Method for realizing formation trajectory tracking by multi-agent system considering delay and packet loss

Abstract

The invention discloses a method for realizing formation trajectory tracking by a multi-agent system considering delay and packet loss, and belongs to the field of networked multi-agent formation control. The method is characterized by comprising the following steps: establishing mathematical models of virtual leaders and followers of the networked multi-agent system; performing trajectory planning on the virtual leader; the problems of target unreachable and local minimum are solved; designing a state observer according to outdated state information of the intelligent agent; designing a predictive control protocol by using an estimated value obtained by the observer; deriving a closed-loop error system according to the predictive control protocol, and obtaining conditions satisfied by a feedback gain matrix of the predictive control protocol; and substituting the feedback gain matrix into a predictive control protocol, and realizing leadership following formation trajectory tracking control by using the predictive control protocol. According to the invention, the influence of time delay and data loss in the network on the control system is overcome, so that the networked multi-agent system achieves the same control effect as a local control system.

Description

Technical Field

[0001] The invention relates to the field of multi-agent system and formation control, and in particular to a method for trajectory tracking control of a leader-follower formation using a state observer. Background Art

[0002] As the most popular research direction in the field of multi-agent systems, the formation control problem has attracted more and more attention in recent years due to its application prospects in various application fields and the challenging theoretical problems it involves. Its control goal is generally to make the state of each agent satisfy certain specified constraints.

[0003] Considering the increasing scale of multi-agent systems, a large amount of information exchanged through the network will cause blockage, resulting in time delays and data loss. The use of predictive control mechanisms can actively compensate for time delays and data loss in the network and achieve the same control effect as the local control system. Trajectory planning for virtual leaders can make formation control more flexible and more realistic. Summary of the invention

[0004] The present invention proposes a method for realizing formation trajectory tracking of a multi-agent system taking into account delay and packet loss, so as to establish a mathematical model of the networked multi-agent system, design a state observer, and solve the formation problem of the networked multi-agent system with communication constraints.

[0005] The present invention proposes a method for realizing trajectory tracking of a leader-follower formation in a networked multi-agent system with time delay and data loss, the method comprising the following steps:

[0006] Step 1: Establish a mathematical model of virtual leaders and followers in a networked multi-agent system and simplify the mathematical model;

[0007] Step 2: Plan the trajectory of the virtual leader and design a path planning algorithm based on the improved artificial potential field method to make the obstacle avoidance trajectory of the virtual leader smoother;

[0008] Step 3: Under the premise of ensuring that the virtual leader can converge to the target point, solve the problem of unreachable target and local minimum in the traditional artificial potential field method;

[0009] Step 4: In order to estimate the current state of the agent, a state observer is designed based on the outdated state information of the agent;

[0010] Step 5: Using the estimates obtained by the observer, design a predictive control protocol that can actively compensate for time delays and data loss in the network;

[0011] Step 6: Derive the closed-loop error system according to the predictive control protocol and obtain the conditions satisfied by the feedback gain matrix of the predictive control protocol;

[0012] Step 7: Substitute the feedback gain matrix into the predictive control protocol and use the predictive control protocol to implement the leader-follower formation trajectory tracking control;

[0013] Furthermore, the networked multi-agent mathematical model in step 1 is expressed as:

[0014] The dynamic model of the follower is described as follows:

[0015] x i (t+1)=x i (t)+Tv i (t)

[0016] v i (t+1)=v i (t)+Tu i (t)

[0017] in, and are the position, velocity and control input vector of the i-th follower at time t, T is the sampling period, i∈{1,2,...N}.

[0018] The dynamic model of the virtual leader is described as follows:

[0019] x0(t+1)=x0(t)+Tv0(t)

[0020] v0(t+1)=v0(t)+Tu0(t)

[0021] in, and are the position, velocity and control input vector of the virtual leader at time t respectively.

[0022] Obviously, the follower dynamics model can be simplified into the following form:

[0023]

[0024] in, and is the system matrix, represents the output vector of the follower, Represents the state vector of the follower.

