Networked multi-robot data-driven formation control method under preview mechanism

Abstract

Disclosed in the present invention is a networked multi-robot data-driven formation control method under a preview mechanism. A leader-follower formation method is used, wherein a preview point is determined on a reference trajectory, and by means of a cross-track error between a current position and the preview point, a model-free adaptive control (MFAC) algorithm is used to control an angular velocity; each follower uses the coordinates of a leader as the preview point, and the angular velocity and a linear velocity are respectively controlled by means of the cross-track error and an along-track error between the current position and the preview point; and in the algorithm, the angular velocity is controlled by single-closed-loop MFAC, the linear velocity is controlled by dual-closed-loop MFAC, an error term is controlled by weighted collaborative errors of each robot, forward prediction is used to compensate for network communication constraints in control algorithms, and a velocity control quantity after predictive compensation is transmitted to an end-device robot by means of an edge-end network, thereby realizing stable specific-pattern coordinated formation of multiple mobile robots. The method has stronger scenario applicability, flexibility and scalability.

Description

A data-driven formation control method for networked multi-robots under a preview mechanism

[0001] This application claims priority to a Chinese patent application filed with the Patent Office of China on January 16, 2024, with Chinese patent application number 2024100605084, and invention title “A networked multi-robot data-driven formation control method under a preview mechanism,” all or part of which is incorporated by reference into this application. Technical Field

[0002] The present invention belongs to the field of intelligent manufacturing technology, and in particular relates to a networked multi-robot data-driven formation control method under a preview mechanism in a collaborative transportation task of a multi-mobile robot system in an intelligent manufacturing industrial Internet. Background Art

[0003] Intelligent manufacturing is a strategic fulcrum for the transformation and upgrading of the manufacturing industry and an important pillar industry in my country. In recent years, intelligent manufacturing technology represented by robots is gradually becoming a new trend in the development of the new generation of artificial intelligence.

[0004] The Industrial Internet is an essential component of the digitalization, networking, and intelligentization of the manufacturing industry. Through the integration and application of technologies such as the Internet of Things and cloud computing in industry, the Industrial Internet fosters a comprehensive interconnection between humans, machines, and objects. Robots and roboticized equipment are widely used in Industrial Internet manufacturing scenarios. Compared to CNC machine tools, roboticized equipment offers advantages such as greater mobility, greater workspace coverage, and robust parallel collaboration. Multi-robot systems, comprised of a certain scale of individual roboticized equipment, can further increase the workspace and dexterity of robotic operations due to their higher efficiency, scalability, high collaboration, and robustness compared to individual robots. These systems have great potential for application in Industrial Internet scenarios, such as in collaborative transportation involving multiple mobile robots.

[0005] As can be seen from the above, designing high-precision and high-reliability control methods for multi-robot systems is of great significance to the intelligent manufacturing industrial Internet. Taking the problem of multi-robot collaborative transportation in the industrial Internet as an example, achieving the stable operation of multiple robots in a preset formation under wireless network coverage faces several technical difficulties:

[0006] (1) Robot modeling problem: As a nonlinear time-varying system, it is difficult to establish an accurate mathematical model for the robot system. It is necessary to avoid tedious system modeling as much as possible.

[0007] (2) Multi-robot formation coordination problem: This involves the tracking problem of each robot (trajectory tracking, point tracking). In order to achieve autonomous tracking of the robots, it is necessary to achieve stable formation through coordination between the robots.

[0008] (3) Network communication constraint problem: When the end device robot communicates with the corresponding edge node and the nodes in the edge network communicate with each other, the communication network itself will generate constraints such as network delay. The constraints need to be compensated from the perspective of the control algorithm to ensure the control effect.

[0009] Currently, pure tracking control and PID control are commonly used for robot trajectory tracking. Existing formation control modes include virtual structure method, artificial potential field method, behavior-based method, etc., which have many shortcomings, which are specifically reflected in the following aspects:

[0010] (1) Model-based methods rely on mathematical modeling of the controlled object. The accuracy of modeling will seriously affect the control effect, resulting in poor generalization and applicability of the method;

[0011] (2) Some data-based methods lack adaptive adjustment of control parameters, are difficult to describe the characteristics of time-varying systems, and lack good applicability;

[0012] (3) Existing formation methods usually assume an ideal communication environment and do not consider network communication constraints;

[0013] (4) Centralized control method The central computing unit undertakes a large number of computing tasks. As the number of robots increases, the consumption of computing resources and the requirements for communication bandwidth also increase accordingly.

[0014] Based on the above problems, a new high-precision and high-reliability control method for multi-robot systems is urgently needed. Summary of the Invention

[0015] In response to the above technical problems, the present invention provides a data-driven formation control method for networked multi-robots under a preview mechanism.

[0016] The technical solution adopted by the present invention to solve the technical problem is:

[0017] A data-driven formation control method for networked multi-robots under a preview mechanism, the method comprising the following steps:

[0018] S100: Configure the robot for the scene, and the sensor obtains the global posture data of each robot and uploads it to the edge node network;

[0019] S200: The leader edge node P1 receives the posture data from the corresponding leader end robot R1 and the posture data of all follower edge nodes N in total. In node P1, the leader moves along the reference trajectory according to the preview mechanism. Find the navigator preview point and get the navigator's lateral tracking error The reference trajectory is a given posture sequence of length M; the follower robot R i, i=2,…,N+1 Take the leader as the preview point and get the lateral tracking error of follower i

[0020] S300: The navigator node P1 calculates the lateral tracking error of the navigator according to the parameter estimation algorithm Pseudo-partial derivative of the angular velocity relative to the leader and the lateral tracking error of follower i Pseudo-partial derivative of the angular velocity of the follower At the same time, the lateral tracking error and Perform forward prediction compensation, and the lateral tracking error after compensation is and The expected values ​​of the lateral tracking errors of the leader robot and all follower robots are defined as and Based on expected value and Establish the leader's lateral tracking error weighted coordinated error for angular velocity Finally, the angular velocity control value of the navigator at the next moment is updated according to the model-free adaptive control MFAC rate

[0021] S400: Follower R i The corresponding node P i ,i∈{2,…,N+1} receives the corresponding follower robot R i The posture data of the leader node P1 and the rest of the follower nodes P j ,j∈{2,…,N+1},j≠i data, in P i In the process, the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i With other followers R j Then take the navigator as the preview point and get the i In, follower R i , Navigator R1 and other robots R j The lateral tracking error is: and At the same time, get followers R i and other followers R j The longitudinal tracking error The lateral tracking error obtained based on the above process and Calculate the pseudo partial derivative of their relative angular velocity and and longitudinal tracking error Relative linear speed compensation The pseudo partial derivative of The lateral tracking error and longitudinal tracking error are forward predicted and compensated. The lateral tracking error after compensation is The longitudinal tracking error after compensation is

[0022] S500: At node P i According to the expected value of the lateral tracking error of all robots Calculate followers R i Lateral tracking error weighted cooperative error for angular velocity Update the follower R according to the MFAC control rate i Angular velocity value at the next moment According to the expected value of the longitudinal tracking error of all followers Get Followers R i Weighted coordinated error of longitudinal tracking error for linear velocity compensation Update the follower R according to the outer loop MFAC control rate in the dual closed-loop MFAC framework i The linear velocity compensation is

[0023] S600: Follower R i Linear speed compensation Add the current linear velocity to the follower R i Expected speed Rv i Subtract to get the linear velocity error Ve i , calculate the pseudo partial derivative of the linear velocity error with respect to the linear velocity According to R i Expected value of linear velocity error The linear velocity error term is calculated as The follower R is obtained by calculating the inner loop MFAC control rate i Next moment linear speed

[0024] S700: Update the angular velocity in the leader node And the updated linear velocity and angular velocity in all follower nodes The angular velocity control input ω1 is transmitted to the corresponding robot simulation model through the edge-to-end wireless communication network, and the actuator of the leader robot model R1 receives the angular velocity control input ω1, and the actuator of the follower robot model receives the linear velocity angular velocity control input (v2, ω2),..., (v j ,ω j ),(v N+1 ,ω N+1), a new global pose is generated through new control input and then control is performed at the next moment.

[0025] Preferably, the scene configuration of the robot in S100 is specifically as follows:

[0026] Set robot R1 as the leader, R i (i=2,…,N+1) represents any follower, R j ,j∈{2,…,N+1} and j≠i represents the difference between R i For the rest of the followers, the preset formation is determined by the relative distance D between the followers and the leader. i and relative angle A i The leader runs at a constant linear velocity of v1, through the preset formation relationship and preset reference trajectory sequence The proportional factor of the follower's speed relative to the leader's speed is as follows:

[0027] Where Δx d (m) = x d (m)-x d (m-1), Δy d (m) = y d (m)-y d (m-1), that is, the relative coordinates between the mth point and the m-1th point on the reference trajectory; θ d (m) and θ d (m-1) are the expected yaw angles of the mth and m-1th points on the reference trajectory, respectively. Since the relative relationship between the robots in the preset formation remains unchanged, the proportional factor of the follower's speed relative to the leader is an identical constant related only to the reference trajectory and the preset formation, that is, δ 1i =δ 1i (m); then the follower R i The expected speed is Rv i =δ 1i v1;

[0028] In edge-to-end wireless communication networks, there is a time delay between edge nodes and corresponding end devices. In edge node networks, there is also a switching delay between nodes. For example, the edge node P i To the end device R i There is a forward communication delay and reverse communication delay Node P i With node P j There is a switching delay between by Indicates that it comes from the end device R i The data at node P i The delay that needs to be compensated in Display terminal device R j The data at node P i The delay that needs to be compensated is as follows:

[0029] The global posture data of each robot in S100 includes 2D global coordinates and yaw angle S = (x, y, θ) and linear velocity angular velocity V = (v, ω).

