the entity i,/> is a set of grids representing the target area within the perceived radius of the entity i in the gray map corresponding to the entity i,/> is a positive control gain constant,/> is a weight function,/> is a non-negative function, satisfying: ,/> Is a piecewise continuous function and satisfies: and/> .
4. The method of claim 1, wherein the interaction speed command is calculated as:
；
Wherein is an interaction speed instruction of the entity i,/> is a control gain constant of a positive value,/> is a set of neighbor entities of the entity i, o i is a set of obstacle points within a perception radius of the entity i,/> is a position of the entity i in a physical space, is a position of the entity or the obstacle point j in the physical space,/> is a speed of the entity i,/> is a speed of the entity j,/> is a weight function, and monotonically decreases in a range from 0 to an expected distance of the entity.
5. The method of claim 4, wherein the weight function is calculated as:
；
Wherein is the expected distance.
6. The method of claim 1, wherein the intelligibility of the orientation of the target shape by the agent itself is calculated according to the following formula:
；
；
Wherein is an understanding value of the speed of the desired formation graph in the physical space by the entity i,/> is an understanding value of the speed of the desired formation graph in the physical space by the entity j,/> and/> , both of which are constant gains,/> is a set of neighbor entities of the entity i,/> is a sign function,/> is a 2-norm calculation symbol,/> is an understanding value of the position of the desired formation graph in the physical space by the entity i, and/> is an understanding value of the position of the desired formation graph in the physical space by the entity j;
Where c 2 is a positive constant gain, is the understanding value of agent i to the direction of the desired formation in physical space, and/> is the understanding value of agent j to the direction of the desired formation in physical space.
7. The method of claim 1, further comprising the step of task allocation:
(1) The initial state judges that all the agents execute the empty task, the initial iteration times are 0, the initial time stamp is different from the initial time stamp of the other agents, and the initial satisfaction degree is judged to be unsatisfied;
(2) If the satisfaction degree is judged to be unsatisfactory, the process goes to (3), otherwise, the process goes to (4);
(3) Based on the distribution strategy generated by the intelligent body, selecting a task which maximizes the individual benefit of the intelligent body, and updating the distribution strategy and the iteration times of the intelligent body, so that the satisfaction degree is judged to be satisfactory;
(4) The method comprises the steps of (1) judging interaction allocation strategies with neighbor intelligent agents, iteration times, time stamps and self satisfaction, selecting the intelligent agent with the largest iteration times from the self and the neighbor intelligent agents of the self as an authoritative intelligent agent, selecting the intelligent agent with the largest time stamp from the authoritative intelligent agent if the number of the intelligent agent with the largest iteration times is a plurality of intelligent agents, if the intelligent agent with the largest time stamp is the authoritative intelligent agent, judging the self allocation strategies, the iteration times, the time stamps and the self satisfaction without change, and turning to (5), otherwise, assigning the self allocation strategies, the iteration times, the time stamps and the self satisfaction by using the allocation strategies, the iteration times, the time stamps and the self satisfaction of the authoritative intelligent agent;
(5) If satisfaction degree judgment of the intelligent agent and all the neighbor intelligent agents is satisfied, the intelligent agent stops iteration, otherwise, the process goes to (2).
8. The method of claim 7, wherein the individual benefit calculation formula is as follows:
；
Representing individual benefits of agent/> in performing task t j with p-1 peers,/> representing the location of agent/> ,/> representing the location of task t j, d max representing the maximum distance between the agent performing task t j and task t j,/> being a weight parameter, n tj representing the minimum number of agents required for task t j.
9. A program product, characterized in that it performs, at run-time, the multi-agent formation control method of the multi-graphic configuration according to any one of claims 1 to 8.
10. An agent comprising a memory and a processor, the memory storing a program that is executed by the processor to perform the multi-agent formation control method of the multi-graphic configuration according to any one of claims 1 to 8.
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