[0025] The virtual leader dynamics equation can be simplified to the following form:

[0026]

[0027] in, is the system matrix, Represents the state vector of the virtual leader.

[0028] Furthermore, the path planning algorithm of the improved artificial potential field method described in step 2 is expressed as:

[0029] Assume that there are N obstacles in the motion space of the agent, and their outer circles have centers and radii x and obsi and R obsi , the position of the agent is x, and the speed is The position of the target point is x tar The shortest distance from the agent to the ith obstacle is ρ i =||xx obsi ||-R obsi , the action distance of each obstacle is ρ0.

[0030] The distance between the agent and the target point||xx tar || is introduced into gravity, and it is only allowed to act on half of the distance. One is to make the path smoother, and the other is to ensure that the intelligent body can converge to the target point. Therefore, gravity is modified to the following form:

[0031]

[0032] Among them, k p and k v Represents position gain and velocity gain respectively, x tar Indicates the location of the target point, x star o x Indicates the horizontal coordinate of the starting point, x tar o x Indicates the horizontal coordinate of the target point, x x Represents the horizontal coordinate of the agent’s current position.

[0033] Furthermore, the solution to the unreachable target and local minimum problem in step 3 is:

[0034] Solutions to local minima:

[0035] In step 2, the velocity term in gravity introduces an offset matrix Γ. When the directions of the position terms in gravity and repulsion are opposite, the resultant force at the equilibrium point is not zero due to the effect of the velocity term offset matrix Γ in gravity, thereby solving the local minimum problem. Therefore, gravity is modified to the following form:

[0036]

[0037] The selection of the offset matrix should not only slightly offset the direction of the velocity term in gravity, but also ensure that it does not have a significant impact on path planning and obstacle avoidance. Therefore, this paper selects the offset matrix

[0038] Solution to the problem of unreachable target:

[0039] The relative distance between the agent and the target point||xx tar ||Introducing repulsion, when the agent approaches the target point, even if there are obstacles near the target point, the repulsion will become smaller, and will not be much greater than the gravitational force, causing the resultant force to remain at a large value, making it impossible for the agent to reach the target point.

[0040] P i =||xx obsi ||-R obsi Find the gradient:

[0041]

[0042] Substituting into the repulsion formula, we can get the coordinate expression of the modified obstacle repulsion:

[0043]

[0044] The total artificial potential field function is Therefore, the net force on the intelligent agent in the artificial potential field is:

[0045]

[0046] Assume the state equation of the agent is:

[0047]

[0048] Let u = F, set the integration interval of the ode45 differential equation solver in MATLAB to a long vector of the same interval, and the interval is the same as the sampling period T. At this time, the state sequence obtained by the solution is equivalent to the state sequence after the trajectory planning of the virtual leader.

[0049] Furthermore, the expression of the state observer in step 4 is:

[0050] For follower agent i, in order to obtain its state, a state observer of the following form is designed:

[0051]

[0052] It indicates that the i-th agent uses the information at time tj to predict the state at time tk, The observer gain matrix can be obtained through observer design.

[0053] Furthermore, the expression of the predictive control protocol according to step 5 is:

[0054]

[0055] in, is the feedback gain matrix to be designed, are non-negative elements of the weighted adjacency matrix, express Relative to The formation offset vector.

[0056] Furthermore, the expression of the closed-loop error system in step 6 is:

[0057] make ε i (t+1) can be written as follows:

[0058]

[0059] The closed-loop error system is

[0060]

[0061] in,

[0062] ε(t)=[ε1(t) T ε2(t) T … ε N (t) T ] T

[0063] E(t)=[e1(t-τ1+1) T e2(t-τ2+1) T … e N (t-τ N +1) T ] T

[0064]

[0065] Θ=diag{AK 0 C,AK 0 C,...,AK 0 C}

[0066] Therefore, the error system can be expressed as:

[0067]

[0068] in,

[0069]

[0070] Ω=-(Υ+Ξ)

[0071] Θ=diag{AK 0 C,AK 0 C,...,AK 0 C}

[0072] If the following conditions are met, the networked multi-agent system can achieve formation trajectory tracking.

