CN114371625A - Multi-agent formation control method with variable node number - Google Patents

Multi-agent formation control method with variable node number Download PDF

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CN114371625A
CN114371625A CN202210025713.8A CN202210025713A CN114371625A CN 114371625 A CN114371625 A CN 114371625A CN 202210025713 A CN202210025713 A CN 202210025713A CN 114371625 A CN114371625 A CN 114371625A
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CN114371625B (en
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高亚斌
李清华
姚蔚然
张之津
左稳
吴立刚
孙光辉
刘健行
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Harbin Institute of Technology
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Abstract

A multi-agent formation control method with variable node number belongs to the technical field of agent formation. The invention aims at the problem that the robustness of a formation method is poor when the number of nodes of multi-agent formation changes and communication abnormity occurs. Firstly, establishing a kinematic system model of an intelligent body; initializing a directed communication topological graph; setting a dynamic change equation of a virtual navigator, and determining an equivalent control term by an integral sliding mode variable of an intelligent agent node; designing an intelligent controller, and setting a speed damping gain and a communication weight; fourthly, realizing multi-agent formation control by adopting a controller; fifthly, when the number of the nodes changes, executing a sixth step; sixthly, verifying the feasibility of the current speed damping gain through a linear matrix inequality, if the feasibility exists, updating the position and the speed of the directed communication topological graph and the virtual pilot, and returning to the second step; otherwise, the speed damping gain is replaced and the speed damping gain returns to six. The invention realizes the formation control of the multi-agent system under the condition of node reduction or node addition.

Description

Multi-agent formation control method with variable node number
Technical Field
The invention relates to a multi-agent formation control method with variable node number, belonging to the technical field of agent formation.
Background
In recent years, integration and development of sensor technology, wireless communication technology and intelligent control technology have led to wide application and remarkable success in military and civil fields of multi-agent systems represented by unmanned vehicles and unmanned aerial vehicles. With the continuous improvement of the requirements on the performance of the multi-agent system, the multi-agent system such as a ground unmanned vehicle and a space unmanned aerial vehicle is difficult to avoid the influence of the external environment when performing diversified tasks such as formation in a complex environment, so that the multi-agent control system is required to have higher robustness, reliability and other performances. Therefore, robust control of multiple intelligent agents is a key technology for multiple intelligent agents such as unmanned aerial vehicles and unmanned vehicles to perform tasks in a complex environment in the future, and especially, a multi-agent formation control technology is a research hotspot in the field of multiple intelligent agents.
It is worth noting that as multi-agent nodes increase and the complexity of the formation control task increases, the chances that they will be exposed and subject to network and physical attacks increase, which greatly impacts the robust control of multi-agent formation. For example, when unmanned aerial vehicle formation communicated through a wireless network is attacked by GPS spoofing, denial of service attack, or direct physical attack, some unmanned aerial vehicles may receive wrong information or abnormal communication, or even lose contact, so that it is difficult to ensure formation by using a conventional unmanned aerial vehicle control method.
Therefore, aiming at the communication abnormal phenomenon brought by the complex environment, the multi-agent formation needs an effective robust control method to ensure the multi-agent to safely operate and complete the task.
Disclosure of Invention
The invention provides a multi-agent formation control method with variable node number, aiming at the problems that the existing formation method has poor robustness and can not ensure the completion of tasks when the node number of multi-agent formation changes and communication abnormity occurs.
The invention relates to a multi-agent formation control method with variable node number, which comprises the following steps,
step one, establishing a kinematic system model of each agent according to the position and speed variation of nodes of the agents; and initializing a directed communication topological graph;
setting a dynamic change equation of a virtual navigator, designing an integral sliding mode variable of each intelligent body node by combining a kinematic system model, and further determining an equivalent control item of sliding mode control;
designing a controller of the intelligent agent according to an equivalent control item of sliding mode control, and setting a speed damping gain in the controller and a communication weight between the intelligent agent node and a virtual pilot;
step four, realizing multi-agent formation control by adopting a controller;
step five, detecting the change of the number of nodes of the multi-agent in real time, and executing step six when the number of the nodes changes;
step six, verifying the feasibility of the current speed damping gain through a linear matrix inequality, and if the feasibility is feasible, executing step seven; otherwise, executing step eight;
step seven, updating the position and the speed of the directed communication topological graph and the virtual navigator, and returning to the step two;
and step eight, replacing the speed damping gain, and returning to the step six until the end.
