Determination method of maximum communication data delay allowed in multi-agent formation system

Abstract

The method for determining the maximum allowable communication data delay of a multi-agent formation system solves the problem of how to effectively determine the maximum allowable communication data delay, and belongs to the field of multi-agents. The present invention includes: S1, obtaining the parameters and iteration step ΔT of the pilot-follower multi-agent formation system; S2, calculating the block matrices C and E; S3, initializing the number of iterations f=1, setting the initial value of the time lag variable d0=ΔT; S4, substituting d0 into the determination condition, calculating the feasible solution of the determination condition, if there is a solution, go to S5, if there is no solution, reduce the iteration step ΔT, go to S2, or replace the Laplace matrix of the communication topology and the communication matrix of the pilot and follower, and go to S3; S5, updating the iteration step f=f+1; S6, d f‑1 =fΔT, d f‑1 Substitute the judgment conditions and calculate the feasible solutions to the judgment conditions. If there is a solution, go to S5. If there is no solution, the maximum communication delay d M is (f‑1)ΔT.

Description

Technical Field

[0001] The invention relates to a method for determining a maximum communication data delay allowed by a multi-agent formation system, and belongs to the field of multi-agents. Background Art

[0002] In recent years, with the integration and development of technologies such as intelligent control, wireless communication, and sensors, multi-agent systems with mobile robots as the background have received widespread attention in the military and civilian fields, and have been successfully applied in the fields of multi-robot collaborative equipment, traffic vehicle control, and drone / aircraft formation control. In the collaborative control process of multi-agent systems, external disturbances are inevitable. For example, drones may be disturbed by wind in the formation, and unmanned boats may be affected by wind and waves during operation. These external factors often affect the control performance of the system and even cause the system to fail in coordination. Therefore, in order to cope with multi-agent formation tasks in complex environments, designing a formation control algorithm with high robustness and strong reliability has become a key issue.

[0003] In actual engineering, intelligent agents can exchange information with adjacent intelligent agents. However, due to network resource constraints, intelligent agents will transmit a large amount of information at the same time, causing network congestion or even paralysis. Since intelligent agents need to constantly exchange information with adjacent intelligent agents and need to calculate and update their control signals in real time, this control strategy not only increases the network communication burden and node calculation burden, but also causes network-induced uncertainty and even network instability. For this problem, event-triggered control strategies are currently used to reduce the communication frequency of the system. However, the introduction of this strategy inevitably causes delays in the state input of the controller. In addition, since multi-agent systems rely on network communication, the communication delay caused by the transmission distance in practical applications is often not negligible. Therefore, for networked multi-agent systems in complex environments, studying the maximum communication data delay allowed under the formation control strategy has important theoretical and practical application value. Summary of the invention

[0004] In order to solve the problem of how to effectively determine the maximum allowable communication data delay, the present invention provides a method for determining the maximum allowable communication data delay of a multi-agent formation system.

[0005] The present invention provides a method for determining a maximum communication data delay allowed by a multi-agent formation system, comprising:

[0006] S1. Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the communication matrix B between the leader and the follower, and the speed damping gain K, and determine the iteration step size ΔT;

[0007] S2, calculate and obtain the block matrices C and E;

[0008]

[0009] S3, initialize the number of iterations f = 1, set the initial value of the time lag variable d0 = ΔT;

[0010] S4, substitute d0 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 S3;

[0011] The judgment conditions are:

[0012]

[0013] P=P T >0, Q=Q T >0 and Z=Z T >0 is the symmetric matrix to be found;

[0014] S5, update the number of iteration steps f=f+1;

[0015] S6, d f-1 =fΔT, d f-1 Substitute the judgment conditions and calculate the feasible solutions to the judgment conditions. If there is a solution, go to S5. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

[0016] The present invention also provides a method for determining the maximum communication data delay allowed by a multi-agent formation system, comprising:

[0017] S1. Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the leader-follower communication matrix B and the velocity damping gain K, determine the iteration step ΔT, initialize the number of iterations f = 1, and set the initial value of the time lag variable d0 = ΔT;

[0018] S2, calculate and obtain the block matrices C and E;

[0019]

[0020] S3, substitute d0 into the decision condition, calculate the feasible solution of the decision condition, if there is a solution, go to S4, if there is no solution, replace the Laplace matrix L of the communication topology and the communication matrix B of the leader and follower, and go to S2;

[0021] The judgment conditions are:

[0022]

