CN116540736A - Formation control method based on man-machine interaction second-order nonlinear multi-agent system - Google Patents
Formation control method based on man-machine interaction second-order nonlinear multi-agent system Download PDFInfo
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Abstract
The invention discloses a formation control method based on a man-machine interaction second-order nonlinear multi-agent system, which belongs to the field of intelligent control and comprises the following steps: constructing a mathematical model of the multi-agent system and the virtual leader, so as to facilitate subsequent deduction; adding human intervention, agents are classified into two categories in the system: a human-controlled intelligent agent and an autonomous intelligent agent; introducing a new multi-agent system model through the classification to obtain an error system; constructing a proper functional function, and obtaining a criterion of system stability by utilizing a Lyapunov stability theory; and the state feedback controller is utilized to enable the error of the multi-intelligent system based on human-computer interaction to be 0, so that the system realizes expected formation. According to the invention, the situation that the multi-agent system easily makes wrong decisions or even loses control in an unknown and complex environment is considered, and human intervention is added in the formation control of the multi-agent system, so that the error rate of the system is reduced, and the multi-agent system can reach the expected formation.
Description
Technical Field
The invention belongs to the technical field of man-machine interaction, and particularly relates to a formation control method based on a man-machine interaction second-order nonlinear multi-agent system.
Background
The multi-agent system is composed of a plurality of independent agents and is a typical complex network; it is well known that a single agent is difficult to accomplish some complex or large tasks, but multiple agents can more effectively solve these problems through collaboration; in recent years, multi-agent systems have been widely used in various fields such as unmanned aerial vehicles, ground mobile robots, unmanned water-surface vessels, and the like; thus, many researchers are focusing on the problem of cooperative control of multi-agent systems, including aggregation, convergence, coherence, formation control, etc., and have achieved a number of important results.
Formation control is one of important research directions of cooperative control, and is widely focused on application in the fields of monitoring, military training, rescue and the like; to date, a number of results have been reported regarding multi-agent system formation control; for example, there is a class of linear complex-valued multi-agent systems in the prior art that have designed an event-triggered control protocol to achieve the desired formation; the affine formation control problem of a second-order nonlinear multi-agent system is solved by adopting a PI control method in the prior art.
According to the current research results about multi-agent system formation control, researchers do not discuss human intervention; however, in unknown and complex operating environments, multi-intelligent systems are prone to making erroneous decisions and even losing control; human intervention is therefore critical for the coordinated control of multi-agent systems; to date, some researchers have primarily studied the problem of collaborative control of multi-agent systems based on human-computer interaction and have achieved some meaningful research results, but the problem of multi-agent system formation control for intervention by joining people has not been considered so far.
Disclosure of Invention
The embodiment of the invention aims to provide a formation control method based on a man-machine interaction second-order nonlinear multi-agent system, aiming at solving the problem that the formation control problem of the multi-agent system for intervention of a joining person has not been considered so far.
The embodiment of the invention is realized in such a way that a formation control method based on a man-machine interaction second-order nonlinear multi-agent system comprises the following steps:
constructing a multi-agent system and a virtual leader model;
human intervention is added to part of the intelligent agents;
introducing a new multi-agent system model to obtain an error system;
constructing a corresponding Lyapunov function to obtain a system formation realization condition;
a multi-agent system based on human-machine interaction achieves the desired formation.
A formation control method based on a man-machine interaction second-order nonlinear multi-agent system comprises the following steps:
step 1: constructing a mathematical model of a second-order nonlinear multi-agent system, wherein the second-order nonlinear multi-agent system comprises a plurality of agents, the number is d=1, 2, the number is N, each agent can obtain the position information of the adjacent agents, the interaction of the information is symmetrical, and a single agent model in the multi-agent system is as follows:
wherein the method comprises the steps ofAnd->Respectively representing a position vector, a velocity vector and a control input vector of the agent, t being a time variable,/->Representing the nonlinear internal dynamics of the agent and satisfying the following inequality:
|φ(t,a 1 ,a 2 )-φ(t,a 3 ,a 4 )|≤ρ 1 |a 1 -a 3 |+ρ 2 |a 2 -a 4 |
for any oneWherein ρ is 1 And ρ 2 Is a positive constant.
To obtain the desired result, the virtual leader is selected as follows:
wherein the method comprises the steps ofAnd->Representing the position vector and the velocity vector of the virtual leader, respectively.
For any given initial state, a multi-intelligent system based on human-computer interaction is said to achieve the desired formation if the following equality relationship holds:
lim t→+∞ ||w d (t)-w * (t)||=0,
where d=1, 2,..,is the desired relative position between agent d and the virtual leader.
Step 2: for the N agents under study, human intervention is added to some agents, considering that agents are prone to making erroneous decisions and even losing control in unknown and complex environments. Agents are therefore classified into two classes in the system: a human-controlled agent and an autonomous agent. The following models can be obtained:
wherein X represents a set of human controlled agents, while other agents are not subject to human intervention.