According to the multi-agent formation control method with variable node number, in the first step, a kinematic system model of each agent is established as follows:
Figure BDA0003464524090000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003464524090000022
is the amount of change, x, in the location of the ith agent nodevi(t) is the speed of the ith agent node,
Figure BDA0003464524090000023
is the speed variation of the ith agent node, ui(t) is the control input of the ith agent node, fi(t) is the interference input quantity of the ith intelligent agent node, t is time, i is 1.
Figure BDA0003464524090000024
Is a real row vector of dimension m, where m represents the spatial dimension in which the multi-agent moves.
According to the multi-agent formation control method with variable node number, in the second step, the dynamic change equation of the virtual pilot is as follows:
Figure BDA0003464524090000025
in the formula (I), the compound is shown in the specification,
Figure BDA0003464524090000026
is the location variation, x, of the virtual navigator nodev0(t) is the velocity of the virtual pilot node,
Figure BDA0003464524090000027
is the velocity variation of the virtual navigator node, f0(t) is a function of the velocity variation for a given virtual navigator node;
Figure BDA0003464524090000028
according to the multi-agent formation control method with variable node number, in the second step, the integral sliding mode variables of each agent node are designed as follows:
Figure BDA0003464524090000029
in the formula si(t) is an integral sliding mode variable of the ith agent node, HiA given sliding mode surface matrix of the ith agent node;
Figure BDA0003464524090000031
and zi(t) is the intermediate variable:
Figure BDA0003464524090000032
xxi(t) is the location of the ith agent node,
Figure BDA0003464524090000033
xx0(t) is the position of the virtual pilot node,
Figure BDA0003464524090000034
hiis a vector from the ith agent node to the virtual pilot node;
Figure BDA0003464524090000035
is an equivalent control item of sliding mode control;
Figure BDA0003464524090000036
is zi(t) rate of change, zi(0) Is zi(t) an initial value of (t),
Figure BDA0003464524090000037
is composed of
Figure BDA0003464524090000038
Is set to the initial value of (a),
Figure BDA0003464524090000039
is composed of
Figure BDA00034645240900000310
Is started.
According to the multi-agent formation control method with variable node number, in the third step, according to the equivalent control item of sliding mode control, the controller of the agent is designed as follows:
Figure BDA00034645240900000311
in the formula
Figure BDA00034645240900000312
Is a switching control item of sliding mode control.
According to the multi-agent formation control method with variable node number, the method for setting the speed damping gain in the controller and the communication weight between the agent nodes and the virtual pilot in the third step comprises the following steps:
Figure BDA00034645240900000313
Figure BDA00034645240900000314
in the formula (I), the compound is shown in the specification,
Figure BDA00034645240900000315
for the adjacent point set of the ith agent node at the time t,
Figure BDA00034645240900000316
for the agent node v at time tiAnd agent adjacent node vjJ is the node viThe serial number of the adjacent node (i) is not equal to j; d (t) is an adjacent node vjTo agent node viCommunication delay of, KiIn order to gain in the damping of the velocity,
Figure BDA00034645240900000317
communication weights for the ith agent node and the virtual pilot;
η1、η2、η3、η4、j1、j2、j3and j4Are all controller design parameters, η1>0，η2>0，η3>0，η4>0；j1>1，0<j2<1，0<j4<1；
j3The values of (A) include:
Figure BDA00034645240900000318
according to the multi-agent formation control method with variable node number, the communication delay d (t) meets the following requirements: d is more than or equal to 0 and less than or equal to tM，dMThe maximum communication delay allowed.
According to the multi-agent formation control method with variable node number, the feasibility of the current speed damping gain verified through the linear matrix inequality in the sixth step comprises the following steps:
the linear matrix inequality is as follows:
Figure BDA0003464524090000041
wherein P, Q and Z are symmetric matrices to be solved:
P＝PT>0，Q＝QT>0，Z＝ZT>0；
c and E are block matrixes respectively.
