Data-driven bipartite-consensus control method for turning large-sized workpiece by means of multi-robot collaboration

Abstract

A data-driven bipartite-consensus control method for turning a large-sized workpiece by means of multi-robot collaboration. The method comprises the following steps: providing a multi-robot system; establishing a dynamic model for follower robots, discretizing the dynamic model, and constructing a lateral error on the basis of position information between the follower robots and a leader robot; constructing an unknown nonlinear function by using the lateral error and a control input as variables, and establishing a lateral-error data model for the follower robots by using a dynamic linearization technique; designing a bipartite-consensus error on the basis of a topological relationship of the multi-robot system and the lateral error, and in combination with the data model, substituting the bipartite-consensus error into a designed objective function to obtain a data-driven bipartite-consensus controller; designing a parameter estimation algorithm to estimate unknown parameters in the controller, wherein when a corresponding resetting algorithm is satisfied, calculated estimated values are involved in the update of the controller; and calculating a front-wheel steering-angle control signal on the basis of a data-driven bipartite-consensus control algorithm. The control method can ensure the precision and safety in the process in which multiple robots collaboratively move and turn a large-sized workpiece.

Description

A data-driven binary consensus control method for multi-machine collaborative rotation of large workpieces

[0001] This application claims the priority of the Chinese patent application submitted to the China Patent Office on September 8, 2023, the application number of the Chinese patent application is 2023111547092, and the name of the invention is "A data-driven binary consistency control method for multi-machine collaborative rotation of large workpieces", all or part of which are incorporated by reference in this application. Technical Field

[0002] The present invention relates to the technical field of multi-robot collaborative handling control, and in particular to a data-driven binary consensus control method for multi-robot collaborative rotation of a large workpiece. Background Art

[0003] In recent years, intelligent manufacturing equipment, exemplified by swarm robots, has become essential for achieving high-quality manufacturing of large, complex components. Thanks to their flexible movements and strong coordination capabilities, swarm robots can efficiently replace human labor in complex environments to complete specific tasks. Therefore, designing autonomous, coordinated control methods for multiple robots is crucial in the field of intelligent manufacturing.

[0004] Mobile robots have evolved from remote control to autonomy, from cable-towed to wireless, and have now become a mature mobile platform. Equipped with appropriate supporting components, mobile platforms can be applied to various intelligent manufacturing scenarios. For example, radar can be installed to achieve 2D mapping, while binocular cameras can be installed to perform 3D scanning of large workpieces. Furthermore, when equipped with a robotic arm, the mobile platform becomes a mobile robot capable of handling, rotation, and assembly tasks. As researchers delve deeper, some have applied mobile robots equipped with robotic arms to grasping and assembly tasks, replace force sensors for contact force measurement, and utilize parallel robotic arms for biomimetic tasks.

[0005] In the field of intelligent manufacturing, multi-robot collaborative handling, as an essential component of the industry, is driving the development of mobile robots from single to multi-robot systems. Although some scholars have conducted some research on this topic, there are still some difficulties that need to be overcome. For example, when multiple robots are handling large workpieces, they are always limited by the workpiece volume and external space. Therefore, achieving the task of rotating large workpieces during handling with a minimum rotation radius is a problem worth studying.

[0006] Summary of the Invention

[0007] The technical problem to be solved by the present invention is that, considering that multiple robots are always limited by the volume of the workpiece and the external space when carrying large workpieces, a data-driven binary consensus control method for the collaborative rotation of large workpieces by multiple machines is provided to achieve the task of completing the workpiece rotation task with the minimum rotation radius.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] A data-driven binary consensus control method for multi-machine collaborative rotation of a large workpiece, the method comprising the following steps:

[0010] S100: setting a multi-robot system for implementing a rotation task to include a static leader robot that only provides a desired signal and two follower robots;

[0011] S200: establishing a rotational dynamics model of the follower robot, discretizing the rotational dynamics model to obtain a corresponding discrete model, and then constructing a lateral error between the follower and the leader robot based on position information between the follower and the leader robot;

