CN115903914A - A method for judging the maximum allowable communication data delay in a multi-agent formation system - Google Patents
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Abstract
多智能体编队系统允许最大通信数据延迟的判定方法，解决了如何有效的判定允许最大通信数据延迟的问题，属于多智能体领域。本发明包括：S1、获取领航‑跟随多智能体编队系统的参数及迭代步长ΔT；S2、计算得到分块矩阵C、E；S3、初始化迭代次数f＝1，设置时滞变量初始值d0＝ΔT；S4、将d0代入判定条件，计算判定条件的可行解，如果有解，转入S5，如果没有解，减少迭代步长ΔT，转入S2，或更换通信拓扑的拉普拉斯矩阵及领航者与跟随者通信矩阵，转入S3；S5、更新迭代步数f＝f+1；S6、df‑1＝fΔT，将df‑1代入判定条件，计算判定条件的可行解，如果有解，转入S5，如果没有解，最大通信延迟dM为(f‑1)ΔT。
The method for judging the maximum allowable communication data delay in a multi-agent formation system solves the problem of how to effectively determine the allowable maximum communication data delay, and belongs to the field of multi-agents. The present invention includes: S1, obtaining the parameters of the pilot-following multi-agent formation system and the iteration step size ΔT; S2, calculating and obtaining the block matrix C, E; S3, initializing the number of iterations f=1, and setting the initial value of the delay variable d 0 = ΔT; S4, substitute d 0 into the judgment condition, calculate the feasible solution of the judgment condition, if there is a solution, go to S5, if there is no solution, reduce the iteration step size ΔT, go to S2, or replace the Lapla of the communication topology The Sri Lankan matrix and the communication matrix between the leader and the follower are transferred to S3; S5, update the number of iteration steps f=f+1; S6, d f-1 = fΔT, substitute d f-1 into the judgment condition, and calculate the feasibility of the judgment condition Solution, if there is a solution, turn to S5, if there is no solution, the maximum communication delay d M is (f‑1)ΔT.
Description
Technical Field
The invention relates to a method for judging the maximum communication data delay allowed by a multi-agent formation system, belonging to the field of multi-agents.
Background
In recent years, the integration and development of technologies such as intelligent control, wireless communication and sensors have attracted extensive attention in the military and civil fields, and the multi-agent system taking a mobile robot as a background is successfully applied in the fields of multi-mechanical arm cooperative equipment, traffic vehicle control, unmanned aerial vehicle/airplane formation control and the like. In the cooperative control process of the multi-agent system, external disturbance cannot be avoided, for example, an unmanned aerial vehicle may be interfered by wind in formation, and an unmanned ship may be influenced by wind waves in the operation process, and the external factors often influence the control performance of the system and even cause cooperative failure of the system. Therefore, in response to multi-agent formation tasks in a complex environment, designing a formation control algorithm with high robustness and strong reliability becomes a key problem.
In actual engineering, an intelligent agent can perform information interaction with an adjacent intelligent agent, however, the intelligent agent is limited by network resources, and the intelligent agent can transmit a large amount of information at the same time, so that network congestion is caused, and even the intelligent agent is paralyzed. Since an agent needs to constantly exchange information with neighboring agents and calculate and update its control signals in real time, this control strategy not only increases the network communication burden and the node calculation burden, but also causes network induced uncertainty and even network instability. For this problem, an event-triggered control strategy is mostly adopted to reduce the communication frequency of the system, however, the introduction of this strategy makes the state input of the controller inevitably delayed. In addition, since the multi-agent system relies on network communication, the communication time lag due to the transmission distance is often not negligible in practical applications. Therefore, for the networked multi-agent system in a complex environment, the research on the maximum communication data delay allowed under the formation control strategy has important theoretical and practical application values.
Disclosure of Invention
Aiming at the problem of how to effectively judge the maximum communication data delay, the invention provides a method for judging the maximum communication data delay allowed by a multi-agent formation system.
The invention provides a method for judging the maximum communication data delay allowed by a multi-agent formation system, which comprises the following steps:
s1, determining a piloting-following multi-agent formation system, obtaining the number N of following agents, the dimension m of a control signal, a Laplace matrix L of a communication topology, a communication matrix B of a pilot and a follower and a speed damping gain K, and determining an iteration step length delta T;
s2, calculating to obtain a block matrix C, E;
s3, initializing the iteration frequency f =1, and setting a time-lag variable initial value d 0 ＝ΔT；
S4, d 0 Substituting the judgment condition, calculating feasible solutions of the judgment condition, if the feasible solutions exist, turning to S5, and if the feasible solutions do not exist, reducing the iteration step length delta T, and turning to S3;
the judgment conditions are as follows:
P＝P T ＞0，Q＝Q T > 0 and Z = Z T More than 0 is a symmetric matrix to be solved;
s5, updating iteration step number f = f +1;
S6、d f-1 = f Δ T, will d f-1 Substituting the judgment condition, calculating feasible solution of the judgment condition, if the solution exists, turning to S5, and if the solution does not exist, the maximum communication delay d M Is (f-1). DELTA.T.