According to the multi-agent formation control method with variable node number, the block matrixes C and E satisfy the following relational expression:
Figure BDA0003464524090000042
in the formula ImIs an m-order identity matrix, INIs an N-order identity matrix;
Figure BDA0003464524090000043
Figure BDA0003464524090000044
l is a Laplace matrix of the directed communication topological graph;
the laplace matrix L is:
L＝[Lij]N×N，
Figure BDA0003464524090000045
Lij＝-aij。
according to the multi-agent formation control method with variable node number, the directed communication topological graph G is as follows:
G＝(V,E,A)，
wherein V is a node set of the directed communication topological graph, E is an edge set of the directed communication topological graph, and A is the directed communication topological graph with a non-negative element aijA abutment moment ofijRepresenting an agent node viAnd agent node vjA connection weight between;
V＝{v1,v2,...,vN}，
Figure BDA0003464524090000046
A＝[aij]N×N；
agent node viSet of adjacent nodes NiComprises the following steps:
Ni＝{j∈V:(i,j)∈E}。
the invention has the beneficial effects that: the invention relates to a method for realizing formation or formation reconstruction of a multi-agent system when the number of nodes of a multi-agent system changes.
The method mainly considers the situation that nodes of multiple intelligent agents are reduced or newly added, takes a dynamic model of the multiple intelligent agents with positions and speeds as measurement as a control object, designs a multi-intelligent-agent formation control algorithm based on improved sliding mode control, solves the problem of formation control of a multi-intelligent-agent system under the situation that the nodes are reduced or newly added, and provides an effective distributed control method for formation control or formation reconstruction by taking the multiple intelligent agents such as unmanned vehicles, unmanned planes and the like as application backgrounds in practice. The control method of the invention has the following features and advantages: the method has adjustable parameters for adjusting the formation speed, provides a parameter solving basis for the controller, can realize the robustness of control disturbance, and can accommodate the phenomenon of node reduction or loss of connection of multiple intelligent agents and the requirement of node increase.
Drawings
FIG. 1 is a flow chart of a multi-agent formation control method with varying node numbers according to the present invention;
FIG. 2 is a diagram illustrating the effects of formation of agents when nodes are reduced in an exemplary embodiment;
FIG. 3 is a diagram illustrating the variation of the abscissa of the control quantity of each agent when the node is decreased in the exemplary embodiment;
FIG. 4 is a diagram illustrating a change in the ordinate of the control quantity of each agent when the node is decreased in the exemplary embodiment;
FIG. 5 is a schematic diagram illustrating changes in the abscissa of tracking errors of the positions of the agents when nodes are reduced in the embodiment;
FIG. 6 is a diagram illustrating changes in the ordinate of tracking error for each agent's location as nodes decrease in an exemplary embodiment;
FIG. 7 is a diagram illustrating changes in tracking error for each agent's velocity as nodes are reduced in an exemplary embodiment;
FIG. 8 is a diagram illustrating the formation effect of agents as nodes are added in the exemplary embodiment;
FIG. 9 is a diagram illustrating the change of control quantities of agents as nodes increase in the exemplary embodiment;
FIG. 10 is a diagram illustrating the variation of the vertical coordinates of the control variables of the agents as nodes increase in the exemplary embodiment;
FIG. 11 is a diagram illustrating changes in the abscissa of the tracking error of each agent's location as nodes increase in the exemplary embodiment;
FIG. 12 is a diagram illustrating changes in the ordinate of tracking error for each agent's location as nodes increase in an exemplary embodiment;
FIG. 13 is a diagram illustrating changes in tracking error of agent velocities as nodes increase in an exemplary embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
Detailed description of the inventionas shown in fig. 1, the present invention provides a method for controlling formation of multi-agent with variable node number, which comprises,
step one, establishing a kinematic system model of each agent according to the position and speed variation of nodes of the agents; and initializing a directed communication topological graph;
setting a dynamic change equation of a virtual navigator, designing an integral sliding mode variable of each intelligent body node by combining a kinematic system model, and further determining an equivalent control item of sliding mode control;
designing a controller of the intelligent agent according to an equivalent control item of sliding mode control, and setting a speed damping gain in the controller and a communication weight between the intelligent agent node and a virtual pilot;
step four, realizing multi-agent formation control by adopting a controller;
step five, detecting the change of the number of nodes of the multi-agent in real time, and executing step six when the number of the nodes changes;
step six, verifying the feasibility of the current speed damping gain through a linear matrix inequality, and if the feasibility is feasible, executing step seven; otherwise, executing step eight;
step seven, updating the position and the speed of the directed communication topological graph and the virtual navigator, and returning to the step two;
and step eight, replacing the speed damping gain, and returning to the step six until the end.