[0030] Preferably, S200 includes:

[0031] S210: The leader node P1 receives its own posture data and the posture data of all follower nodes, specifically:

[0032] in, The posture data and speed data of the corresponding robot R1 received by node P1. The posture data includes 2D global coordinates and yaw angle, and the speed data includes linear speed and angular speed. Due to the reverse delay in the communication network during the transmission process from the leader R1 to the corresponding node P1, Therefore, the time item of this part of the data is and Node P1 receives data from follower node P i The posture data and velocity data of the follower R i To the corresponding node P i There is a reverse delay in the transmission process communication network And the follower node P i There is an exchange delay in the communication network with the leader node P1 Therefore, the time item of this part of the data is

[0033] S220: According to the preview mechanism, find the navigator's preview point on the reference trajectory Ref, and according to the preview distance L f Traverse the reference trajectory and find the one whose distance from the current position of the navigator is greater than L f The nearest trajectory point As the current preview point, then according to the navigator's current posture data With the preview point coordinates (x d1 ,y d1 ) The lateral tracking error of the navigator is obtained as follows:

[0034] Among them, L f is the preview distance; is the coordinate of the navigator's preview point; The received horizontal and vertical coordinates and yaw angle data of the navigator are included in middle, Indicates that there is a reverse delay in P1 The lateral tracking error of the leader at time ;

[0035] S230: Follower i takes the navigator's coordinates as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower's coordinates. Coordinates with the navigator The lateral tracking error is obtained as follows:

[0036] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Indicates the received horizontal and vertical coordinates and yaw angle data of follower i, included in the data middle, Indicates that there is a reverse delay in P1 and switching delay The lateral tracking error of follower i is .

[0037] Preferably, S300 includes:

[0038] S310: The pseudo partial derivative is updated or reset in the leader node P1 according to the parameter estimation algorithm, and the pseudo partial derivative of the leader's lateral tracking error relative to the angular velocity ω1 is calculated as follows:

[0039] Where η is the step size factor, μ>0 is the weight factor, Δω1(t)=ω1(t)-ω1(t-1) is the angular velocity increment of the leader at the last moment, and are the pseudo partial derivative obtained by the navigator at the previous moment and the lateral tracking error after forward prediction compensation;

[0040] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0041] Then, the lateral tracking error of follower i at node P1 relative to its angular velocity ω is calculated according to the parameter estimation algorithm. i The pseudo partial derivative of is as follows:

[0042] Similarly, where η is the step size factor, μ>0 is the weight factor, Δω i (t) = ω i (t)-ω i (t-1) is the angular velocity increment of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation;

[0043] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0044] S320: Lateral tracking error of the leader at node P1 The forward prediction compensation is performed as follows:

[0045] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0046] When recursively The lateral tracking error is obtained when again We can get:

[0047] The lateral tracking error after leader compensation in node P1 is obtained

[0048] Lateral tracking error of follower i The forward prediction compensation is performed as follows:

[0049] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0050] When recursively The lateral tracking error is obtained when again We can get:

[0051] The lateral tracking error after follower i compensation in node P1 is obtained

[0052] Preferably, in S300, the expected values ​​of the lateral tracking errors of all robots are calculated. Get the weighted coordinated error of the lateral tracking error of the leader for angular velocity According to the MFAC control rate, the angular velocity control value of the navigator at the next moment is updated as follows: include:

[0053] S330: Based on the formation relationship, the expected value of the robot's lateral tracking error is as follows:

[0054] The error between the lateral tracking error of the leader and follower i and their expected value at node P1 is obtained as follows:

[0055] The weighted coordinated error of the lateral tracking error of the leader for angular velocity is obtained:

[0056] where h 1n is the coordination error coefficient between the leader and followers;

[0057] S340: The MFAC control rate in node P1 updates the navigator angular velocity control input as follows:

[0058] Where ρ,λ>0 are controller parameters.

[0059] Preferably, in S400, the follower R i The corresponding node P i ,i∈{2,…,N+1} receives the corresponding follower robot R i The posture data of the leader node P1 and the rest of the follower nodes P j ,j∈{2,…,N+1},j≠i data, in P i In the process, the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i With other followers R j Then take the navigator as the preview point and get the i In, follower R i , Navigator R1 and other robots R j The lateral tracking error is: and The lateral tracking error obtained based on the above process and Calculate the pseudo partial derivative of their relative angular velocity and The lateral tracking error is forward predicted and compensated, and the compensated lateral tracking error is: Specifically include:

[0060] S410: Follower node P i Receive from the end robot R i Data Data from node P1 and from the remaining follower nodes P j Data

[0061] S420: At node P i According to the preview mechanism, the navigator's preview point is found on the reference trajectory Ref Current location via Navigator The lateral tracking error of the navigator obtained from the preview point is as follows:

[0062] Among them, L f is the preview distance; is the coordinate of the navigator's preview point; P i The received navigator's horizontal and vertical coordinates and yaw angle data are included in middle, Indicates that in P i There is a reverse delay in and switching delay The lateral tracking error of the leader in the case of

[0063] S430: Follower i takes the navigator as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower coordinates. The current position of follower i is received. Position with the navigator The lateral tracking error of follower i is obtained as follows:

[0064] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Respectively represent P i The received horizontal, vertical coordinates and yaw angle data of follower i are included in the data middle, P iThe horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in The lateral tracking error of follower i is:

[0065] S440: Other followers j use the navigator as the preview point. The preview distance is the Euclidean distance between the follower and the navigator. The current position of follower j is received. Position with the navigator The lateral tracking error of follower j is obtained as follows:

[0066] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the two-dimensional Euclidean distance between the leader and follower j. Respectively represent P i The received horizontal and vertical coordinates and yaw angle data of follower j are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in and switching delay The lateral tracking error of follower j in the case;

[0067] S450: At follower node P i The lateral tracking error of follower i is calculated based on the parameter estimation algorithm Relative angular velocity ω i Pseudo partial derivatives are as follows:

[0068] Where η is the step size factor, μ>0 is the weight factor, Δω i (t) = ω i (t)-ω i (t-1) is the angular velocity increment of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation;

[0069] If satisfied Δω i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0070] Then calculate the node P according to the parameter estimation algorithm i Lateral tracking error of the pilot The pseudo partial derivative with respect to its angular velocity ω1 is as follows:

[0071] Where η is the step size factor, μ>0 is the weight factor, Δω1(t)=ω1(t)-ω1(t-1) is the angular velocity increment of the leader at the last moment, and are the pseudo partial derivative obtained by the navigator at the previous moment and the lateral tracking error after forward prediction compensation;

[0072] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0073] At follower node P i The lateral tracking error of follower j is calculated according to the parameter estimation algorithm Relative angular velocity ω j Pseudo partial derivatives are as follows:

[0074] Where η is the step size factor, μ>0 is the weight factor, Δω j (t) = ω j (t)-ω j (t-1) is the angular velocity increment of follower j at the previous moment, and are the pseudo partial derivative obtained by follower j at the previous moment and the lateral tracking error after forward prediction compensation;

[0075] If satisfied Δω j (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0076] S460: At node P i Lateral tracking error of follower i The forward prediction compensation is performed as follows:

[0077] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0078] When recursively The lateral tracking error is obtained when again We can get:

[0079] Get at node P i Lateral tracking error after follower i compensation

[0080] At node P i Lateral tracking error of the pilot The forward prediction compensation is performed as follows:

[0081] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged.