The invention also provides a method for judging the maximum communication data delay allowed by the multi-agent formation system, which comprises the following steps:
s1, determining a piloting-following multi-agent formation system, obtaining the number N of following agents, the dimension m of a control signal, a Laplace matrix L of a communication topology, a communication matrix B of a pilot and a follower and a speed damping gain K, determining an iteration step length delta T, initializing the iteration times f =1, and setting a time-lag variable initial value d 0 ＝ΔT；
S2, calculating to obtain a block matrix C, E;
s3, mixing d 0 Substituting the judgment condition, calculating a feasible solution of the judgment condition, if the solution exists, turning to S4, and if the solution does not exist, replacing a Laplace matrix L of the communication topology and a communication matrix B of the navigator and the follower, and turning to S2;
the judgment conditions are as follows:
P＝P T ＞0，Q＝Q T > 0 and Z = Z T More than 0 is a symmetric matrix to be solved;
s4, updating iteration step number f = f +1;
S5、d f-1 = f Δ T, will d f-1 Substituting the judgment condition, calculating feasible solution of the judgment condition, if the solution exists, turning to S4, and if the solution does not exist, the maximum communication delay d M Is (f-1). DELTA.T.
The method has the advantages that the method has the following characteristics and advantages: the method can be used for judging the feasibility of the current adjacency matrix, iteratively obtaining the maximum communication delay of communication topology dependence, and meanwhile, can be used for selecting the controller parameters.
Drawings
FIG. 1 is a flow chart of a method for determining the maximum allowable communication data delay of a multi-agent queuing system;
FIG. 2 is a flow chart of a method for determining the maximum communication data delay allowed for a multi-agent formation system;
FIG. 3 is a diagram of multi-agent formation trajectories for three communication delay scenarios;
FIG. 4 is a graph of follower 1 velocity tracking error for three communication delay scenarios;
FIG. 5 is a graph of follower 2 velocity tracking error for three communication delay scenarios;
fig. 6 is a diagram of follower 3 speed tracking error under three communication delay situations;
FIG. 7 is a graph of follower 4 velocity tracking error for three communication delay scenarios;
fig. 8 is a graph of follower 5 speed tracking error for three communication delay scenarios.
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 obtained by a person skilled in the art without inventive efforts based on the embodiments of the present invention, shall fall within the scope of protection 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.
The method mainly considers a multi-agent system with interval time lag, establishes a dynamic model of the multi-agent system under the condition that position and speed information has delay by using a state space method, adopts a distributed formation control strategy based on an integral sliding mode, obtains a time lag related stability judgment condition of the multi-agent formation control system by using a Lyapunov functional analysis method, and designs an iterative algorithm by combining a linear matrix inequality to solve an upper time lag boundary on the basis of the stability judgment condition, thereby providing an effective method for judging the maximum allowable communication data delay for formation control taking an unmanned aerial vehicle and the like as an application background in practice. The determination method has the following features and advantages: the method can be used for judging the feasibility of the current adjacency matrix, iteratively obtaining the maximum communication delay of communication topology dependence, and meanwhile, can be used for selecting the controller parameters.
The embodiment aims at a multi-agent system with time-varying communication delay, a directed subgraph is used for defining and describing the communication relation among following agents, and a directed communication topological graph G is defined as follows: g = (V, E, a), where V is a set of nodes of the directed communication topology graph, E is a set of edges of the directed communication topology graph, and a is the directed communication topology graph having a non-negative element a ij A adjacency matrix of ij Representing the connection weight between agent node i and agent node j; when a is ij At 0, node i does not receive the information transmitted by node j. When a is ij When 1, the node i can receive the information transmitted by the node j. When a node i exists in the graph G, so that any other point in the graph can be reached from the point along the directed edge, the graph G is called to comprise a directed spanning tree, and the node is called a root node. V = {1,2, ·, N },
A＝[a ij ] N×N (ii) a Set of adjacent nodes N of agent node i i Comprises the following steps: n is a radical of hydrogen i And (j) is larger than the value of the current in the current path. Directed graph->
Representing a communication topology consisting of a pilot and N followers, wherein->
The communication weight matrix between the pilot and the follower is B = diag (B) 1 ,b 2 ,b 3 ,...,b N )，b i ＞0，b i Representing the connection weight between the intelligent agent node i and the pilot, if the follower i can receive the information of the pilot, otherwise, b i And =0. Further, a Laplace matrix of the communication topology is defined, L = D-A, whereinD＝diag(d 1 ,d 2 ,d 3 ,...,d N )，d i ＝v j∈V a ij 。
The embodiment is based on a system formation control mode of a virtual pilot-follower, and takes the following two-order nonlinear kinematics model of the virtual pilot in the formation system into consideration:
wherein,
and &>
Respectively representing the position and speed of a virtual pilot, in conjunction with a control unit>
And &>
Respectively representing the amount of position change and the amount of speed change, u, of the virtual pilot 0 (t) is a given speed variation function, i.e. the acceleration of the virtual pilot. 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. By designing the control signal u of the piloting vehicle 0 (t) so as to specify the motion trail, and further indirectly design the motion trail of formation. The pilot is used for controlling the traveling route of the whole formation in the formation process, and the formation shape can be controlled by keeping a certain relative deviation between the pilot and the member as a follower. The navigator can be a real individual member or a virtual navigator. The navigator considered by the invention is a virtual moving body node becauseAnd a pilot entity does not exist, and the problem that the pilot breaks down is not needed to be worried about.