[0073] (1)

[0074] (2)

[0075] Among them, ||·|| represents the norm of the vector, is the estimation error at time t.

[0076] From the definition, if the error system is stable, then when t→∞, i=1,2,...,N, ε i (t)→0,e i (t)→0.

[0077] From t→∞, e i (t)→0, we get:

[0078]

[0079] From t→∞, ε i (t)→0, we get:

[0080]

[0081] Therefore, when the matrix and AK 0 When C is Schur stable, the multi-agent system can achieve formation trajectory tracking under the control protocol; and the linear matrix inequality toolbox in MATLAB is used to solve the following problem:

[0082]

[0083] AK 0 C<0

[0084] The feedback gain matrices K1 and K2 and the observer gain matrix K can be obtained 0 .

[0085] Furthermore, in step 7, the feedback gain matrices K1 and K2 obtained in step 6 are substituted into the networked multi-agent system formation trajectory tracking predictive control protocol in step 5 to realize the leader-follower formation trajectory tracking of the networked multi-agent system with time delay and data loss;

[0086] The beneficial technical effects of the present invention are:

[0087] The present invention studies a method for realizing leader-follower formation trajectory tracking in a networked multi-agent system, taking into account the impact of time delay and data loss on the networked multi-agent system, and taking into account the trajectory planning for the virtual leader. Compared with the existing multi-agent system that does not consider the problems of time delay and data loss, the protocol design of the present invention can overcome the impact of time delay and data loss in the network on the control system, achieve the same control effect as the local control system, and improve the problem that most existing formation trajectory tracking control studies only consider tracking fixed reference trajectories, which has greater theoretical and practical significance. With the help of mathematical tools such as graph theory and matrix theory, the feedback gain matrix is ​​solved based on linear matrix inequalities, so that the system can achieve the desired leader-follower formation trajectory tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood by reading the detailed description below with reference to the accompanying drawings. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, in which:

[0089] Figure 1 A flow chart of a method for realizing formation trajectory tracking by a multi-agent system taking into account delay and packet loss according to the present invention;

[0090] Figure 2 A communication topology diagram of a networked multi-agent system in an embodiment of the present invention;

[0091] Figure 3 A schematic diagram of the position trajectory of a virtual leader of a networked multi-agent system in an embodiment of the present invention to achieve obstacle avoidance control under an artificial potential field method;

[0092] Figure 4 It is a schematic diagram of realizing formation trajectory tracking control of the position trajectory of the networked multi-agent system under the action of the predictive control protocol in an embodiment of the present invention;

[0093] Figure 5 This is an example diagram of the velocity trajectory of the agent in the x direction in an embodiment of the present invention;

[0094] Figure 6 This is an example diagram of the velocity trajectory of the agent in the y direction in an embodiment of the present invention; DETAILED DESCRIPTION

[0095] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided only to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. On the contrary, these embodiments are provided to make the present disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0096] Those skilled in the art know that the embodiments of the present invention can be implemented as a system, device, equipment, method or computer program product. Therefore, the present disclosure can be specifically implemented in the following forms, namely: complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. In this article, it is to be understood that any number of elements in the drawings is for illustration and not limitation, and any naming is only for distinction and does not have any limiting meaning.

[0097] In order to overcome the influence of time delay and data loss on the trajectory tracking control of leader-follower formation in networked multi-agent system, the present invention proposes a method for realizing formation trajectory tracking of multi-agent system considering delay and packet loss, such as Figure 1 As shown, the method specifically comprises the following steps:

[0098] Step 1: Establish a mathematical model of virtual leaders and followers in a networked multi-agent system and simplify the mathematical model;

[0099] Step 2: Plan the trajectory of the virtual leader and design a path planning algorithm based on the improved artificial potential field method to make the obstacle avoidance trajectory of the virtual leader smoother;

[0100] Step 3: Under the premise of ensuring that the virtual leader can converge to the target point, solve the problem of unreachable target and local minimum in the traditional artificial potential field method;

[0101] Step 4: In order to estimate the current state of the agent, a state observer is designed based on the outdated state information of the agent;

[0102] Step 5: Using the estimates obtained by the observer, design a predictive control protocol that can actively compensate for time delays and data loss in the network;

[0103] Step 6: Derive the closed-loop error system according to the predictive control protocol and obtain the conditions satisfied by the feedback gain matrix of the predictive control protocol;

[0104] Step 7: Substitute the feedback gain matrix into the predictive control protocol and use the predictive control protocol to implement the leader-follower formation trajectory tracking control;

[0105] The present invention is described in detail below.