[0082] Right now:

[0083] When recursively The lateral tracking error is obtained when again We can get:

[0084] Get at node P i Lateral tracking error after compensation by the Navigator

[0085] At node P i The lateral tracking error of follower j The forward prediction compensation is performed as follows:

[0086] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0087] When recursively The lateral tracking error is obtained when again Available

[0088] Get at node P i The lateral tracking error after follower j compensation

[0089] Preferably, in S400, the node P is obtained. i The longitudinal tracking error of follower i and other followers j is Thus calculate their relative linear velocity compensation The pseudo partial derivative of The longitudinal tracking error is forward predicted and compensated, and the compensated longitudinal tracking error is: Specifically include:

[0090] S470: Node P i The follower i takes the navigator as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower coordinates. Position with the navigator The longitudinal tracking error of follower i is obtained as follows:

[0091] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Represents P i The received horizontal, vertical coordinates and yaw angle data of follower i are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in The longitudinal tracking error of follower i is:

[0092] Node P i Other followers j also use the navigator as the preview point, and the preview distance is also the Euclidean distance between the navigator and its coordinates. Position with the navigator The lateral tracking error of follower j is obtained as follows:

[0093] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the two-dimensional Euclidean distance between the leader and follower j. Represents P i The received horizontal and vertical coordinates and yaw angle data of follower j are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in and switching delay The longitudinal tracking error of follower j in the case;

[0094] S480: Node P i Calculate the pseudo partial derivative of the longitudinal tracking error of follower i and follower j relative to the linear velocity compensation, and get the pseudo partial derivative of follower i and the pseudo-partial derivative of follower j as follows:

[0095] Where η is the step size factor, μ>0 is the weight factor, Δc i (t) = c i (t)-c i (t-1) is the increment of the linear velocity compensation of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the longitudinal tracking error after forward prediction compensation;

[0096] If satisfied Δc i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0097] Where η is the step size factor, μ>0 is the weight factor, Δc j (t) = c j (t)-c j (t-1) is the increment of the linear velocity compensation of follower j at the last moment, and are the pseudo partial derivative obtained by follower j at the previous moment and the longitudinal tracking error after longitudinal prediction compensation;

[0098] If satisfied Δc j (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0099] S490: Longitudinal tracking error of follower i and follower j Perform forward prediction compensation to obtain the longitudinal tracking errors of follower i and follower j after compensation and

[0100] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0101] When recursively The longitudinal tracking error is obtained when again We can get:

[0102] Get at node P i The longitudinal tracking error after follower i compensation

[0103] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0104] When recursively The longitudinal tracking error is obtained when again We can get:

[0105] Get at node P i The longitudinal tracking error after follower j compensation

[0106] Preferably, in S500, at node P i According to the expected value of the lateral tracking error of all robots Calculate the lateral tracking error weighted coordination error of follower i for angular velocity Update the angular velocity value of follower i according to the MFAC control rate Specifically include:

[0107] S510: Based on the formation relationship, the expected values ​​of the lateral tracking errors of follower i, leader, and follower j are as follows:

[0108] So we get the node P i The error between the lateral tracking error of follower i, leader and follower j and their expected value as follows:

[0109] The weighted cooperative error of the lateral tracking error of follower i for angular velocity is obtained:

[0110] where h in is the collaborative error coefficient of other robots relative to follower i;

[0111] S520: Node P i The MFAC control rate updates the angular velocity of follower i at the next moment as follows:

[0112] Where ρ,λ>0 are controller parameters.

[0113] Preferably, in S500, the expected longitudinal tracking errors of all followers are calculated based on the expected longitudinal tracking errors of all followers. Get Followers R i Weighted coordinated error of longitudinal tracking error for linear velocity compensation Update the follower R according to the outer loop MFAC control rate i The linear velocity compensation is Specifically include:

[0114] S530: Based on the formation relationship, the expected longitudinal tracking errors of follower i and follower j are as follows:

[0115] Get in P i The longitudinal tracking error of each follower and the expected error value are as follows:

[0116] The longitudinal tracking error weighted coordination error of follower i for the linear velocity compensation is obtained:

[0117] where h in is the collaborative error coefficient of other robots relative to follower i;

[0118] S540: At node Pi The outer loop MFAC control rate of the dual closed-loop MFAC framework for linear speed control updates the linear speed compensation of follower i at the next moment as follows:

[0119] Where ρ,λ>0 are controller parameters.

[0120] Preferably, S600 includes:

[0121] Follower i linear velocity compensation Add the current linear velocity to the follower R i Expected speed Rv i The linear velocity error obtained by subtraction is as follows:

[0122] Calculate Ve i Pseudo-partial derivative of relative linear velocity

[0123] Where η is the step size factor, μ>0 is the weight factor, Δv i (t) = v i (t)-v i (t-1) is the linear velocity increment of follower i at the previous moment, and Ve i (t) are the pseudo partial derivative and linear velocity error obtained by follower j at the previous moment;

[0124] If satisfied Δv i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0125] Calculating the error term The expected value of the linear velocity error The linear velocity of follower i at the next moment is obtained by calculating the inner loop MFAC control rate

[0126] Where ρ,λ>0 are controller parameters.

[0127] Preferably, S700 includes: From the above, it can be seen that the updated angular velocity in the leader node is The updated linear and angular velocities in all follower nodes are The angular velocity control input received by the leader robot R1 actuator is ω1(t+1), and the linear velocity control input received by the follower robot actuator is {v2(t+1),ω2(t+1)},...,{v N+1 (t+1),ω N+1 (t+1)}, that is, during the transmission process through the edge-to-end wireless communication network:

[0128] A new global pose is generated through new control input and then control is performed at the next moment.

[0129] In the above-mentioned networked multi-robot data-driven formation control method under the preview mechanism, the end-device mobile robot has a corresponding node in the edge node network under the wireless edge-to-end wireless communication network architecture. The sensor obtains the global posture of the mobile robot, and the data is transmitted bidirectionally between nodes and between nodes and corresponding end devices. A leader-follower formation method is adopted, in which the leader robot has a constant linear velocity and uses a preview mechanism to determine the preview point on the reference trajectory. The angular velocity is controlled by the model-free adaptive control (MFAC) algorithm through the lateral tracking error between the current position and the preview point; the follower uses the leader's coordinates as the preview point, and controls the angular velocity and linear velocity respectively through the lateral tracking error and longitudinal tracking error between the current position and the preview point, so as to achieve the effect of tracking the leader in a preset formation; in the algorithm, the angular velocity control adopts a single closed-loop MFAC framework, the linear velocity control adopts a double closed-loop MFAC framework, the control error term adopts the weighted collaborative error of each robot, and the forward prediction is used in the control algorithm to compensate for the network communication constraints. The speed control quantity after prediction compensation is transmitted to the end device robot via the edge-to-end wireless communication network, realizing a stable specific formation collaborative formation of multiple mobile robots. The method is data-driven control, and the calculation process only uses the input and output data of the controlled system. There is no need to model the system, which effectively solves the strong dependence of the model-driven control algorithm on the mathematical model of the controlled object and the interference of the system modeling accuracy on the control effect; the forward prediction mechanism in the method predicts and compensates for the communication delay in the physical communication network, effectively reducing the impact of network communication constraints on the control effect; this invention provides an effective and feasible method for multi-robot collaborative transportation and other operational tasks in industrial Internet manufacturing scenarios, which has stronger scenario applicability, flexibility and scalability than traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] FIG1 is a flow chart of a networked multi-robot data-driven formation control method under a preview mechanism according to one embodiment of the present invention;

[0131] FIG2 is a control block diagram of a networked multi-robot data-driven formation control method under a preview mechanism according to one embodiment of the present invention;

[0132] FIG3 is a schematic diagram of an edge-to-end wireless communication network configuration according to an embodiment of the present invention;

[0133] FIG4 is a diagram of a preset formation in one embodiment of the present invention;

[0134] FIG5 is a 3D collaborative formation simulation effect of three robots in the simulation software Coppeliasim according to one embodiment of the present invention;

[0135] FIG6 is a 2D plane trajectory of three robots in a cooperative formation according to an embodiment of the present invention;

[0136] FIG7 is a lateral tracking error (CTE) attenuation curve of each robot in one embodiment of the present invention;

[0137] FIG8 is an attenuation curve of the longitudinal tracking error (ATE) of each robot in one embodiment of the present invention;

[0138] FIG9 is an angular velocity control input curve of each robot in one embodiment of the present invention;

[0139] FIG10 is a linear velocity control input curve of each robot in one embodiment of the present invention;

[0140] FIG11 is an adaptive adjustment curve of the pseudo partial derivative of the lateral tracking error with respect to the angular velocity according to one embodiment of the present invention;

[0141] FIG12 is an adaptive adjustment curve of the pseudo-partial derivative of the longitudinal tracking error relative to the linear velocity compensation amount in one embodiment of the present invention;

[0142] FIG13 is an adaptive adjustment curve of the pseudo-partial derivative of the linear velocity error with respect to the linear velocity in one embodiment of the present invention. DETAILED DESCRIPTION

[0143] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0144] In one embodiment, as shown in FIG1 and FIG2 , a data-driven formation control method for a networked multi-robot system under a preview mechanism is provided, the method comprising the following steps:

[0145] S100: Configure the robot for the scene, and the sensor obtains the global posture data of each robot and uploads it to the edge node network;

[0146] S200: The leader edge node P1 receives the posture data from the corresponding leader end robot R1 and the posture data of all follower edge nodes N in total. In node P1, the leader moves along the reference trajectory according to the preview mechanism. Find the navigator preview point and get the navigator's lateral tracking error The reference trajectory is a given posture sequence of length M; the follower robot R i , i=2,…,N+1 Take the leader as the preview point and get the lateral tracking error of follower i