In the present embodiment, the construction of the multi-agent model having a variable number of nodes includes:
firstly, a multi-agent model under the condition of adding or reducing nodes is constructed. In actual use, when the communication environment is poor, communication between intelligent bodies such as unmanned vehicles may fail or be interrupted; on the other hand, the multi-agent system needs to add new nodes according to the situation, so the network topology of the multi-agent system changes accordingly. In general, the communication of any link changes, meaning that a new network topology is formed. Thus, the topology in this case is described as a time-varying or switching network topology, and the number of nodes is counted from the original N0Become N ═ N0±N1In which N is1The number of nodes to be newly added or reduced. The newly formed network topology graph is regarded as one of sub-graphs of a series of switching topology graphs, and therefore the problem is converted into multi-agent reconstruction formation control with time-varying communication topology.
Further, in step one, considering the actual position and speed variation of the multi-agent, the kinematic system model of each agent is established as follows:
Figure BDA0003464524090000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003464524090000062
is the amount of change, x, in the location of the ith agent nodevi(t) is the speed of the ith agent node,
Figure BDA0003464524090000063
is the speed variation of the ith agent node, ui(t) is the control input of the ith agent node, fi(t) is the interference input quantity of the ith intelligent agent node, t is time, i is 1.
Figure BDA0003464524090000071
Is a real row vector of dimension m, where m represents the spatial dimension in which the multi-agent moves.
Designing a formation controller based on improved integral sliding mode control:
in order to realize multi-agent formation control under the condition of node number change, a formation control mode based on a virtual pilot is adopted, namely N agents surround or follow the virtual pilot to form a formation. The virtual navigator serves as a virtual node, and a dynamic change equation of the virtual navigator is defined as follows:
Figure BDA0003464524090000072
in the formula (I), the compound is shown in the specification,
Figure BDA0003464524090000073
is the location variation, x, of the virtual navigator nodev0(t) is the velocity of the virtual pilot node,
Figure BDA0003464524090000074
is the velocity variation of the virtual navigator node, f0(t) is the speed variation function of a given virtual navigator node, i.e. the acceleration of the virtual navigator; therefore, the whole formation model forms a multi-intelligent model of an actual follower-virtual navigator, wherein the information of the virtual navigator is shared by each intelligent agent, and each intelligent agent can realize respective movement by acquiring the information of the virtual navigator and the information of the neighbor nodes so as to achieve the final formation purpose.
Figure BDA0003464524090000075
In order to describe the influence of node number change on formation control more accurately, a time-varying communication topology is considered in control design, and the control of each individual is designed into a distributed control law related to the number of neighbor nodes. According to the characteristics of quick response and good robustness of a control system, which can be realized by sliding mode control, the invention designs a distributed control law based on improved integral sliding mode control. For the ith agent, the integral sliding mode variables are designed as follows:
Figure BDA0003464524090000076
in the formula si(t) is an integral sliding mode variable of the ith agent node, HiA given sliding mode surface matrix of the ith agent node;
Figure BDA0003464524090000077
and zi(t) is the intermediate variable:
Figure BDA0003464524090000078
xxi(t) is the location of the ith agent node,
Figure BDA0003464524090000079
xx0(t) is the position of the virtual pilot node,
Figure BDA00034645240900000710
hiis a vector from the ith agent node to the virtual pilot node;
Figure BDA0003464524090000081
is an equivalent control item of sliding mode control;
Figure BDA0003464524090000082
is zi(t) rate of change, zi(0) Is zi(t) an initial value of (t),
Figure BDA0003464524090000083
is composed of
Figure BDA0003464524090000084
Is set to the initial value of (a),
Figure BDA0003464524090000085
is composed of
Figure BDA0003464524090000086
Is started.
Further, in step three, according to a multi-agent system model with a communication switching topology, and according to an equivalent control item of sliding mode control, aiming at the change of the number of nodes, a controller of the ith agent is designed as follows:
Figure BDA0003464524090000087
in the formula
Figure BDA0003464524090000088
Is a switching control item of sliding mode control.
Still further, the method for setting the velocity damping gain in the controller and the communication weight between the intelligent node and the virtual pilot in the third step comprises the following steps:
Figure BDA0003464524090000089
Figure BDA00034645240900000810
in the formula (I), the compound is shown in the specification,
Figure BDA00034645240900000811
for the adjacent point set of the ith agent node at the time t,
Figure BDA00034645240900000812
for the agent node v at time tiAnd agent adjacent node vjJ is the node viThe serial number of the adjacent node (i) is not equal to j; d (t) is an adjacent node vjTo agent node viCommunication delay of, KiFor velocity damping gain, Ki>0，
Figure BDA00034645240900000813
Is a preset velocity damping gain set;
Figure BDA00034645240900000814
communication weights for the ith agent node and the virtual pilot; when the ith agent contains virtual navigator information,
Figure BDA00034645240900000815
greater than 0; if not, then,
Figure BDA00034645240900000816
equal to 0.