[0106] In step one, a mathematical model of virtual leaders and followers of a networked multi-agent system is first established and simplified.

[0107] According to the embodiment of the present invention, the intelligent agents are regarded as the vertices of the graph and a communication topology graph is defined. To describe the communication relationship between N agents, is the vertex set of the agent, For edge sets, is a non-negative weighted adjacency matrix. A directed edge (i, j)∈E from node i to node j indicates that the jth agent can receive information from the ith agent through the network. The adjacent element a associated with the edge (i, j) ji is positive, that is For any node i, if (i, j) ∈ E, then node j is called a neighbor node of node i; the set of all neighbor nodes of node i is denoted as Laplacian matrix of weighted graph Defined as

[0108] The dynamic model of the follower is described as follows:

[0109]

[0110] in, and are the position, velocity and control input vector of the i-th follower at time t, T is the sampling period, i∈{1,2,…N}.

[0111] The dynamic model of the virtual leader is described as follows:

[0112]

[0113] in, and are the position, velocity and control input vector of the virtual leader at time t respectively.

[0114] Obviously, the follower dynamics model of formula (1) can be simplified into the following form:

[0115]

[0116] in, and is the system matrix, represents the output vector of the follower, Represents the state vector of the follower.

[0117] Similarly, the virtual leader dynamics equation of formula (2) can be simplified into the following form:

[0118]

[0119] in, is the system matrix, Represents the state vector of the virtual leader.

[0120] In step 2, trajectory planning is performed on the virtual leader, and a path planning algorithm based on the improved artificial potential field method is designed to make the obstacle avoidance trajectory of the virtual leader smoother;

[0121] Assume that there are N obstacles in the motion space of the agent, and their outer circles have centers and radii x and obsi and R obsi , the position of the agent is x, and the speed is The position of the target point is x tar The shortest distance from the agent to the ith obstacle is ρ i =||xx obsi ||-R obsi , the action distance of each obstacle is ρ0.

[0122] The distance between the agent and the target point||xx tar || is introduced into gravity, and it is only allowed to act on half of the distance. One is to make the path smoother, and the other is to ensure that the intelligent body can converge to the target point. Therefore, gravity is modified to the following form:

[0123]

[0124] Among them, k p and k v Represents position gain and velocity gain respectively, x tar Indicates the location of the target point, x star o x Indicates the horizontal coordinate of the starting point, x tar o x Indicates the horizontal coordinate of the target point, x x Represents the horizontal coordinate of the agent’s current position.

[0125] In step three, under the premise of ensuring that the virtual leader can converge to the target point, the unreachable target and local minimum problems in the traditional artificial potential field method are solved.

[0126] Solutions to local minima:

[0127] In step 2, the velocity term in gravity introduces an offset matrix Γ. When the directions of the position terms in gravity and repulsion are opposite, the resultant force at the equilibrium point is not zero due to the effect of the velocity term offset matrix Γ in gravity, thereby solving the local minimum problem. Therefore, gravity is modified to the following form:

[0128]

[0129] The selection of the offset matrix should not only slightly offset the direction of the velocity term in gravity, but also ensure that it does not have a significant impact on path planning and obstacle avoidance. Therefore, this paper selects the offset matrix

[0130] Solution to the problem of unreachable target:

[0131] The relative distance between the agent and the target point||xx tar ||Introducing repulsion, when the agent approaches the target point, even if there are obstacles near the target point, the repulsion will become smaller, and will not be much greater than the gravitational force, causing the resultant force to remain at a large value, making it impossible for the agent to reach the target point.