The kinematic model of the following agent in the formation system is as follows:
wherein,
indicates the location of the ith agent, based on the status of the agent>
Indicates the speed of the ith agent, based on the status of the sensor>
Indicates a position shift amount, based on the ith agent>
Indicates a speed shift amount, based on the ith agent>
Representing the amount of control for the ith agent.
The formation protocol of the present embodiment is a distributed control law based on linear state feedback. From the multi-agent system model with communication delay, the controller of the ith agent is designed as follows:
wherein, K i > 0 represents the velocity damping gain and,
to presetA set of velocity damping gains; h is i Representing a vector from the ith node to the virtual pilot; d i (t) is expressed as the position of the adjacent node and the transmission delay time of the speed information, and satisfies 0 ≦ d i (t)≤d M ，d M The maximum communication delay allowed.
To analyze the dynamics of a multi-agent error system, an augmented error vector ε (t) is defined as follows:
wherein,
the error variable of the agent is augmented by the Kronecker product to obtain a multi-agent error augmentation system, which comprises the following steps:
wherein the block matrix C, E is defined as follows:
and (3) carrying out stability analysis on the error system after the amplification, and obtaining the following calculable judgment condition based on a linear matrix inequality:
wherein, P = P T ＞0，Q＝Q T > 0 and Z = Z T > 0 is the symmetric matrix to be solved.
The feasibility of the multi-agent formation system under the condition of time-varying communication time delay can be judged according to the stability conditions. This condition constitutes a set of directly solvable linear matrix inequalities, and includesIncluding a delay time parameter d f-1 . Due to the parameter d f-1 The maximum communication delay d allowed by the current multi-agent system can be obtained through numerical iteration calculation according to the condition that the maximum communication delay d is in a coupling relation with system parameters M . The method for determining the maximum allowable communication data delay of the multi-agent formation system according to the embodiment is as shown in fig. 1, and the flow is as follows:
The present embodiment further provides another method for determining the maximum communication data delay allowed by the multi-agent formation system, as shown in fig. 2, the flow is as follows:
In order to verify and show the effectiveness of the formation control algorithm, the invention verifies the judgment method of the maximum communication delay allowed by the multi-agent formation system by taking the three-dimensional unmanned aerial vehicle as the background, and respectively shows the formation effect of the multi-agent formation system under the condition of state input delay.
The simulation of many unmanned aerial vehicle formation system is provided with 1 virtual pilot node and 5 follower nodes, and the communication topology Laplacian matrix that corresponds sets up to:
setting communication parameters B = diag (4,4,4,4,4) of following agent and pilot agent, and speed damping gain
According to the algorithm, the iteration step length delta T =0.001s is selected under the parameter, and the allowed maximum communication data delay of the multi-unmanned aerial vehicle formation system is 0.920s.
The initial positions of the follower nodes are respectively set as x x1 (0)＝[0-0.7528-0.2392] T ，x x2 (0)＝[0-1.6472-0.5298] T ，x x3 (0)＝[0-1.6472-1.4702] T ，x x4 (0)＝[0-0.75281.7608] T ，x x5 (0)＝[0-0.2-1] T The initial speeds are all set to x vi (0)＝[000] T I = 1.., 5. The initial position of the navigator node is set to x x0 (0)＝[000] T Initial position velocity set to x v0 (0)＝[000] T Control signal input u 0 (t)＝[0.50.10.5] T . Setting followers to form a regular pentagonal formation, wherein expected formation vectors from the followers to the leader are respectively set as h 1 ＝[1.23613.80420] T ，h 2 ＝[-3.23612.35110] T ，h 3 ＝[-3.2361-2.35110] T ，h 4 ＝[1.2361-3.80420] T ，h 1 ＝[400] T . The maximum allowable delay d can be obtained according to the proposed decision method M =0.920s. Based on the adopted linear feedback control rate, a multi-agent formation control effect graph with input time lag is obtained at three different communication time lags d =0.3s, d =0.6s and d =0.9s, and the graphs are shown in fig. 3-8.