[0147] S300: The navigator node P1 calculates the lateral tracking error of the navigator according to the parameter estimation algorithm Pseudo-partial derivative of the angular velocity relative to the leader and the lateral tracking error of follower i Pseudo-partial derivative of the angular velocity of the follower At the same time, the lateral tracking error and Perform forward prediction compensation, and the lateral tracking error after compensation is and The expected values ​​of the lateral tracking errors of the leader robot and all follower robots are defined as and Based on expected value and Establish the leader's lateral tracking error weighted coordinated error for angular velocity Finally, the angular velocity control value of the navigator at the next moment is updated according to the model-free adaptive control MFAC rate

[0148] S400: Follower corresponding node P i ,i∈{2,…,N+1} receives the corresponding follower robot R i The posture data of the leader node P1 and the rest of the follower nodes P j ,j∈{2,…,N+1},j≠i data, in P i In the process, the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i With other followers R j Then take the navigator as the preview point and get the i In, follower R i , Navigator R1 and other robots R j The lateral tracking error is: and At the same time, get followers R i and other followers Rj The longitudinal tracking error The lateral tracking error obtained based on the above process and Calculate the pseudo partial derivative of their relative angular velocity and and longitudinal tracking error Relative linear speed compensation The pseudo partial derivative of The lateral tracking error and longitudinal tracking error are forward predicted and compensated. The lateral tracking error after compensation is The longitudinal tracking error after compensation is

[0149] S500: At node P i According to the expected value of the lateral tracking error of all robots Calculate followers R i Lateral tracking error weighted cooperative error for angular velocity Update the follower R according to the MFAC control rate i Angular velocity value at the next moment According to the expected value of the longitudinal tracking error of all followers Get Followers R i Lateral tracking error weighted cooperative error for angular velocity Update the follower R according to the outer loop MFAC control rate in the dual closed-loop MFAC framework i The linear velocity compensation is

[0150] S600: Follower R i Linear speed compensation Add the current linear velocity to the follower R i Expected speed Rv i Subtract to get the linear velocity error Ve i , calculate the pseudo partial derivative of the linear velocity error with respect to the linear velocity According to R i Expected value of linear velocity error The error term for linear velocity is calculated as The follower R is obtained by calculating the inner loop MFAC control rate i Next moment linear speed

[0151] S700: Update the angular velocity in the leader node And the updated linear velocity and angular velocity in all follower nodes The angular velocity control input ω1 is transmitted to the corresponding robot simulation model through the edge-to-end wireless communication network, and the actuator of the leader robot model R1 receives the angular velocity control input ω1, and the actuator of the follower robot model receives the linear velocity angular velocity control input (v2, ω2),..., (v j ,ω j ),(v N+1 ,ω N+1 ), a new global pose is generated through new control input and then control is performed at the next moment.

[0152] In one embodiment, the scene configuration of the robot in S100 is specifically as follows:

[0153] Set robot R1 as the leader, R i (i=2,…,N+1) represents any follower, P j ,j∈{2,…,N+1} and j≠i represents the difference between R i For the rest of the followers, the preset formation is determined by the relative distance D between the followers and the leader. i and relative angle A i The leader runs at a constant linear velocity of v1, through the preset formation relationship and preset reference trajectory sequence The proportional factor of the follower's speed relative to the leader's speed is as follows:

[0154] Where Δx d (m) = x d (m)-x d (m-1), Δy d (m) = y d (m)-y d (m-1), that is, the relative coordinates between the mth point and the m-1th point on the reference trajectory; θ d (m) and θ d (m-1) are the expected yaw angles of the mth and m-1th points on the reference trajectory, respectively. Since the relative relationship between the robots in the preset formation remains unchanged, the proportional factor of the follower's speed relative to the leader is an identical constant related only to the reference trajectory and the preset formation, that is, δ 1i =δ 1i (m); then the follower R i The expected speed is Rv i =δ 1i v1;

[0155] In edge-to-end wireless communication networks, there is a time delay between edge nodes and corresponding end devices. In edge node networks, there is also a switching delay between nodes. For example, the edge node P i To the end device R i There is a forward communication delay and reverse communication delay Node P i With node P j There is a switching delay between by Indicates that it comes from the end device R i The data at node P i The delay that needs to be compensated in Display terminal device R j The data at node P i The delay that needs to be compensated is as follows:

[0156] That is, the total delay corresponding to the current node in a certain node consists of two parts (the forward and reverse delays between the node and the corresponding end device), and the total delay corresponding to other nodes in the node consists of three parts (the forward and reverse delays between other nodes and the end devices corresponding to other nodes, and the exchange delay between other nodes and the node);

[0157] The global posture data of each robot in S100 includes 2D global coordinates and yaw angle S = (x, y, θ) and linear velocity angular velocity V = (v, ω).

[0158] Specifically, the edge-to-end wireless communication network configuration diagram is shown in FIG3 , where R i With R j Represents two follower robots, R1 is the leader robot, P1, P i ,P j They represent their corresponding edge nodes in the edge node network. Taking the navigator as an example, there is a forward communication delay between the navigator node P1 and the navigator robot R1 through the edge-to-end wireless communication network. and reverse communication delay P1 and other edge nodes P i ,P j There is a switching delay between In the simulation example, we set all forward and reverse communication delays to 3 time steps and the exchange delay to 2 time steps.

[0159] Furthermore, the preset formation is shown in FIG4 ; wherein R i With R j represents two follower robots, R1 is the leader robot, the relative distance between each follower and the leader is 1.5m, and the relative angle is 60°, that is, D i =D j =1.5(m),A i =Aj =60°.

[0160] In one embodiment, S200 includes:

[0161] S210: The leader node P1 receives its own posture data and the posture data of all follower nodes, specifically:

[0162] in, The posture data and speed data of the corresponding robot R1 received by node P1 include the 2D global coordinates and yaw angle, and the speed data include linear speed and angular speed. Due to the reverse delay in the communication network during the transmission process from R1 to the corresponding node P1, Therefore, the time item of this part of the data is and Node P1 receives data from follower node P i The posture data and velocity data of the follower R i To the corresponding node P i There is a reverse delay in the transmission process communication network And the follower node P i There is an exchange delay in the communication network with the leader node P1 Therefore, the time item of this part of the data is

[0163] S220: According to the preview mechanism, find the navigator's preview point on the reference trajectory Ref, and according to the preview distance L f Traverse the reference trajectory and find the one whose distance from the current position of the navigator is greater than L f The nearest trajectory point As the current preview point, then according to the navigator's current posture data With the preview point coordinates (x d1 ,y d1 ) The lateral tracking error of the navigator is obtained as follows:

[0164] Among them, L f is the preview distance; is the coordinate of the navigator's preview point; The received horizontal and vertical coordinates and yaw angle data of the navigator are included in middle, Indicates that there is a reverse delay in P1 The lateral tracking error of the leader at time ;

[0165] S230: Follower i takes the navigator's coordinates as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower's coordinates. Coordinates with the navigator The lateral tracking error is obtained as follows:

[0166] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Indicates the received horizontal and vertical coordinates and yaw angle data of follower i, included in the data middle, Indicates that there is a reverse delay in P1 and switching delay The lateral tracking error of follower i is .

[0167] In one embodiment, S300 includes:

[0168] S310: The pseudo partial derivative is updated or reset in the leader node P1 according to the parameter estimation algorithm, and the pseudo partial derivative of the leader's lateral tracking error relative to the angular velocity ω1 is calculated as follows:

[0169] Where η is the step size factor, μ>0 is the weight factor, Δω1(t)=ω1(t)-ω1(t-1) is the angular velocity increment of the leader at the last moment, and are the pseudo partial derivative obtained by the navigator at the previous moment and the lateral tracking error after forward prediction compensation;

[0170] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0171] Then, the lateral tracking error of follower i at node P1 relative to its angular velocity ω is calculated according to the parameter estimation algorithm. i The pseudo partial derivative of is as follows:

[0172] Similarly, where η is the step size factor, μ>0 is the weight factor, Δω i (t) = ω i (t)-ω i (t-1) is the angular velocity increment of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation;

[0173] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0174] S320: Lateral tracking error of the leader at node P1 The forward prediction compensation is performed as follows:

[0175] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0176] When recursively The lateral tracking error is obtained when again We can get:

[0177] The lateral tracking error after leader compensation in node P1 is obtained

[0178] Lateral tracking error of follower i The forward prediction compensation is performed as follows:

[0179] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0180] When recursively The lateral tracking error is obtained when again We can get:

[0181] The lateral tracking error after follower i compensation in node P1 is obtained

[0182] In one embodiment, in S300, the expected values ​​of the lateral tracking errors of all robots are calculated. Get the weighted coordinated error of the lateral tracking error of the leader for angular velocity According to the MFAC control rate, the angular velocity control value of the navigator at the next moment is updated as follows: include:

[0183] S330: Based on the formation relationship, the expected value of the robot's lateral tracking error is as follows:

[0184] The error between the lateral tracking error of the leader and follower i and their expected value at node P1 is obtained as follows:

[0185] The weighted coordinated error of the lateral tracking error of the leader for angular velocity is obtained:

[0186] where h 1n is the coordination error coefficient between the leader and followers;

[0187] S340: At node P1, the MFAC control rate updates the navigator angular velocity control input as follows:

[0188] Where ρ,λ>0 are controller parameters.