[0132] P i =||xx obsi ||-R obsi Find the gradient:

[0133]

[0134] Substituting into the repulsion formula, we can get the coordinate expression of the modified obstacle repulsion:

[0135]

[0136] The total artificial potential field function is Therefore, the net force on the intelligent agent in the artificial potential field is:

[0137]

[0138] Assume the state equation of the agent is:

[0139]

[0140] Let u = F, set the integration interval of the ode45 differential equation solver in MATLAB to a long vector of the same interval, and the interval is the same as the sampling period T in equation (2). At this time, the state sequence obtained by solving is equivalent to the state sequence after trajectory planning in equation (2).

[0141] In step 4, in order to estimate the current state of the agent, a state observer is designed based on the outdated state information of the agent.

[0142] For follower agent i, in order to obtain its state, a state observer of the following form is designed:

[0143]

[0144] It indicates that the i-th agent uses the information at time tj to predict the state at time tk, The observer gain matrix can be obtained through observer design.

[0145] In step five, the estimates obtained by the observer are used to design a predictive control protocol that can actively compensate for time delays and data losses in the network.

[0146]

[0147] in, is the feedback gain matrix to be designed, are non-negative elements of the weighted adjacency matrix, express Relative to The formation offset vector.

[0148] In step six, a closed-loop error system is derived according to the predictive control protocol, and the conditions satisfied by the feedback gain matrix of the predictive control protocol are obtained.

[0149] make ε i (t+1) can be written as follows:

[0150]

[0151] The closed-loop error system is

[0152]

[0153] E(t+1)=ΘE(t)

[0154] in,

[0155] ε(t)=[ε1(t) T ε2(t) T … ε N (t) T ] T

[0156] E(t)=[e1(t-τ1+1) T e2(t-τ2+1) T … e N (t-τ N +1) T ] T

[0157]

[0158] Θ=diag{AK 0 C,AK 0 C,...,AK 0 C}

[0159] Therefore, the error system can be expressed as:

[0160]

[0161] in,

[0162]

[0163] Ω=-(Υ+Ξ)

[0164] Θ=diag{AK 0 C,AK 0 C,...,AK 0 C}

[0165] If the following conditions are met, the networked multi-agent system can achieve formation trajectory tracking.

[0166] (1)

[0167] (2)

[0168] Among them, ||·|| represents the norm of the vector, is the estimation error at time t.

[0169] From the definition, if the error system is stable, then when t→∞, i=1,2,...,N, ε i (t)→0,e i (t)→0.

[0170] From t→∞, e i (t)→0, we get:

[0171]

[0172] From t→∞, ε i (t)→0, we get:

[0173]

[0174] Therefore, when the matrix and AK 0When C is Schur stable, the multi-agent systems (3) and (4) can achieve formation trajectory tracking under the control protocol (11); and the linear matrix inequality toolbox in MATLAB is used to solve the following problem:

[0175]

[0176] The feedback gain matrices K1 and K2 and the observer gain matrix K can be obtained 0 .

[0177] In step seven, the feedback gain matrix that meets the conditions is substituted into the predictive control protocol to implement the leader-follower formation trajectory tracking of the networked multi-agent system with time delay and data loss;

[0178] The technical effect of the present invention is further verified through simulation experiments.

[0179] In the simulation experiment, it is assumed that the starting point of the virtual leader is (0,0) and the target point is (100,100). It is assumed that there are two obstacles in the motion space of the intelligent agent. The two obstacles are equal in size and can be represented by an outer circle with a radius of 10. The coordinates of the center of the circle are (35,65) and (55,35) respectively. The action distance of the two obstacles is 20. The gravitational force generated by the target point and the repulsive force generated by the obstacle are in accordance with equations (6) and (7) respectively. The position coefficient of gravity k p and speed factor k v are set to 0.4 and 1.3 respectively, the repulsion coefficient η is set to 50, and the virtual leader is stationary at the initial moment and moves under the action of the resultant force formula (8).