In the handover control, si(t) is an integral sliding mode variable, eta, designed in the formula (3)1、η2、η3、η4、j1、j2、j3And j4Are all controller design parameters, η1>0，η2>0，η3>0，η4>0；j1>1，0<j2<1，0<j4<1；
j3The values of (A) include:
Figure BDA00034645240900000817
the communication delay d (t) satisfies: d is more than or equal to 0 and less than or equal to tM，
dMThe maximum communication delay allowed.
From the time-varying topological relationships between agents, Γ ═ G can be defined1,G2,...,GpThe is the set of all possible p directed topologies, where p ≧ 1. Then, the relationship between the time period corresponding to each directed graph and the directed graph is defined as a switching signal σ (t): [0, + ∞) → {1, 2. Therefore, at a certain moment t, the topological graph of the multiple agents is a directed fixed topological graph GσE Γ, and defining an adjacency matrix at time t as
Figure BDA0003464524090000091
Laplacian matrix is LσThe set of adjacent points of the node i is
Figure BDA0003464524090000092
Establishing a parameter solving basis of the controller:
the verification of the feasibility of the current velocity damping gain through a linear matrix inequality in the sixth step comprises the following steps:
the distributed integral sliding mode control law is as the formula (4), and formation of the considered multi-agent in limited time can be realized. Parameter matrix KiSet of (2)
Figure BDA0003464524090000093
The method can be obtained by solving and verifying the following linear matrix inequality:
Figure BDA0003464524090000094
wherein P, Q and Z are symmetric matrices to be solved:
P＝PT>0，Q＝QT>0，Z＝ZT>0；
c and E are block matrixes respectively.
The block matrixes C and E satisfy the following relational expression:
Figure BDA0003464524090000095
in the formula ImIs an m-order identity matrix, INIs an N-order identity matrix;
Figure BDA0003464524090000096
Figure BDA0003464524090000097
l is a Laplace matrix of the directed communication topological graph;
the laplacian matrix L is defined as:
L＝[Lij]N×N，
Figure BDA0003464524090000098
Lij＝-aij，i≠j。
aiming at a multi-agent system with a time-varying communication topology, a directed graph is used for defining and describing communication relations among agents, and a directed communication topological graph G is defined as follows:
G＝(V,E,A)，
wherein V is a node set of the directed communication topological graph, E is an edge set of the directed communication topological graph, and A is the directed communication topological graph with a non-negative element aijA abutment moment ofijRepresenting an agent node viAnd agent node vjA connection weight between; when a isijWhen 0, node viNode v is not acceptedjThe information to be transferred. When a isijWhen 1, node viCan receive node vjThe information to be transferred. When node v exists in graph GiSo that starting from this point any other point in the graph can be reached along the directed edge, then the graph G is said to contain a directed spanning tree and the node is said to be the root node.
V＝{v1,v2,...,vN}，
Figure BDA0003464524090000101
A＝[aij]N×N；
Agent node viSet of adjacent nodes NiComprises the following steps:
Ni＝{j∈V:(i,j)∈E}。
in summary, the method of the present invention is designed for the problem of formation reconfiguration under the situation of increasing or decreasing the number of nodes of the plurality of agents, and the formation reconfiguration and formation control algorithm of the formation designed by the method comprises the following steps:
initializing multi-agent formation information including communication topology G and each moving agent position x according to the constructed multi-agent model formula (1)xiAnd velocity xvi，i＝1,...,N；
Acquiring the position x of the target formation informationx0And velocity xv0Position and velocity in equation (2);
setting parameter K of controller formula (4) of each agentiAnd bi；
Updating and executing control according to the designed control law to realize formation control;
acquiring the formation of the multi-agent and detecting the node number change in real time, and if the change is changed, reducing or increasing N1And become N ═ N0±N1Continuing to execute the sixth step; otherwise, keeping the original control state unchanged;
sixthly, verifying the feasibility of new team shape reconstruction under the condition, verifying by using a formula (5), and if feasible, continuing to execute the step (c); otherwise, executing the step b;
seventhly, updating communication topology structure GσE Γ and new formation information position xx0And velocity xv0Repeating the second to the fifth steps.