[0023] P=P T >0, Q=QT >0 and Z=Z T >0 is the symmetric matrix to be found;

[0024] S4, update the number of iteration steps f=f+1;

[0025] S5, d f-1 =fΔT, d f-1 Substitute the decision conditions and calculate the feasible solutions to the decision conditions. If there is a solution, go to S4. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

[0026] The beneficial effects of the present invention are as follows: the determination method of the present invention has the following characteristics and advantages: it can be used to determine the feasibility of the current adjacency matrix, iteratively obtain the maximum communication delay dependent on the communication topology, and can also be used to select controller parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of a method for determining the maximum communication data delay allowed for a multi-agent formation system;

[0028] Figure 2 A flow chart of a method for determining the maximum communication data delay allowed for a multi-agent formation system;

[0029] Figure 3 The trajectory diagrams of multi-agent formations under three communication delay conditions;

[0030] Figure 4 The velocity tracking error diagram of follower 1 under three communication delay conditions;

[0031] Figure 5 The velocity tracking error diagram of follower 2 under three communication delay conditions;

[0032] Figure 6 The velocity tracking error diagram of follower 3 under three communication delay conditions;

[0033] Figure 7 The speed tracking error diagram of follower 4 under three communication delay conditions;

[0034] Figure 8 Figure 2 shows the velocity tracking error of follower 5 under three communication delay conditions. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0037] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0038] This implementation mainly considers a multi-agent system with interval time delays. Using the state space method, a dynamic model of a multi-agent with delayed position and velocity information is established. A distributed formation control strategy based on integral sliding mode is adopted. The time-delay-related stability judgment condition of the multi-agent formation control system is obtained by using the Lyapunov functional analysis method. On the basis of this stability judgment condition, an iterative algorithm is designed in combination with linear matrix inequalities to solve the upper bound of the time delay, which provides an effective method for determining the maximum allowable communication data delay for formation control in actual application backgrounds such as drones. This determination method has the following characteristics and advantages: it can be used to determine the feasibility of the current adjacency matrix, iteratively obtain the maximum communication delay dependent on the communication topology, and can also be used to select controller parameters.

[0039] This embodiment is aimed at a multi-agent system with time-varying communication delay. A directed subgraph is used to define the communication relationship between the following agents. The directed communication topology graph G is defined as: G = (V, E, A), where V is the node set of the directed communication topology graph, E is the edge set of the directed communication topology graph, and A is the non-negative element a of the directed communication topology graph. ij The adjacency matrix of ij represents the connection weight between agent node i and agent node j; when a ij When a is 0, node i cannot receive the information transmitted by node j. ij When V is 1, node i can receive information transmitted by node j. When there is a node i in the graph G such that any other point in the graph can be reached along the directed edge from this point, then the graph G is said to contain a directed spanning tree, and the node is called the root node. V = {1, 2, ..., N}, A=[a ij ] N×N ; The adjacent node set N of agent node i i For: N i ={j∈V:(i,j)∈E}. Directed graph represents a communication topology consisting of a leader and N followers, where The communication weight matrix between the leader and the follower is: B = diag (b1, b2, b3, ..., b N ), b i >0,b irepresents the connection weight between the intelligent node i and the navigator. If the follower i can receive the information from the navigator, otherwise, b i = 0. In addition, the Laplace matrix of the communication topology is defined, L = DA, where D = diag (d1, d2, d3, ..., d N ), d i =v j∈V a ij .

[0040] This implementation is based on a system formation control mode of a virtual leader-follower, and considers the second-order nonlinear kinematic model of the virtual leader in the formation system as follows:

[0041]

[0042] in, and Respectively represent the position and speed of the virtual navigator, and Respectively represent the position change and speed change of the virtual navigator, u0(t) is the given speed change function, that is, the acceleration of the virtual navigator. Therefore, the entire formation model constitutes a multi-intelligent model of "actual follower-virtual navigator", in which the information of the virtual navigator is shared by each intelligent agent, and each intelligent agent can realize its own movement by obtaining the information of the virtual navigator and the information of the neighboring nodes to achieve the ultimate formation purpose. By designing the control signal u0(t) of the navigating moving body, its motion trajectory is specified, and then the motion trajectory of the formation is indirectly designed. In the formation process, the role of the navigator is to control the route of the entire formation. As a follower member, the formation can be controlled by maintaining a certain relative deviation between the navigator and the navigator. The navigator can be either a real individual member or a virtual navigator. The navigator considered in the present invention is a virtual moving body node. Since there is no navigator entity, there is no need to worry about the problem of navigator failure.