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 various dependent claims and the features described 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 (6)
1. A method for determining a maximum communication data delay allowed for a multi-agent queuing system, the method comprising:
s1, determining a piloting-following multi-agent formation system, obtaining the number N of following agents, the dimension m of a control signal, a Laplace matrix L of a communication topology, a communication matrix B of a pilot and a follower and a speed damping gain K, and determining an iteration step length delta T;
s2, calculating to obtain a block matrix C, E;
s3, initializing the iteration frequency f =1, and setting a time lag variable initial value d 0 ＝ΔT；
S4, d 0 Substituting the judgment condition, calculating feasible solutions of the judgment condition, if the feasible solutions exist, turning to S5, and if the feasible solutions do not exist, reducing the iteration step length delta T, and turning to S3;
the judgment conditions are as follows:
P＝P T ＞0，Q＝Q T > 0 and Z = Z T More than 0 is a symmetric matrix to be solved;
s5, updating iteration step number f = f +1;
S6、d f-1 = f Δ T, will d f-1 Substituting the judgment condition, calculating feasible solution of the judgment condition, if the solution exists, turning to S5, and if the solution does not exist, the maximum communication delay d M Is (f-1). DELTA.T.
2. A method for determining a maximum communication data delay allowed for a multi-agent queuing system, the method comprising:
s1, determining a pilot-following multi-agent formation system, obtaining the number N of following agents, the dimension m of a control signal, a Laplace matrix L of a communication topology, a pilot-follower communication matrix B and a speed damping gain K, determining an iteration step length delta T, initializing the iteration times f =1, and setting a time-lag variable initial value d 0 ＝ΔT；
S2, calculating to obtain a block matrix C, E;
s3, mixing d 0 Substituting the judgment condition, calculating feasible solutions of the judgment condition, if the solutions exist, turning to S4,if not, replacing the Laplace matrix L of the communication topology and the communication matrix B of the navigator and the follower, and turning to S2;
the judgment conditions are as follows:
P＝P T ＞0，Q＝Q T > 0 and Z = Z T More than 0 is a symmetric matrix to be solved;
s4, updating iteration step number f = f +1;
S5、d f-1 = f Δ T, will d f-1 Substituting the judgment condition, calculating feasible solutions of the judgment condition, if the feasible solutions exist, turning to S4, and if the feasible solutions do not exist, calculating the maximum communication delay d M Is (f-1). DELTA.T.
3. A method for determining maximum communication data delay allowed by a multi-agent queuing system as claimed in claim 1 or 2, wherein the queuing protocol of said multi-agent queuing system is a distributed control law based on linear state feedback.
4. The method for determining maximum communication data delay allowed by a multi-agent queuing system according to claim 3, wherein the control quantity of the controller of the agent node i in the multi-agent queuing system is:
i＝1,2,...,N，N i set of neighbor nodes representing agent node i, b i Representing the connection weight between the agent node i and the pilot;
a ij representing the connection weight between agent node i and agent node j; d i (t) represents the position of the adjacent node of the agent node i and the transmission delay time of the speed information, and d is more than or equal to 0 i (t)≤d M ，d M For maximum communication allowedDelaying time; d j (t) respectively representing the position of the adjacent node of the agent node j and the transmission delay time of the speed information, and satisfying d being more than or equal to 0 i (t)≤d M ，d M Maximum communication delay allowed; h is i A vector representing from agent node i to the virtual pilot; h is a total of j A vector representing from agent node j to the virtual pilot; k i > 0 represents velocity damping gain; x is the number of x0 (t) represents the position of the virtual pilot; x is a radical of a fluorine atom v0 (t) represents the velocity of the virtual pilot; x is a radical of a fluorine atom vi (t) represents the velocity of agent node i; x is the number of xi (t) represents the location of agent node i; x is the number of xj (t) represents the location of agent node j; x is the number of vj (t) represents the velocity of agent node j.
5. A computer-readable storage device storing a computer program, wherein the computer program when executed implements a method for determining a maximum communication data delay allowed for a multi-agent queuing system as claimed in any one of claims 1 to 2.
6. An apparatus for determining maximum communication data delay allowed by a multi-agent queuing system, comprising a storage device, a processor and a computer program stored in the storage device and executable on the processor, wherein the processor executes the computer program to implement the method for determining maximum communication data delay allowed by the multi-agent queuing system as claimed in any one of claims 1 to 2.
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