If there are other controller parameters KiIf not used, the controller parameters are replaced by other controller parameters
Figure BDA0003464524090000102
Performing the step of (c); otherwise, the new formation is informed that the new formation can not be reconstructed or set untilAnd (6) ending.
The specific embodiment is as follows:
in order to verify and show the effectiveness of the formation control algorithm, the simulation verification of multi-agent formation control is carried out by taking a two-dimensional ground unmanned vehicle as a background, and the formation effects of the multi-agents under the conditions of reduction and addition of multi-agent nodes are respectively shown.
(1) Formation situations when multiple agents are in motion with reduced nodes
The simulation is initially provided with 6 intelligent agent nodes, the number of the nodes is reduced to 5 in the operation process, the system reconstructs a formation target after detecting the reduction of the nodes, and finally formation is realized. In the simulation process, before the nodes are reduced, the number of the multiple intelligent agents is N-N06, the corresponding communication topology Laplacian matrix is set as:
Figure BDA0003464524090000111
let the 6 th agent suddenly be detected to lose contact at a certain moment, i.e. the number of the multi-agents becomes N-N01-5, after the number of nodes is reduced by one, the corresponding communication topology Laplacian matrix becomes:
Figure BDA0003464524090000112
given each agent communication weight bi＝5，
Figure BDA0003464524090000113
Velocity damping gain KiIs arranged as
Figure BDA0003464524090000114
Velocity variation function (resistance) f of virtual pilot0(t) is 0, and the disturbance input amount (resistance) f of the followeri(t) is fi(t)＝0.01sin(0.1(xvi(t))), the virtual navigator initial position is set to xx0(0)＝[4.500 4.5981]TInitial velocity is set to xv0(0)＝[0 0]T. The initial positions of the follower nodes are respectively set as xx1(0)＝[1 0]T，xx2(0)＝[0.25 0.25]T，xx3(0)＝[0 1]T，xx4(0)＝[-1 0]T，xx5(0)＝[-0.25 -0.25]T，xx6(0)＝[0 -1]TThe initial speeds are all set to xvi(0)＝[0 0]T1., 6. The expected vectors of the nodes which do not reduce the front follower nodes to the pilot are respectively set as h1＝[-1.5 -2.5981]T，h2＝[1.5 -2.5981]T，h3＝[3 0]T，h4＝[1.5 2.5981]T，h5＝[-1.5 2.5981]T，h6＝[-3 0]TThe expected vectors of node reduction followed by follower node to leader are set to h respectively1＝[0 -3]T，h2＝[3 0]T，h3＝[3 3]T，h4＝[0 3]T，h5＝[-3 0]T，η1＝η2＝η3＝η4＝0.01001，j1＝2，j2＝0.5，j40.5, the maximum communication delay is set to dM0.12 s. According to the conditional expression (5), it is verified that these parameters satisfy the condition by calculation.
As shown in FIG. 2, the black dot dashed hexagon in the figure represents the initial position of the multi-agent node; the solid line hexagon adjacent to the hexagon represents that the nodes of the multi-agent reduce the formation of the instantaneous formation, and at the moment, the multi-agent is supposed to reduce one node; the dotted line pentagon immediately behind the point pentagon represents that the formation at the moment when the node reduction is detected, the formation of the multi-agent formation needs to be reconstructed at the moment, the reconstructed formation is a pentagon, namely, the uppermost solid line hexagon in the figure represents a regressive formation target; the dashed hexagons, which almost coincide with this hexagon, represent the actual formation of the multi-agent under the designed formation control laws. As shown in fig. 3 and fig. 4, the control component changes of the control quantity of each agent in the ordinate and abscissa directions when the node is reduced are shown, respectively, wherein the black line represents the change of the actual control quantity of the lost node itself. .
As in fig. 5 and 6, the black line indicates the change in tracking error of the position of the decoupled node itself; as in fig. 7, the black line indicates the actual speed change of the decoupled node itself. . Obviously, the 6 th intelligent agent node is not controlled by normal formation after loss of connection, the position is obviously deviated, and other intelligent agent nodes are still effectively controlled by formation.