[0043] The kinematic model of the following agent in the formation system is as follows:

[0044]

[0045] in, represents the position of the ith agent, represents the speed of the ith agent, represents the position change of the ith agent, represents the speed change of the ith agent, Represents the control amount for the i-th agent.

[0046] The formation protocol of this embodiment is a distributed control law based on linear state feedback. According to the multi-agent system model with communication delay, the controller of the i-th agent is designed as follows:

[0047]

[0048] Among them, K i >0 indicates velocity damping gain, is the preset velocity damping gain set; h i represents the vector from the i-th node to the virtual navigator; d i (t) represents the transmission delay time of the position and speed information of the adjacent nodes, satisfying 0≤d i (t)≤d M , d M is the maximum allowed communication delay.

[0049] In order to analyze the dynamic characteristics of the multi-agent error system, the augmented error vector ε(t) is defined as follows:

[0050]

[0051] in, The Kronecker product is used to augment the error variables of the agent, and the multi-agent error augmentation system is obtained as follows:

[0052]

[0053] The block matrices C and E are defined as follows:

[0054]

[0055] The stability analysis of the augmented error system is carried out, and the following computable judgment conditions based on linear matrix inequality are obtained:

[0056]

[0057] Where P = P T >0, Q=Q T >0 and Z=Z T >0 is the symmetric matrix to be found.

[0058] The above stability conditions can be used to determine the feasibility of the multi-agent formation system in the presence of time-varying communication delays. This condition constitutes a set of linear matrix inequalities that can be directly solved and includes the delay time parameter d f-1 Since the parameter d f-1There is a coupling relationship with the system parameters. According to this condition, the maximum communication delay d allowed by the current multi-agent system can be obtained through numerical iteration calculation. M The method for determining the maximum communication data delay allowed by the multi-agent formation system of this embodiment is as follows: Figure 1 As shown, the process is as follows:

[0059] Step 1: Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the communication matrix B between the leader and the follower, and the speed damping gain K, and determine the iteration step length ΔT;

[0060] Step 2: Use formula (4) to calculate the block matrices C and E;

[0061] Step 3, initialize the number of iterations f = 1, and set the initial value of the time lag variable d0 = ΔT;

[0062] Step 4: Substitute d0 into the judgment condition formula (5) to calculate the feasible solution of the judgment condition. If there is a solution, go to step 5. If there is no solution, reduce the iteration step size ΔT and go to step 3.

[0063] Step 5: Update the number of iteration steps f=f+1;

[0064] Step 6, d f-1 =fΔT, d f-1 Substitute the decision condition formula (5) and calculate the feasible solution of the decision condition. If there is a solution, go to step 5. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

[0065] This embodiment also provides another method for determining the maximum communication data delay allowed by a multi-agent formation system, such as Figure 2 As shown, the process is as follows:

[0066] Step 1: Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the leader-follower communication matrix B and the velocity damping gain K, determine the iteration step length ΔT, initialize the number of iterations f = 1, and set the initial value of the time lag variable d0 = ΔT;

[0067] Step 2: Use formula (4) to calculate the block matrices C and E;

[0068] Step 3: Substitute d0 into the judgment condition formula (5) to calculate the feasible solution of the judgment condition. If there is a solution, go to step 4. If there is no solution, replace the Laplace matrix L of the communication topology and the communication matrix B of the leader and follower, and go to step 2.

[0069] Step 4: Update the number of iteration steps f=f+1;

[0070] Step 5, d f-1 =fΔT, d f-1 Substitute the decision condition formula (5) and calculate the feasible solution of the decision condition. If there is a solution, go to step 4. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

[0071] In order to verify and demonstrate the effectiveness of the formation control algorithm of the present invention, the present invention will verify the determination method of the maximum communication delay allowed by the multi-agent formation system with three-dimensional drones as the background, and demonstrate the formation effect of the multi-drone system in the case of state input delay.

[0072] The multi-UAV formation system simulation is set up with 1 virtual leader node and 5 follower nodes, and the corresponding communication topology Laplacian matrix is ​​set as:

[0073]

[0074] Set the communication parameters between the follower agent and the leader agent B = diag(4,4,4,4,4), speed damping gain According to the above algorithm, under this parameter, the iteration step size ΔT = 0.001s is selected, and the maximum allowable communication data delay of the multi-UAV formation system is 0.920s.