[0189] In one embodiment, the follower node P in S400 i ,i∈{2,…,N+1} receives the corresponding follower robot R i The posture data of the leader node P1 and the rest of the follower nodes P j ,j∈{2,…,N+1},j≠i data, in P i In the process, the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i With other followers R j Then take the navigator as the preview point and get the i In, follower R i , Navigator R1 and other robots R j The lateral tracking error is: and The lateral tracking error obtained based on the above process and Calculate the pseudo partial derivative of their relative angular velocity and The lateral tracking error is forward predicted and compensated, and the compensated lateral tracking error is: Specifically include:

[0190] S410: Follower node P i Receive from the end robot R i Data (R i To P i There is a time delay in the communication network during the transmission process Therefore, the time item of this part of the data is ), data from node P1 (There is a delay in the communication network during the transmission from R1 to P1 And P i There is a switching delay in the communication network with P1 Therefore, the time item of this part of the data is ) and from the remaining follower nodes P j Data (The rest of the followers are short robots R j To P j There is a time delay in the communication network during the transmission process And P i With P j There is a switching delay in the communication network Therefore, the time item of this part of the data is

[0191] S420: At node P i According to the preview mechanism, the navigator's preview point is found on the reference trajectory Ref Current location via Navigator The lateral tracking error of the navigator obtained from the preview point is as follows:

[0192] Among them, L f is the preview distance; is the coordinate of the navigator's preview point; P i The received navigator's horizontal and vertical coordinates and yaw angle data are included in middle, Indicates that in P i There is a reverse delay in and switching delay The lateral tracking error of the leader in the case of

[0193] S430: Follower i takes the navigator as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower coordinates. The current position of follower i is received. Position with the navigator The lateral tracking error of follower i is obtained as follows:

[0194] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Represents P i The received horizontal, vertical coordinates and yaw angle data of follower i are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in The lateral tracking error of follower i is:

[0195] S440: Other followers j use the navigator as the preview point. The preview distance is the Euclidean distance between the follower and the navigator. The current position of follower j is received. Position with the navigator The lateral tracking error of follower j is obtained as follows:

[0196] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the two-dimensional Euclidean distance between the leader and follower j. Represents P i The received horizontal and vertical coordinates and yaw angle data of follower j are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in and switching delay The lateral tracking error of follower j in the case of

[0197] S450: At follower node P i The lateral tracking error of follower i is calculated based on the parameter estimation algorithm Relative angular velocity ω i Pseudo partial derivatives are as follows:

[0198] Where η is the step size factor, μ>0 is the weight factor, Δω i (t) = ω i (t)-ω i (t-1) is the angular velocity increment of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation;

[0199] If satisfied Δω i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0200] Then calculate the node P according to the parameter estimation algorithm i Lateral tracking error of the pilot The pseudo partial derivative with respect to its angular velocity ω1 is as follows:

[0201] Where η is the step size factor, μ>0 is the weight factor, Δω1(t)=ω1(t)-ω1(t-1) is the angular velocity increment of the leader at the last moment, and are the pseudo partial derivative obtained by the navigator at the previous moment and the lateral tracking error after forward prediction compensation;

[0202] If satisfied Δω1(t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0203] At follower node P i The lateral tracking error of follower j is calculated according to the parameter estimation algorithm Relative angular velocity ω j Pseudo partial derivatives are as follows:

[0204] Where η is the step size factor, μ>0 is the weight factor, Δω j (t) = ω j (t)-ω j (t-1) is the angular velocity increment of follower j at the previous moment, and are the pseudo partial derivative obtained by follower j at the previous moment and the lateral tracking error after forward prediction compensation;

[0205] If satisfied Δωj (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0206] S460: At node P i Lateral tracking error of follower i The forward prediction compensation is performed as follows:

[0207] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0208] When recursively The lateral tracking error is obtained when again We can get:

[0209] Get at node P i Lateral tracking error after follower i compensation

[0210] At node P i Lateral tracking error of the pilot The forward prediction compensation is performed as follows:

[0211] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0212] When recursively The lateral tracking error is obtained when again We can get:

[0213] Get at node P i Lateral tracking error after compensation by the Navigator

[0214] At node P i The lateral tracking error of follower j The forward prediction compensation is performed as follows:

[0215] in Similarly, k ranges from 1 to The pseudo partial derivative in the recursive process The value remains unchanged, that is:

[0216] When recursively The lateral tracking error is obtained when again Available

[0217] Get at node P i The lateral tracking error after follower j compensation

[0218] In one embodiment, S400 obtains the i The longitudinal tracking error of follower i and other followers j is Thus, their relative linear velocity compensation is calculated The pseudo partial derivative of The longitudinal tracking error is forward predicted and compensated, and the compensated longitudinal tracking error is: Specifically include:

[0219] S470: Node P i The follower i takes the navigator as the preview point, and the preview distance is the Euclidean distance between the navigator and the follower coordinates. Position with the navigator The longitudinal tracking error of follower i is obtained as follows:

[0220] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the two-dimensional Euclidean distance between the leader and follower i. Respectively represent P i The received horizontal, vertical coordinates and yaw angle data of follower i are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in The longitudinal tracking error of follower i is:

[0221] Node Pi Other followers j also use the navigator as the preview point, and the preview distance is also the Euclidean distance between the navigator and its coordinates. Position with the navigator The lateral tracking error of follower j is obtained as follows:

[0222] Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the two-dimensional Euclidean distance between the leader and follower j. Respectively represent P i The received horizontal and vertical coordinates and yaw angle data of follower j are included in the data middle, P i The horizontal and vertical coordinates of the navigator received, Indicates that in P i There is a reverse delay in and switching delay The longitudinal tracking error of follower j in the case;

[0223] S480: Node P i Calculate the pseudo partial derivative of the longitudinal tracking error of follower i and follower j relative to the linear velocity compensation, and get the pseudo partial derivative of follower i and the pseudo-partial derivative of follower j as follows:

[0224] Where η is the step size factor, μ>0 is the weight factor, Δc i (t) = c i (t)-c i (t-1) is the increment of the linear velocity compensation of follower i at the previous moment, and are the pseudo partial derivative obtained by follower i at the previous moment and the longitudinal tracking error after forward prediction compensation;

[0225] If satisfied Δc i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0226] Where η is the step size factor, μ>0 is the weight factor, Δcj (t) = c j (t)-c j (t-1) is the increment of the linear velocity compensation of follower j at the last moment, and are the pseudo partial derivative obtained by follower j at the previous moment and the longitudinal tracking error after longitudinal prediction compensation;

[0227] If satisfied Δc j (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0228] S490: Longitudinal tracking error of follower i and follower j Perform forward prediction compensation to obtain the longitudinal tracking errors of follower i and follower j after compensation and

[0229] in k ranges from 1 to Perform recursion, pseudo partial derivatives in the recursive process The value remains unchanged, that is:

[0230] When recursively The longitudinal tracking error is obtained when again We can get:

[0231] Get at node P i The longitudinal tracking error after follower i compensation

[0232] in Similarly, k ranges from 1 to Pseudo-partial derivatives in recursive procedures The value remains unchanged, that is:

[0233] When recursively The longitudinal tracking error is obtained when again We can get:

[0234] Get at node P i The longitudinal tracking error after follower j compensation

[0235] In one embodiment, in S500, at node P i According to the expected value of the lateral tracking error of all robots Calculate the lateral tracking error weighted coordination error of follower i for angular velocity Update the angular velocity value of follower i according to the MFAC control rate Specifically include:

[0236] S510: Based on the formation relationship, the expected values ​​of the lateral tracking errors of follower i, leader, and follower j are as follows:

[0237] So we get the node P i The error between the lateral tracking error of follower i, leader and follower j and their expected value as follows:

[0238] The weighted cooperative error of the lateral tracking error of follower i for angular velocity is obtained:

[0239] where h in is the collaborative error coefficient of other robots relative to follower i;

[0240] S520: Node P i The MFAC control rate updates the angular velocity of follower i at the next moment as follows:

[0241] Where ρ,λ>0 are controller parameters.

[0242] In one embodiment, in S500, the expected longitudinal tracking errors of all followers are calculated based on the expected longitudinal tracking errors of all followers. Get Followers R i Weighted coordinated error of longitudinal tracking error for linear velocity compensation Update the follower R according to the outer loop MFAC control rate i The linear velocity compensation is Specifically include:

[0243] S530: Based on the formation relationship, the expected values ​​of the longitudinal tracking errors of follower i and follower j are as follows:

[0244] Get in P i The longitudinal tracking error of each follower and the expected error value are as follows:

[0245] The longitudinal tracking error weighted coordination error of follower i for the linear velocity compensation is obtained:

[0246] where h in is the collaborative error coefficient of other robots relative to follower i;

[0247] S540: At node P i The outer loop MFAC control rate of the dual closed-loop MFAC framework for linear speed control updates the linear speed compensation of follower i at the next moment as follows:

[0248] Where ρ,λ>0 are controller parameters.