(2) Formation situation of multi-agent when nodes increase during exercise:
simulation initial setting is N ═ N0Consider a node increase to N-N during operation, 6 nodes0And when 8 nodes are detected to be added, the system reconstructs a new target formation, and finally formation is realized. In the simulation process, a communication topology Laplacian matrix before the addition of the nodes is set as follows:
Figure BDA0003464524090000121
2 newly-added agent nodes are required to be arranged at a certain moment, and a corresponding communication topology Laplacian matrix is changed into:
Figure BDA0003464524090000131
in the initial stage, the adopted controller parameters are the same as the initial conditions and the control parameters of the multi-agent under the condition of reducing the nodes in the (1) th mode; setting the newly added 2 multi-agents as the 7 th and 8 th nodes respectively, and setting the corresponding initial condition as xx7(0)＝[0 0]T，xx8(0)＝[2 -1]T(ii) a The expected vectors of the follower and the virtual pilot after the node addition are respectively set as h1＝[-2 -2]T，h2＝[0 -6]T，h3＝[2 -2]T，h4＝[4 0]T，h5＝[2 2]T，h6＝[0 6]T，h7＝[-2 2]T，h8＝[-4 0]TI.e. to reconstruct the new target formation. In this case, the design is utilizedAnd (3) obtaining a formation control effect diagram of the multi-agent under the condition of node addition by the formation control law, as shown in fig. 6 to 9.
As in fig. 8, the black dot-dashed line indicates the initial position of each node in the formation; the hexagonal realization thereafter represents the shape of the node increasing instant formation, and simultaneously assumes that two nodes are newly added to the multi-agent at the moment; the dotted octagon adjacent to the dotted octagon represents an instant multi-intelligent formation when the node addition is completed; the solid line octagon represents a target formation reconstructed when a node is newly added; the dashed octagon that almost coincides with this target formation represents the actual formation of the multi-agent under the designed formation control laws. Therefore, the effective formation can be realized by utilizing the designed formation control aiming at the situation that the nodes are newly added by the multiple intelligent agents. The control components of the multi-agent in the node adding situation are shown in fig. 9 and 10, where the black lines in the figure indicate the control component changes of the 7 th and 8 th agents when the agents are added, respectively. .
As shown in fig. 11 and 12, during the operation of the multi-agent before and after adding two new nodes, the change components of the position tracking error change of each agent on the vertical axis and the horizontal axis are shown, wherein the black lines in the diagram respectively show the position tracking error change components of the two new multi-agents; fig. 13 shows the actual speed tracking error changes of each agent during the operation of the agents before and after the two new nodes are added, wherein the black lines in the graph represent the actual speed tracking error changes of the two new agents.
Through the verification of the specific embodiment, the multi-agent formation aiming at the node number change has a good control effect, and due to the introduction of the improved sliding mode control law, the multi-agent formation can realize rapid formation reconfiguration control at the same time.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (10)

1. A multi-agent formation control method with variable node number is characterized by comprising the following steps,
step one, establishing a kinematic system model of each agent according to the position and speed variation of nodes of the agents; and initializing a directed communication topological graph;
setting a dynamic change equation of a virtual navigator, designing an integral sliding mode variable of each intelligent body node by combining a kinematic system model, and further determining an equivalent control item of sliding mode control;
designing a controller of the intelligent agent according to an equivalent control item of sliding mode control, and setting a speed damping gain in the controller and a communication weight between the intelligent agent node and a virtual pilot;
step four, realizing multi-agent formation control by adopting a controller;
step five, detecting the change of the number of nodes of the multi-agent in real time, and executing step six when the number of the nodes changes;
step six, verifying the feasibility of the current speed damping gain through a linear matrix inequality, and if the feasibility is feasible, executing step seven; otherwise, executing step eight;
step seven, updating the position and the speed of the directed communication topological graph and the virtual navigator, and returning to the step two;
and step eight, replacing the speed damping gain, and returning to the step six until the end.
2. The method for multi-agent formation control of node count variation according to claim 1,
in the first step, a kinematic system model of each agent is established as follows:
Figure FDA0003464524080000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003464524080000012
is the amount of change, x, in the location of the ith agent nodevi(t) is the speed of the ith agent node,
Figure FDA0003464524080000013
is the speed variation of the ith agent node, ui(t) is the control input of the ith agent node, fi(t) is the interference input quantity of the ith intelligent agent node, t is time, i is 1.
Figure FDA0003464524080000014
Figure FDA0003464524080000015
Is a real row vector of dimension m, where m represents the spatial dimension in which the multi-agent moves.