[0075] The initial positions of the follower nodes are set to 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 velocity is set to x vi (0) =

[000] T , i=1,...,5. The initial position of the leader node is set to x x0 (0) =

[000] T , the initial position velocity is set to x v0 (0) =

[000] T , control signal input u0(t) = [0.50.10.5] TThe followers are set to form a regular pentagonal formation, where the expected formation vectors from the follower node to the leader node are set to h1 = [1.23613.80420] T , h2 = [-3.23612.35110] T , h3=[-3.2361-2.35110] T , h4=[1.2361-3.80420] T , h1 =

[400] T According to the proposed determination method, the maximum allowable delay d can be obtained M =0.920s. Based on the linear feedback control rate adopted, the control effect diagram of multi-agent formation with input time delay is obtained at three different communication time delays d = 0.3s, d = 0.6s, and d = 0.9s, see Figure 3 to Figure 8 .

[0076] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary 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 the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A method for determining the maximum communication data delay allowed by a multi-agent formation system, characterized in that: The method comprises: S1. Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the communication matrix B between the leader and the follower, and the speed damping gain K, and determine the iteration step size ΔT; S2, calculate and obtain the block matrices C and E; S3, initialize the number of iterations f = 1, set the initial value of the time lag variable d0 = ΔT; S4, substitute d0 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 S3; The judgment conditions are: P=P T >0, Q=Q T >0 and Z=Z T >0 is the symmetric matrix to be found; S5, update the number of iteration steps f=f+1; S6, d f-1 =fΔT, d f-1 Substitute the judgment conditions and calculate the feasible solutions to the judgment conditions. If there is a solution, go to S5. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

2. A method for determining the maximum communication data delay allowed by a multi-agent formation system, characterized in that: The method comprises: S1. Determine the leader-follower multi-agent formation system, obtain the number of follower agents N, the control signal dimension m, the Laplace matrix L of the communication topology, the leader-follower communication matrix B and the velocity damping gain K, determine the iteration step ΔT, initialize the number of iterations f = 1, and set the initial value of the time lag variable d0 = ΔT; S2, calculate and obtain the block matrices C and E; S3, substitute d0 into the decision condition, calculate the feasible solution of the decision condition, if there is a solution, go to S4, if there is no solution, replace the Laplace matrix L of the communication topology and the communication matrix B of the leader and follower, and go to S2; The judgment conditions are: P=P T >0, Q=Q T >0 and Z=Z T >0 is the symmetric matrix to be found; S4, update the number of iteration steps f=f+1; S5, d f-1 =fΔT, d f-1 Substitute the decision conditions and calculate the feasible solutions to the decision conditions. If there is a solution, go to S4. If there is no solution, the maximum communication delay d M is (f-1)ΔT.

3. According to the method for determining the maximum communication data delay allowed by a multi-agent formation system according to claim 1 or 2, the formation protocol of the multi-agent formation system is a distributed control law based on linear state feedback.

4. The method for determining the maximum communication data delay allowed by a multi-agent formation system according to claim 3, characterized in that: The control quantity of the controller of agent node i in the multi-agent formation system is: i=1,2,...,N,N i represents the set of neighbor nodes of agent node i, b i represents the connection weight between agent node i and the navigator; a ij represents the connection weight between agent node i and agent node j; d i (t) represents the transmission delay time of the position and speed information of the neighboring nodes of the intelligent node i, satisfying 0≤d i (t)≤d M , d M is the maximum allowed communication delay; d j (t) represents the transmission delay time of the position and speed information of the neighboring nodes of the intelligent node j, satisfying 0≤d i (t)≤d M , d M is the maximum communication delay allowed; h i represents the vector from agent node i to the virtual navigator; h j represents the vector from agent node j to the virtual navigator; K i >0 indicates velocity damping gain; x x0 (t) represents the position of the virtual navigator; x v0 (t) represents the speed of the virtual navigator; x vi (t) represents the speed of agent node i; x xi (t) represents the position of agent node i; x xj (t) represents the position of agent node j; x vj (t) represents the speed of agent node j.

5. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed, it implements the method for determining the maximum communication data delay allowed by the multi-agent formation system as described in any one of claims 1 to 2.

6. A device for determining the maximum communication data delay allowed by a multi-agent formation system, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes the computer program to implement a method for determining the maximum communication data delay allowed by a multi-agent formation system as described in any one of claims 1 to 2.

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