[0249] In one embodiment, S600 includes:

[0250] Follower i linear velocity compensation Add the current linear velocity to the follower R i Expected speed Rv i The linear velocity error obtained by subtraction is as follows:

[0251] Calculate Ve i Pseudo-partial derivative of relative linear velocity

[0252] Where η is the step size factor, μ>0 is the weight factor, Δv i (t) = v i (t)-v i (t-1) is the linear velocity increment of follower i at the previous moment, and Ve i (t) are the pseudo partial derivative and linear velocity error obtained by follower j at the previous moment;

[0253] If satisfied Δv i (t)≤ε or If any of the conditions are met, the parameters will be reset, namely: Where ε is a positive constant, and its value is set to 10 -5 , sign(·) is a sign function that outputs the positive or negative value in the brackets;

[0254] Calculating the error term The expected value of the linear velocity error The linear velocity of follower i at the next moment is obtained by calculating the inner loop MFAC control rate

[0255] Where ρ,λ>0 are controller parameters.

[0256] In one embodiment, S700 includes: From the above, it can be seen that the updated angular velocity in the leader node is The updated linear and angular velocities in all follower nodes are The angular velocity control input of the leader robot R1 actuator is ω1(t+1), and the follower robots R2, R3, ..., R N+1 The actuator accepts linear velocity and angular velocity control inputs as {v2(t+1),ω2(t+1)},...,{v N+1 (t+1),ω N+1 (t+1)}, that is, during the transmission process through the edge-to-end infinite communication network:

[0257] A new global pose is generated through new control input and then control is performed at the next moment.

[0258] In one embodiment of the present invention, the 3D collaborative formation simulation effect of three robots in the simulation software Coppeliasim is shown in Figure 5, where the white track is the reference track of the leader robot R1, and the sphere is the visualization of the preview point found by the leader robot R1 on the reference track according to the preview mechanism. The robot in the front (corresponding to the middle robot) is R1, and the corresponding track is the visualized driving track of R1. The two robots in the back, namely the robot in the inner circle and the robot in the outer circle, are the follower robots R2 and R3 respectively, and the corresponding tracks are the visualized driving tracks of R2 and R3 respectively. It can be seen that the preset formation effect is well achieved in the 3D simulation process.

[0259] The 2D plane trajectory of three robots in a collaborative formation in one embodiment of the present invention is shown in Figure 6. A leader robot R1 and two follower robots R2 and R3 are set. It can be seen that R1 travels along the reference trajectory well, and R2 and R3 perform formation tracking well from different positions according to the preset formation.

[0260] In one embodiment of the present invention, the lateral tracking error (CTE) attenuation curves for each robot are shown in Figure 7. It can be seen that the lateral tracking errors of all three robots converge to the values ​​corresponding to the preset formation. The longitudinal tracking error (ATE) attenuation curves for each robot are shown in Figure 8. It can be seen that the lateral tracking errors of both followers converge to the values ​​corresponding to the preset formation. The angular velocity control input curves for each robot are shown in Figure 9. It can be seen that the angular velocities of all three robots converge on the time axis. Since the ideal formation trajectory is a triple concentric circle, the angular velocities of all three robots converge to the same value. The linear velocity control input curves for each robot are shown in Figure 10. It can be seen that the linear velocities of both robots converge on the time axis. Since follower R3 is on the outside, its linear velocity converges to a larger value. The adaptive adjustment curve of the pseudo-partial derivative of the lateral tracking error with respect to the angular velocity is shown in Figure 11. The adaptive adjustment of the pseudo-partial derivative is clearly visible. The adaptive adjustment curve of the pseudo-partial derivative of the longitudinal tracking error with respect to the linear velocity compensation is shown in Figure 12. The adaptive adjustment of the pseudo-partial derivative is clearly visible. The adaptive adjustment curve of the pseudo partial derivative of the linear velocity error relative to the linear velocity is shown in FIG13 , from which the adaptive adjustment of the pseudo partial derivative can be intuitively seen.

[0261] In the above-mentioned networked multi-robot data-driven formation control method under the preview mechanism, the end-device mobile robot has a corresponding node in the edge node network under the wireless edge-to-end wireless communication network architecture. The sensor obtains the global posture of the mobile robot, and the data is transmitted bidirectionally between nodes and between nodes and corresponding end devices. A leader-follower formation method is adopted, in which the leader robot has a constant linear velocity and uses a preview mechanism to determine the preview point on the reference trajectory. The angular velocity is controlled by the model-free adaptive control (MFAC) algorithm through the lateral tracking error between the current position and the preview point; the follower uses the leader's coordinates as the preview point, and controls the angular velocity and linear velocity respectively through the lateral tracking error and longitudinal tracking error between the current position and the preview point, so as to achieve the effect of tracking the leader in a preset formation; in the algorithm, the angular velocity control adopts a single closed-loop MFAC framework, the linear velocity control adopts a double closed-loop MFAC framework, the control error term adopts the weighted collaborative error of each robot, and the forward prediction is used in the control algorithm to compensate for the network communication constraints. The speed control quantity after prediction compensation is transmitted to the end device robot via the edge-to-end wireless communication network, realizing a stable specific formation collaborative formation of multiple mobile robots. The method is data-driven control, and the calculation process only uses the input and output data of the controlled system. There is no need to model the system, which effectively solves the strong dependence of the model-driven control algorithm on the mathematical model of the controlled object and the interference of the system modeling accuracy on the control effect; the forward prediction mechanism in the method predicts and compensates for the communication delay in the physical communication network, effectively reducing the impact of network communication constraints on the control effect; this invention provides an effective and feasible method for multi-robot collaborative transportation and other operational tasks in industrial Internet manufacturing scenarios, which has stronger scenario applicability, flexibility and scalability than traditional methods.

[0262] The above is a detailed introduction to the networked multi-robot data-driven formation control method under a preview mechanism provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only intended to help understand the core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A data-driven formation control method for networked multi-robots under a preview mechanism, characterized in that The method includes the following steps: S100: Configure the scenario for the robot, and the sensor acquires the global pose data of each robot and uploads it to the edge node network; S200: The leader edge node P1 receives the pose data from the corresponding leader - side robot R1 and the pose data of all follower edge nodes with a total number of N. In node P1, the leader, according to the preview mechanism, on the reference trajectory Search for the preview point to obtain the lateral tracking error of the leader Among them, the reference trajectory is a given attitude sequence with a length of M; the follower robot R i , i = 2, …, N + 1 uses the leader as the preview point to obtain the lateral tracking error of the follower i S300: Calculate the lateral tracking error of the leader in node P1 according to the parameter estimation algorithm Pseudo-partial derivative of the relative angular velocity with respect to the leader and the lateral tracking error of follower i Pseudo partial derivative with respect to the follower angular velocity Meanwhile, for the lateral tracking error and Perform forward prediction compensation, and the lateral tracking error after compensation is and Define the expected values of the lateral tracking errors of the leader robot and all follower robots as And and based on the expected value And Establish the weighted collaborative error of the lateral tracking error of the leader with respect to the angular velocity Finally, update the angular velocity control quantity of the leader at the next moment according to the MFAC control rate S400: Follower Node P i , i ∈ {2, …, N + 1} receives the attitude data of the corresponding follower - side robot R i , the data of the leader node P1, and the data of the remaining follower nodes P j , j ∈ {2, …, N + 1}, j ≠ i. In P i , the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i and other followers R j take the leader as the preview point to obtain the lateral tracking errors of the follower R i in the node P i , the leader R1, and other robots R j , that is: And Simultaneously obtain follower R i and other followers R j longitudinal tracking error Lateral tracking error obtained based on the above process And Calculate the pseudo-partial derivative of their relative angular velocity And and longitudinal tracking error Relative linear velocity compensation amount Pseudo-partial derivative Perform forward prediction compensation on the lateral tracking error and the longitudinal tracking error. The compensated lateral tracking error is The compensated longitudinal tracking error is S500: At node P i among them, according to the expected values of the lateral tracking errors of all robots Calculating follower R i Lateral tracking error weighted cooperation error for angular velocity Update the follower R according to the MFAC control rate i Angular velocity value at the next moment According to the expected value of the longitudinal tracking error of all followers Obtain follower R i Longitudinal tracking error weighted collaborative error for linear velocity compensation amount Update the follower R according to the outer-loop MFAC control rate in the double-closed-loop MFAC framework i The linear velocity compensation amount of S600: Follower R i Linear velocity compensation amount Add it to the linear velocity at the current moment and compare it with the follower R i Desired velocity Rv i Subtract to obtain the linear velocity error Ve i , calculate the pseudo partial derivative of the linear velocity error with respect to the linear velocity According to R i Expected value of linear velocity error Calculate the error term for the linear velocity as The follower R is calculated through the inner-loop MFAC control rate i Linear velocity at the next moment S700: The updated angular velocity in the pilot node and the updated linear and angular velocities in all follower nodes It is transmitted to the corresponding end-robot simulation model through the edge-end wireless communication network. The actuator of the leader robot model R1 receives the angular velocity control input ω1, and the actuators of the follower robot models receive the linear velocity and angular velocity control inputs (v2, ω2),..., (v j , ω j ), (v N+1 , ω N+1 ). New global poses are generated through the new control inputs for the control at the next moment.