[0180] Consider that four followers follow the obstacle avoidance trajectory planned by the virtual leader and form the desired formation. Let the sampling period T = 0.1s and n = 2. At this time, the system matrices of the virtual leader and followers are as follows:

[0181]

[0182] Assume that the upper bounds of the time delay and data loss generated by the follower agent during the communication process are τ1 = 3, τ2 = 4, τ3 = 5, and τ4 = 6, respectively, and the observer gain matrix K 0 The linear matrix inequality LMI method is used to solve the problem and the AK 0 A feasible solution whose eigenvalue of C lies within the unit circle. That is:

[0183]

[0184] Similarly, the feedback gain matrix in the control protocol is solved by the linear matrix inequality LMI method and the result is A feasible solution whose eigenvalue lies within the unit circle. That is:

[0185]

[0186] The initial states of the four follower agents are:

[0187]

[0188] The formation vector is designed as follows:

[0189]

[0190] Therefore, the designed predictive control protocol can realize the trajectory tracking control of the leader-follower formation of the networked multi-agent system.

[0191] The experimental results are as follows Figure 3-Figure 6 As shown, Figure 3 is the position trajectory of the virtual leader, which shows that the virtual leader of the networked multi-agent system can achieve obstacle avoidance control under the artificial potential field method. Figure 4 The position trajectories of all agents are shown, which illustrates that the networked multi-agent system can achieve leader-follower formation trajectory tracking control under the designed predictive control protocol. Figure 5 and Figure 6 is the speed trajectory of the intelligent agent, which shows that the speed trajectory of the intelligent agent will eventually converge over time.

Claims

1. A method for realizing formation trajectory tracking of a multi-agent system considering delay and packet loss, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of virtual leaders and followers in a networked multi-agent system and simplify the mathematical model; Step 2: Plan the trajectory of the virtual leader and design a path planning algorithm based on the improved artificial potential field method to make the obstacle avoidance trajectory of the virtual leader smoother; Step 3: Under the premise of ensuring that the virtual leader can converge to the target point, solve the problem of unreachable target and local minimum in the traditional artificial potential field method; Step 4: In order to estimate the current state of the agent, a state observer is designed based on the outdated state information of the agent; Step 5: Using the estimates obtained by the observer, design a predictive control protocol that can actively compensate for time delays and data loss in the network; Step 6: Derive the closed-loop error system according to the predictive control protocol and obtain the conditions satisfied by the feedback gain matrix of the predictive control protocol; Step 7: Substitute the feedback gain matrix into the predictive control protocol and use the predictive control protocol to implement the leader-follower formation trajectory tracking control.

2. According to the method for realizing formation trajectory tracking of a multi-agent system considering delay and packet loss according to claim 1, the step 1 is: The dynamic model of the follower is described as follows: x i (t+1)=x i (t)+Tv i (t) v i (t+1)=v i (t)+Tu i (t) in, and are the position, velocity and control input vector of the i-th follower at time t, T is the sampling period, i∈{1,2,…N}. The dynamic model of the virtual leader is described as follows: x0(t+1)=x0(t)+Tv0(t) v0(t+1)=v0(t)+Tu0(t) in, and are the position, velocity and control input vector of the virtual leader at time t respectively. Obviously, the follower dynamics model can be simplified into the following form: in, and is the system matrix, represents the output vector of the follower, Represents the state vector of the follower. The virtual leader dynamics equation can be simplified to the following form: in, is the system matrix, Represents the state vector of the virtual leader.

3. According to the networked multi-agent system of claim 2, a path planning algorithm based on an improved artificial potential field method is designed to plan the trajectory of the virtual leader, characterized in that: The second step is: Assume that there are N obstacles in the motion space of the agent, and their outer circles have centers and radii x and obsi and R obsi , the position of the agent is x, and the speed is The position of the target point is x tar The shortest distance from the agent to the ith obstacle is ρ i =||xx obsi ||-R obsi , the action distance of each obstacle is ρ0. The distance between the agent and the target point||xx tar || is introduced into gravity, and it is only allowed to act on half of the distance. One is to make the path smoother, and the other is to ensure that the intelligent body can converge to the target point. Therefore, gravity is modified to the following form: Among them, k p and k v Represents position gain and velocity gain respectively, x tar Indicates the location of the target point, x star o x Indicates the horizontal coordinate of the starting point, x tar o x Indicates the horizontal coordinate of the target point, x x Represents the horizontal coordinate of the agent’s current position.