For convenience, for v d (t) separatingClass:
further, the construction of a single agent model in a new multi-agent system is as follows:
wherein c d Representing human control constant, c d =1 (d e X) indicates that the agent is controlled by the person,indicating that the agent is not subject to human intervention.
The model of the person considered by the present invention is represented by the following linear differential equation:
wherein d is E X,and->Representing the status of the person, the input of the person and the output of the person, respectively; />And->Is a known constant matrix. For convenience of derivation, in->In this case, the serial number of the person (dummy person) who controls the agent is set to d.
Step 3: the control protocol is designed as follows in combination with the human control input and the autonomous agent control input:
wherein the method comprises the steps ofIs constant (I)>For the communication weight matrix between the agents, if there is communication between the agent d and the agent q, then +.>Otherwise-> Furthermore, the->
Step 4: definition of the definitionAnd->The error system can be expressed as:
wherein,,
step 5: multi-intelligent system based on man-machine interaction realizes expected formation if positive definite matrix existsSo that the following conditions are satisfied:
wherein the method comprises the steps of
For the error system (1), the following Lyapunov function is constructed:
wherein,,
can obtain the derivative of the above type
Combining inequality techniques with (2), V (t) tends to be 0, further resulting inTrend towards 0; thus, the multi-agent system based on human-machine interaction achieves the desired formation under the control protocol.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a novel formation control method based on a man-machine interaction second-order nonlinear multi-agent system; considering that the multi-agent system is easy to make wrong decisions and even lose control in an unknown and complex environment, the invention adds human intervention in the formation control of the multi-agent system for the first time, reduces the error rate of the system and improves the stability of the system; for each agent, only the position and speed information of the agent adjacent to the agent is needed to realize formation control. From an implementation point of view, the invention requires fewer computing resources and the required control amount is easier to obtain; compared with the traditional formation control protocol, the control protocol combines the control input of the human-controlled intelligent agent and the autonomous intelligent agent, and effectively solves the problem of unstable whole system caused by the error of the autonomous intelligent agent; the formation control method based on the man-machine interaction multi-agent system is applicable to any practical system modeled by the mathematical model of the single agent considered by the invention, and has wide application range.
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FIG. 1 is a flow chart of a multi-agent system formation control based on human-machine interaction;
FIG. 2 is a communication topology of a multi-agent system;
fig. 3 and 4 are analysis diagrams of simulation results of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
It will be understood that the terms "first," "second," and the like, as used herein, may be used to describe various elements, but these elements are not limited by these terms unless otherwise specified. These terms are only used to distinguish one element from another element. For example, a first xx script may be referred to as a second xx script, and similarly, a second xx script may be referred to as a first xx script, without departing from the scope of the present application.
As shown in fig. 1, step 1: the construction of a single agent model in a second-order nonlinear multi-agent system is as follows:
wherein the method comprises the steps ofAnd->Respectively representing a position vector, a velocity vector and a control input vector of the agent, t being a time variable,/->Representing the nonlinear internal dynamics of the agent and satisfying the following inequality:
|φ(t,a 1 ,a 2 )-φ(t,a 3 ,a 4 )|≤ρ 1 |a 1 -a 3 |+ρ 2 |a 2 -a 4 |
for any oneWherein ρ is 1 And ρ 2 Is a positive constant.
To obtain the desired result, the virtual leader is selected as follows:
wherein the method comprises the steps ofAnd->Representing the position vector and the velocity vector of the virtual leader, respectively.
For any given initial state, a multi-intelligent system based on human-computer interaction is said to achieve the desired formation if the following equality relationship holds:
lim t→+∞ ||w d (t)-w * (t)||=0,
where d=1, 2,..,is the desired relative position between agent d and the virtual leader.
Step 2: for the N agents under study, human intervention is added to some agents, considering that agents are prone to making erroneous decisions and even losing control in unknown and complex environments. Agents are therefore classified into two classes in the system: a human-controlled agent and an autonomous agent. The following models can be obtained:
wherein X represents a set of human controlled agents, while other agents are not subject to human intervention.
For convenience, for v d (t) classifying:
further, the construction of a single agent model in a new multi-agent system is as follows:
wherein c d Representing human control constant, c d =1 (d e X) indicates that the agent is controlled by the person,indicating that the agent is not subject to human intervention.
The model of the person considered by the present invention is represented by the following linear differential equation:
wherein d is E X,and->Representing the status of the person, the input of the person and the output of the person, respectively; />And->Is a known constant matrix; for convenience of derivation, in->In this case, the serial number of the person (dummy person) who controls the agent is set to d.