2. The method according to claim 1, wherein The specific scenario configuration for the robot in S100 is: Set the robot R1 as the leader, R i , i = 2, …, N + 1 represents any one of the followers, R j , j ∈ {2, …, N + 1} and j ≠ i represents the other followers except R i The preset formation is composed of the relative distance D i of the followers relative to the leader and the relative angle A i . The leader runs at a constant linear velocity of v1. Through the preset formation relationship and the preset reference trajectory sequence The proportionality factor of the follower's speed relative to the leader's speed can be obtained as follows: where, Δx d (m) = x d (m) - x d (m - 1), Δy d (m) = y d (m) - y d (m - 1), that is, the relative coordinates between the m-th point and the (m - 1)-th point on the reference trajectory; θ d (m) and θ d (m - 1) are the expected yaw angles of the m-th point and the (m - 1)-th point on the reference trajectory respectively. Since the relative relationship between the robots in the preset formation remains unchanged, the proportionality factor of the follower's speed relative to the leader is a constant identical only related to the reference trajectory and the preset formation, that is, δ 1i = δ 1i (m); then the expected speed of the follower R i is Rv i = δ 1i v1; In the edge-terminal wireless communication network, there is a time delay between the edge node and the corresponding terminal device. In the edge node network, there is also an exchange time delay between nodes. For example, for edge node P i to terminal device R i there is a forward communication time delay and reverse communication delay Node P i With Node P j There is an exchange delay With Indicates the latency that needs to be compensated for the data from the terminal device R i in node P i and Indicates the end device R j The data at node P i The delay that needs to be compensated is as follows: The global pose data of each robot in S100 includes 2D global coordinates and yaw angle S = (x, y, θ) and linear velocity and angular velocity V = (v, ω).

3. The method according to claim 2, characterized in that, S200 includes: S210: The leader node P1 receives its own attitude data and the attitude data of all follower nodes, specifically: Among them, The attitude data and speed data of the corresponding end robot R1 received by node P1. The attitude data includes 2D global coordinates and yaw angle, and the speed data includes linear velocity and angular velocity. Since there is reverse time delay in the communication network during the transmission from R1 to node P1 Therefore, the time term is t - while For node P1 to receive attitude data and velocity data from follower node P i Since there is reverse time delay in the communication network during the transmission to the corresponding node P i i ​​ And the follower node P i There is an exchange delay with the leader node P1 Therefore, the data time item for this part is S220: Search for the leader preview point on the reference trajectory Ref according to the preview mechanism, and traverse the reference trajectory according to the preview distance L f to find the one that is related to the current position of the leader The distance is greater than L f of the nearest trajectory point As the current look-ahead point, and then according to the look-ahead point coordinates With the current pose data of the leader The lateral tracking error of the leader is obtained as follows: Among them, L f is the preview distance; is the leader preview point coordinate; The received leader's horizontal and vertical coordinates and yaw angle data, included in Among them, Indicates the existence of reverse time delay in P1 The lateral tracking error of the leader at... S230: Follower i uses the leader's coordinates as the preview point, and the preview distance is the Euclidean distance between the leader's and follower's coordinates. Based on the received pose of follower i With the coordinates of the leader The following lateral tracking error is obtained: Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the Euclidean distance of the two-dimensional coordinates between the leader and the follower i. Indicates the received horizontal and vertical coordinates and yaw angle data of follower i, included in the data In Indicates the existence of reverse time delay in P1 and switching delay The lateral tracking error of follower i at...

4. The method according to claim 3, wherein S300 includes: S310: In the leader node P1, perform pseudo partial derivative update or reset according to the parameter estimation algorithm, and calculate the pseudo partial derivative of the leader's lateral tracking error with respect to the relative angular velocity ω1 as follows: where η is the step factor, μ > 0 is the weight factor, Δω1(t) = ω1(t) - ω1(t - 1) is the angular velocity increment of the leader at the previous moment, and They are respectively the pseudo partial derivatives obtained by the leader at the previous moment and the lateral tracking error after forward prediction compensation; If satisfied Δω1(t) ≤ ε or For any of the conditions, parameter reset is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; Then, according to the parameter estimation algorithm, calculate the pseudo partial derivative of the lateral tracking error of follower i in node P1 relative to its angular velocity ω i as follows: Similarly, where η is the step factor, μ > 0 is the weight factor, and Δω i (t) = ω i (t) - ω i (t - 1) is the angular velocity increment of the follower i at the previous moment, and They are respectively the pseudo partial derivatives obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation; If satisfied Δω1(t) ≤ ε or For any of these conditions, parameter resetting is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; S320: Perform lateral tracking error of the leader in node P1 Perform forward prediction compensation as follows: Among them k ranges from 1 to Perform recursion, and the pseudo partial derivative during the recursion Remain unchanged, i.e.: When recursing to when obtaining a lateral tracking error Also It can be obtained that: Obtain the lateral tracking error after leader compensation in node P1 Lateral tracking error of follower i Perform forward prediction compensation as follows: Among them Similarly, k ranges from 1 to Pseudo-partial derivatives in the recursive process Remain unchanged, i.e.: When recursing to When the lateral tracking error is obtained Also It can be obtained that: Obtain the compensated lateral tracking error of follower i in node P1 5. The method according to claim 4, wherein In S300, according to the expected values of the lateral tracking errors of all robots Obtain the weighted collaborative error of the lateral tracking error of the leader with respect to the angular velocity Update the angular velocity control quantity of the leader at the next moment according to the MFAC control law as Including: S330: The expected value of the lateral tracking error of the robot is obtained according to the formation relationship as follows: The error value between the lateral tracking error of the leader and follower i in node P1 and its expected value is obtained as follows: Obtain the weighted collaborative error of the leader for the lateral tracking error with respect to the angular velocity: where h 1n is the collaborative error coefficient between the leader and the followers; S340: The MFAC control rate update in node P1 for the leader angular velocity control input is as follows: Where ρ, λ > 0 are controller parameters.