4. According to claim 3, the path planning algorithm for the virtual leader according to step 2 solves the problem of unreachable target and local minimum, characterized in that: The step three is: Solutions to local minima: In step 2, the velocity term in gravity introduces an offset matrix Γ. When the directions of the position terms in gravity and repulsion are opposite, the resultant force at the equilibrium point is not zero due to the effect of the velocity term offset matrix Γ in gravity, thereby solving the local minimum problem. Therefore, gravity is modified to the following form: The selection of the offset matrix should not only slightly offset the direction of the velocity term in gravity, but also ensure that it does not have a significant impact on path planning and obstacle avoidance. Therefore, this paper selects the offset matrix Solution to the problem of unreachable target: The relative distance between the agent and the target point||xx tar ||Introducing repulsion, when the agent approaches the target point, even if there are obstacles near the target point, the repulsion will become smaller, and will not be much greater than the gravitational force, causing the resultant force to remain at a large value, making it impossible for the agent to reach the target point. P i =||xx obsi ||-R obsi Find the gradient: Substituting into the repulsion formula, we can get the coordinate expression of the modified obstacle repulsion: The total artificial potential field function is Therefore, the net force on the intelligent agent in the artificial potential field is: Assume the state equation of the agent is: Let u = F, set the integration interval of the ode45 differential equation solver in MATLAB to a long vector of the same interval, and the interval is the same as the sampling period T. At this time, the state sequence obtained by the solution is equivalent to the state sequence after the trajectory planning of the virtual leader.

5. According to the mathematical model of the networked multi-agent system in claim 2, a state observer is designed based on the outdated state information of the agent to estimate the state of the system at the current moment, characterized in that: The step four is: For follower agent i, in order to obtain its state, a state observer of the following form is designed: It indicates that the i-th agent uses the information at time tj to predict the state at time tk, The observer gain matrix can be obtained through observer design.

6. According to claim 5, the predictive control protocol is designed based on the estimated value of the state of the mathematical model of the networked multi-agent system according to step 4, characterized in that: The step five is: in, is the feedback gain matrix to be designed, are non-negative elements of the weighted adjacency matrix, express Relative to The formation offset vector.

7. According to the consistency control protocol designed according to step 5 of claim 6, the closed-loop error system is derived to obtain the conditions satisfied by the feedback gain matrix of the predictive control protocol, characterized in that: The step six is: make ε i (t+1) can be written as follows: The closed-loop error system is E(t+1)=ΘE(t) in, ε(t)=[ε1(t) T ε2(t) T e N (t) T ] T E(t)=[e1(t-τ1+1) T e2(t-τ2+1) T e N (t-t N +1) T ] T Θdiag{AK 0 C,AK 0 C,...,AK 0 C} Therefore, the error system can be expressed as: in, Ω=-(Υ+Ξ) Θdiag{AK 0 C,AK 0 C,...,AK 0 C} If the following conditions are met, the networked multi-agent system can achieve formation trajectory tracking. (1) (2) Among them, ||·|| represents the norm of the vector, is the estimation error at time t. From the definition, if the error system is stable, then when t→∞, i=1,2,...,N, ε i (t)→0,e i (t)→0. From t→∞, e i (t)→0, we get: t→∞ From t→∞, ε i (t)→0, we get: t→∞ Therefore, when the matrix and AK 0 When C is Schur stable, the multi-agent system can achieve formation trajectory tracking under the control protocol; and the linear matrix inequality toolbox in MATLAB is used to solve the following problem: A-K 0 C<0 8. According to claim 7, the feedback gain matrix that satisfies the conditions is substituted into the predictive control protocol to realize the leader-follower formation trajectory tracking of the networked multi-agent system with time delay and data loss, characterized in that: The step seven is: Substitute the feedback gain matrices K1 and K2 obtained in step 6 into the networked multi-agent system formation trajectory tracking predictive control protocol in step 5 to realize the leader-follower formation trajectory tracking of the networked multi-agent system with time delay and data loss.

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