3. The method for multi-agent formation control of node count variation according to claim 2,
in the second step, the dynamic change equation of the virtual pilot is as follows:
Figure FDA0003464524080000016
in the formula (I), the compound is shown in the specification,
Figure FDA0003464524080000017
is the location variation, x, of the virtual navigator nodev0(t) is the velocity of the virtual pilot node,
Figure FDA0003464524080000018
is the velocity variation of the virtual navigator node, f0(t) is a function of the velocity variation for a given virtual navigator node;
Figure FDA0003464524080000019
4. the method for multi-agent formation control of node count variation according to claim 3,
in the second step, the integral sliding mode variables of each intelligent agent node are designed as follows:
Figure FDA0003464524080000021
in the formula si(t) is an integral sliding mode variable of the ith agent node, HiA given sliding mode surface matrix of the ith agent node;
Figure FDA0003464524080000022
and zi(t) is the intermediate variable:
Figure FDA0003464524080000023
xxi(t) is the location of the ith agent node,
Figure FDA0003464524080000024
xx0(t) is the position of the virtual pilot node,
Figure FDA0003464524080000025
hiis a vector from the ith agent node to the virtual pilot node;
Figure FDA0003464524080000026
is an equivalent control item of sliding mode control;
Figure FDA0003464524080000027
is zi(t) rate of change, zi(0) Is zi(t) an initial value of (t),
Figure FDA0003464524080000028
is composed of
Figure FDA0003464524080000029
Is set to the initial value of (a),
Figure FDA00034645240800000210
is composed of
Figure FDA00034645240800000211
Is started.
5. The method for multi-agent formation control of node count variation according to claim 4,
in the third step, according to the equivalent control item of sliding mode control, the controller of the intelligent agent is designed as follows:
Figure FDA00034645240800000212
in the formula
Figure FDA00034645240800000213
Is a switching control item of sliding mode control.
6. The method for multi-agent formation control of node count variation according to claim 5,
the method for setting the speed damping gain in the controller and the communication weight between the intelligent node and the virtual pilot in the step three comprises the following steps:
Figure FDA00034645240800000214
in the formula (I), the compound is shown in the specification,
Figure FDA00034645240800000215
for the adjacent point set of the ith agent node at the time t,
Figure FDA00034645240800000216
for the agent node v at time tiAnd agent adjacent node vjJ is the node viThe serial number of the adjacent node (i) is not equal to j; d (t) is an adjacent node vjTo agent node viCommunication delay of, KiIn order to gain in the damping of the velocity,
Figure FDA00034645240800000217
communication weights for the ith agent node and the virtual pilot;
η1、η2、η3、η4、j1、j2、j3and j4Are all controller design parameters, η1>0，η2>0，η3>0，η4>0；j1>1，0<j2<1，0<j4<1；
j3The values of (A) include:
Figure FDA0003464524080000031
7. the method for multi-agent formation control of node count variation according to claim 6,
the communication delay d (t) satisfies: d is more than or equal to 0 and less than or equal to tM，
dMThe maximum communication delay allowed.
8. The method for multi-agent formation control of node count variation according to claim 7,
the verification of the feasibility of the current velocity damping gain through a linear matrix inequality in the sixth step comprises the following steps:
the linear matrix inequality is as follows:
Figure FDA0003464524080000032
wherein P, Q and Z are symmetric matrices to be solved:
P＝PT>0，Q＝QT>0，Z＝ZT>0；
c and E are block matrixes respectively.
9. The method for multi-agent formation control of node count variation according to claim 8,
the block matrixes C and E satisfy the following relational expression:
Figure FDA0003464524080000033
in the formula ImIs an m-order identity matrix, INIs an N-order identity matrix;
Figure FDA0003464524080000034
Figure FDA0003464524080000035
l is a Laplace matrix of the directed communication topological graph;
the laplace matrix L is:
L＝[Lij]N×N，
Figure FDA0003464524080000041
10. the method for multi-agent formation control of node count variation according to claim 9,
the directed communication topological graph G is as follows:
G＝(V,E,A)，
wherein V is a node set of the directed communication topological graph, E is an edge set of the directed communication topological graph, and A is the directed communication topological graph with a non-negative element aijA abutment moment ofijRepresenting an agent node viAnd agent node vjA connection weight between;
V＝{v1,v2,...,vN}，
Figure FDA0003464524080000042
A＝[aij]N×N；
agent node viSet of adjacent nodes NiComprises the following steps:
Ni＝{j∈V:(i,j)∈E}。
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