Step 3: the control protocol is as follows, combining the control input of the person and the control input of the autonomous agent:
wherein the method comprises the steps ofIs constant (I)>For the communication weight matrix between the agents, if there is communication between the agent d and the agent q, then +.>Otherwise-> Furthermore, the->
Step 4: definition of the definitionAnd->The error system can be expressed as:
wherein,,
step 5: multi-intelligent system based on man-machine interaction realizes expected formation if positive definite matrix existsSo that the following conditions are satisfied:
wherein the method comprises the steps of
For the error system (1), the following Lyapunov function is constructed:
wherein the method comprises the steps of
Can obtain the derivative of the above type
Combining inequality techniques with (2), V (t) tends to be 0, further resulting inTrend towards 0; thus, the multi-agent system based on human-machine interaction achieves the desired formation under the control protocol.
Step 6: selecting an example for simulation verification;
selectingClearly, it is easy to verify that φ (t,. Cndot.) satisfies the following inequality:
|φ(t,a 1 ,a 2 )-φ(t,a 3 ,a 4 )|≤2|a 1 -a 3 |+0.4|a 2 -a 4 |
for any oneAssuming that agents 1,4,5 are under human control, x= {1,4,5}.
Selecting:
B=diag(3.5,8.6,7.6,3.1,3.6),D 1 =--0.1,D 2 =2.25,D 3 =1,D 4 =2.5,with the MATLAB YALMIP Toolbox tool, z= 0.1275 can be found so that (2) holds. Thus, the multi-agent system can achieve a desired formation.
The initial state of the intelligent agent is as follows:
p 1 =[0.6,0.4] T ,p 2 =[0.83,0.3] T ,p 3 =[0.6,0.5] T ,p 4 =[0.5,0.5] T ,p 5 =[0.35,0.3] T 。
the initial state of the selected person is as follows:
the relative distance between each agent and the virtual leader is defined as:
fig. 3 and 4 depict the process of the position and velocity of an agent over time, respectively. As can be seen from fig. 3, the position of the agent gradually tends to be in the form of a design with time. As can be seen from fig. 4, the velocity of the agent eventually tends to be the same over time.
It should be understood that, although the steps in the flowcharts of the embodiments of the present invention are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in various embodiments may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of the sub-steps or stages of other steps or other steps.
Those skilled in the art will appreciate that all or part of the processes in the methods of the above embodiments may be implemented by a computer program for instructing relevant hardware, where the program may be stored in a non-volatile computer readable storage medium, and where the program, when executed, may include processes in the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing examples illustrate only a few embodiments of the invention and are described in detail herein without thereby limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. The formation control method based on the man-machine interaction second-order nonlinear multi-agent system is characterized by comprising the following steps of:
constructing a multi-agent system and a virtual leader model;
human intervention is added to part of the intelligent agents;
introducing a new multi-agent system model to obtain an error system;
constructing a corresponding Lyapunov function to obtain a system formation realization condition;
a multi-agent system based on human-machine interaction achieves the desired formation.
2. The method for controlling formation based on a human-computer interaction second-order nonlinear multi-agent system according to claim 1, wherein the step of constructing a multi-agent system and a virtual leader model comprises constructing a second-order multi-agent system mathematical model and a virtual leader model in the multi-agent system, wherein the second-order multi-agent system mathematical model is
Wherein the method comprises the steps ofAnd->Respectively representing a position vector, a velocity vector and a control input vector of the agent, t being a time variable,/->Representing the nonlinear internal dynamics of the agent.
3. The method for controlling formation based on a man-machine interaction second-order nonlinear multi-agent system according to claim 2, wherein the virtual leader model in the multi-agent system is:
wherein the method comprises the steps ofAnd->Representing the position vector and the velocity vector of the virtual leader, respectively.
4. The method of forming a team based on a human-machine interactive second order nonlinear multi-agent system according to claim 1, wherein the step of constructing a multi-agent system and a virtual leader model further comprises constructing a new second order multi-agent system mathematical model:
wherein c d Representing human control constant, c d =1 (d e X) indicates that the agent is controlled by the person,indicating that the agent is not subject to human intervention.
5. The method for controlling formation based on a man-machine interaction second-order nonlinear multi-agent system according to claim 1, wherein the human intervention is represented by a linear differential equation:
wherein d is E X,and->Representing the status of the person, the input of the person and the output of the person, respectively; />And->Is a known constant matrix.
6. The method for controlling formation based on a man-machine interaction second-order nonlinear multi-agent system according to claim 5, wherein for human intervention, the control protocol is as follows in combination with human control input and autonomous agent control input:
wherein the method comprises the steps ofIs constant (I)>For the communication weight matrix between the agents, if there is communication between the agent d and the agent q, then +.>Otherwise-> Furthermore, the->
7. The method for controlling formation based on man-machine interaction second-order nonlinear multi-agent system according to claim 1, wherein when determining the systematic error, definingAndthen the systematic error is:
wherein,,
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