6. The method according to claim 5, characterized in that, Follower node P in S400 i , i ∈ {2, …, N + 1} receives the attitude data of the corresponding follower - side robot R i , the data of the leader node P1, and the data of the remaining follower nodes P j , j ∈ {2, …, N + 1}, j ≠ i, in P i , the leader searches for its preview point on the reference trajectory Ref according to the preview mechanism, while the follower R i and other followers R j take the leader as the preview point, obtaining in the node P i , the lateral tracking errors of the follower R i , the leader R1, and other robots R j , that is: and the lateral tracking error obtained based on the above - mentioned process and calculate the pseudo - partial derivative of their relative angular velocity perform forward - prediction compensation on the lateral tracking error, and the compensated lateral tracking error is Specifically, it includes: S410: Follower node P i Receives data from the end robot R i ​ Data from node P1 and data from the remaining follower nodes P j ​ S420: Search for the leader preview point on the reference trajectory Ref according to the preview mechanism at node P i ​ Through the current position of the navigator The lateral tracking error of the leader with respect to the preview point is as follows: Among them, L f is the preview distance; is the coordinates of the leader preview point; Respectively P i The received leader's horizontal and vertical coordinates and yaw angle data, which are included in In Indicates the existence of reverse time delay in P i ​ and switching delay The lateral tracking error of the leader in the case of... S430: Follower i uses the leader as the preview point, and the preview distance is the Euclidean distance between the leader's and the follower's coordinates. Based on the currently received pose of follower i With the pose of the leader The lateral tracking error of follower i is obtained as follows: Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the Euclidean distance of the two-dimensional coordinates between the leader and the follower i. Respectively represent P i The received horizontal and vertical coordinates and yaw angle data of follower i, included in the data In For P i Received navigator horizontal and vertical coordinates Indicates the existence of reverse time delay in P i ​ The lateral tracking error of follower i at... S440: Other follower j uses the leader as the preview point, and the preview distance is the Euclidean distance of the coordinates between the follower and the leader. Based on the currently received pose of follower j With the pose of the leader The following is the lateral tracking error of follower j: Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the Euclidean distance of the two-dimensional coordinates between the leader and the follower j. respectively represent P i the received horizontal and vertical coordinates and yaw angle data of follower j, included in the data In For P i Received pilot's horizontal and vertical coordinates Indicates the existence of reverse time delay in P i ​ and switching delay The lateral tracking error of follower j in the case of... S450: In the follower node P i perform pseudo partial derivative update or reset according to the parameter estimation algorithm, and calculate the lateral tracking error of follower i relative to its angular velocity ω i The pseudo partial derivative is as follows: where η is the step size factor, μ > 0 is the weight factor, and Δω i (t) = ω i (t) - ω i (t - 1) is the angular velocity increment of follower i at the previous moment, And They are respectively the pseudo partial derivatives obtained by follower i at the previous moment and the lateral tracking error after forward prediction compensation; If satisfied Δω i (t) ≤ ε or For any of these conditions, parameter reset is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; Then calculate the lateral tracking error of the leader in node P according to the parameter estimation algorithm i ​ Pseudo-partial derivative with respect to its angular velocity ω1, as follows: where η is the step factor, μ > 0 is the weight factor, Δω1(t) = ω1(t) - ω1(t - 1) is the angular velocity increment of the leader at the previous moment, And They are respectively the pseudo partial derivatives obtained by the leader at the previous moment and the lateral tracking error after forward prediction compensation; If satisfied Δω1(t) ≤ ε or For any of these conditions, parameter resetting is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , and sign(·) is the sign function, which outputs the positive or negative value of the number within the parentheses; At the follower node P i calculate the lateral tracking error of follower j according to the parameter estimation algorithm with respect to its angular velocity ω j the pseudo partial derivative is as follows: where η is the step factor, μ > 0 is the weight factor, and Δω j (t) = ω j (t) - ω j (t - 1) is the angular velocity increment of follower j at the previous moment, And They are respectively the pseudo partial derivatives obtained by follower j at the previous moment and the lateral tracking error after forward prediction compensation; If satisfied Δω j (t) ≤ ε or For any of these conditions, parameter resetting is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; S460: At node P i for the lateral tracking error of follower i Perform forward prediction compensation as follows: Among them k ranges from 1 to Perform recursion, and during the recursion process, the pseudo partial derivative Remain unchanged, i.e.: When recursively reaching to obtain a lateral tracking error Also It can be obtained that: Obtain the compensated lateral tracking error of follower i at node P i ​ At node P i for the lateral tracking error of the leader Perform forward prediction compensation as follows: Among them Similarly, k ranges from 1 to Pseudo partial derivatives in the recursive process The value remains unchanged, i.e.: When recursing to to obtain a lateral tracking error Also It can be obtained that: Obtain the lateral tracking error after leader compensation at node P i ​ At node P i the lateral tracking error of follower j Perform forward prediction compensation as follows: Among them Similarly, k ranges from 1 to Pseudo-partial derivatives in the recursive process The value remains unchanged, i.e.: When recursing to a lateral tracking error is obtained Also It can be obtained Obtain the compensated lateral tracking error of follower j at node P i ​ 7. The method according to claim 6, wherein Obtained at node P in S400 i In it, the longitudinal tracking errors of follower i and other followers j Thereby calculating their relative linear velocity compensation amounts Of the pseudo partial derivatives Perform forward prediction compensation on the longitudinal tracking error, and the compensated longitudinal tracking error is Specifically include: S470: Node P i In this, follower i uses the leader as the preview point, and the preview distance is the Euclidean distance between the leader's and the follower's coordinates. Based on the currently received pose of follower i With the pose of the leader The longitudinal tracking error of follower i is obtained as follows: Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,i) is the Euclidean distance of the two-dimensional coordinates between the leader and the follower i. Respectively represent P i The horizontal and vertical coordinates and yaw angle data of the received follower i, which are included in the data In For P i Received navigator horizontal and vertical coordinates Indicates the existence of reverse time delay in P i ​ The longitudinal tracking error of follower i at... Node P i Among the other followers j, they also use the leader as the preview point, and the preview distance is also the Euclidean distance between the leader and its coordinates. Based on the currently received pose of follower j With the pose of the leader The following is the lateral tracking error of follower j: Among them, dist(·,·) represents the Euclidean distance operator, and dist(1,j) is the Euclidean distance of the two-dimensional coordinates between the leader and the follower j. Respectively represent P i The received horizontal and vertical coordinates and yaw angle data of follower j, which are included in the data In For P i Received pilot horizontal and vertical coordinates Indicates the existence of reverse time delay in P i ​ and switching delay The longitudinal tracking error of follower j in the case of... S480: Node P i Calculate the pseudo partial derivative of the longitudinal tracking error of follower i and follower j with respect to the linear velocity compensation amount in [Node P], and obtain the pseudo partial derivative of follower i and the pseudo partial derivative of follower j As follows: where η is the step size factor, μ > 0 is the weight factor, and Δc i (t) = c i (t) - c i (t - 1) is the increment of the linear velocity compensation of follower i at the previous moment, and They are respectively the pseudo partial derivatives obtained by follower i at the previous moment and the longitudinal tracking error after forward prediction compensation; If satisfied Δc i (t) ≤ ε or For any of the conditions, parameter reset is performed, i.e.: where ε represents a positive constant, whose value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; where η is the step factor, μ > 0 is the weight factor, and Δc j (t) = c j (t) - c j (t - 1) is the increment of the linear velocity compensation of follower j at the previous moment, And They are respectively the pseudo partial derivatives obtained by follower j at the previous moment and the longitudinal tracking error after longitudinal prediction compensation; If satisfied Δc j (t) ≤ ε or For any of these conditions, parameter resetting is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; S490: Longitudinal tracking error of follower i and follower j Perform forward prediction compensation to obtain the longitudinal tracking errors of the compensated follower i and follower j And Among them k ranges from 1 to Perform recursion, and the pseudo partial derivative during the recursion The value remains unchanged, i.e.: When recursing to to obtain a longitudinal tracking error Also It can be obtained that: Obtain the compensated longitudinal tracking error of follower i at node P i ​ Among them Similarly, k ranges from 1 to Pseudo-partial derivatives in the recursive process The value remains unchanged, i.e.: When recursing to When the longitudinal tracking error is obtained Also It can be obtained that: Obtain the compensated longitudinal tracking error of follower j at node P i ​ 8. The method according to claim 7, wherein In S500 at node P i According to the expected values of all robots' lateral tracking errors Calculate the weighted collaborative error of the lateral tracking error of follower i with respect to the angular velocity Update the angular velocity value of follower i according to the MFAC control law Specifically including: S510: The expected values of the lateral tracking errors of the follower i, the leader, and the follower j according to the formation relationship are as follows: Thus, the error values of the lateral tracking errors of follower i, the leader, and follower j and their expected values at node P are obtained i ​ As follows: Obtain the weighted collaborative error of the lateral tracking error of follower i with respect to the angular velocity: where h in is the collaborative error coefficient of other robots relative to follower i; S520: Node P i The MFAC control rate in it updates the angular velocity of follower i at the next moment As follows: Where ρ, λ > 0 are controller parameters.

9. The method according to claim 8, wherein The expected value of the longitudinal tracking error of all followers in S500 to obtain the follower R i The longitudinal tracking error weighted collaborative error for the linear velocity compensation amount Update the follower R according to the outer loop MFAC control rate i The linear velocity compensation amount of Specifically include: S530: The expected values of the longitudinal tracking errors of follower i and follower j according to the formation relationship are as follows: The longitudinal tracking errors of each follower in P i and the expected error values are as follows: Obtain the longitudinal tracking error weighted collaborative error of follower i with respect to the linear velocity compensation amount: where h in is the collaborative error coefficient of other robots relative to follower i; S540: At node P i Update the follower i's next moment linear velocity compensation amount with the outer-loop MFAC control rate of the double-closed-loop MFAC framework for linear velocity control As follows: Where ρ, λ > 0 are controller parameters.

10. The method according to claim 9, characterized in that S600 includes: Linear velocity compensation amount of follower i Add it to the linear velocity at the current moment and subtract it from the follower R i Desired velocity Rv i Subtract to obtain the linear velocity error as follows: Calculate Ve i Pseudo partial derivative of the relative linear velocity where η is the step factor, μ > 0 is the weight factor, and Δv i (t) = v i (t) - v i (t - 1) is the linear velocity increment of the follower i at the previous moment, and Ve i (t) are the pseudo partial derivative and the linear velocity error obtained by follower j at the previous moment, respectively; If satisfied Δv i (t) ≤ ε or If any of the conditions is met, parameter reset is performed, i.e.: where ε represents a positive constant, and its value is set to 10 -5 , sign(·) is the sign function, which outputs the positive or negative value of the number inside the parentheses; Calculation error term where the expected value of the linear velocity error The linear velocity of follower i at the next moment is calculated by the inner-loop MFAC control rate Where ρ, λ > 0 are controller parameters.

11. The method according to claim 10, wherein S700 includes: As described above, the angular velocity is updated in the leader node as The linear velocity and angular velocity are updated in all follower nodes as It is transmitted to the corresponding end-robot simulation model through the edge-end wireless communication network. The actuator of the leader robot R1 receives the angular velocity control input as ω1(t + 1), and the followers robots R2, R3,..., R N+1 The actuator receives the linear velocity and angular velocity control inputs as {v2(t + 1), ω2(t + 1)},..., {v N+1 (t + 1), ω N+1 (t + 1)}, that is, during the transmission through the edge-end wireless communication network: Generate a new global pose through the new control input and then perform the control for the next moment.

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