[0012] S300: Based on the discrete model, an unknown nonlinear function is constructed with the lateral error and the control input as variables, and a lateral error data model of the follower robot is established by applying a dynamic linearization technique to the unknown nonlinear function;

[0013] S400: Based on the topological relationship of the multi-robot system and the lateral error between the follower and leader robots, a bipartite consensus error is constructed for the rotation task. The bipartite consensus error and lateral error data model are substituted into the designed control input objective function to solve the data-driven bipartite consensus controller. A parameter estimation algorithm is designed to estimate the unknown parameters in the controller. The calculated estimated values ​​participate in the controller update under the condition that the designed reset algorithm is satisfied. The parameter estimation algorithm, reset algorithm and controller together constitute a data-driven bipartite consensus control algorithm for the coordinated rotation of large workpieces by multiple robots.

[0014] S500: Calculate the front wheel angle control signal based on the data-driven binary consensus control algorithm and input it to the multi-robot system to complete the rotation control of the large workpiece.

[0015] Preferably, the multi-robot system in S100 includes: a quadrotor representing a leader robot and two robotic arm mobile robots as followers, wherein there is an antagonistic effect between the follower robots, wherein the antagonistic effect means that the running direction is opposite to the direction of the front wheel turning angle.

[0016] Preferably, S200 includes:

[0017] S210: Establish a rotational dynamics model for a single follower robot, specifically:

[0018] Where n∈{1,2} represents the nth follower robot, x n is the lateral displacement of the nth follower robot, y n is the longitudinal displacement of the nth follower robot system, θ n is the heading angle of the nth follower robot system, v0 is the constant speed of the follower robot system during the rotation process, u n The control input signal represents the front wheel steering angle of the nth follower robot system, L is the wheelbase of the follower robot, and are the lateral displacement x of the nth follower robot system n , longitudinal displacement y n and heading angle θ n The first derivative of ;

[0019] S220: Discretize the rotational dynamics model of the single follower robot to obtain a discrete model of the single follower robot, specifically:

[0020] Where, T s is the sampling time, k∈{1,2,…,∞} is the discrete moment, x n (k+1),y n (k+1) and θ n (k+1) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the k+1th moment, x n (k), y n (k) and θ n (k) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the kth moment, L and v0 are the wheelbase and constant speed, u n (k) is the control input signal of the nth follower robot system at the kth moment, i.e., the front wheel angle;

[0021] S230: Constructing a lateral error between the follower robot and the leader robot based on the position information between the follower robot and the leader robot.

[0022] Preferably, the lateral error between the nth follower and the leader robot at the kth moment in S230 is specifically: n (k) = l d ·cos(α n (k))

[0023] Where, in and is the expected signal required by the nth follower provided by the leader; l d is the forward sight distance.

[0024] Preferably, S300 includes:

[0025] S310: Based on the discrete model, an unknown nonlinear function is constructed with the lateral error and control input as variables, specifically: n (k+1)=f n (u n (k),…,u n (kn u +1),e n (k),…,e n (kn e +1),x n (k),y n (k),θ n (k))

[0026] Where, e n (k+1) is the lateral error of the nth follower robot at the k+1th time; f n (…) is an unknown scalar nonlinear function that u +n e All variables are partially derivative and the partial derivatives are continuous, where n u and n e are two unknown positive integers, used to represent the input and output orders of the system; u n (kn u +1) and e n (kn e +1) are the nth follower robot in the knth u The control input at time +1 and the control input at time kn e +1 moment lateral error;

[0027] S320: By using the dynamic linearization technology on the unknown nonlinear system function, a lateral error data model of the follower robot is established, specifically:

[0028] Where, is the pseudo gradient of the nth robot; ΔH n (k)=[Δu n (k),…,Δu n (kL u +1),Δe n (k),…,Δe n (kL e +1)] Tis the vector of all control input increments and system output increments of the nth robot; where 1≤L u ≤n u and 0≤L e ≤n e are two positive integers selected according to the complexity of the system, L e , L u are the pseudo-orders of input and output of the multi-robot system respectively; Δu n (k)=u n (k)-u n (k-1); Δe n (k) = e n (k)-e n (k-1).

[0029] Preferably, S400 includes:

[0030] S410: Constructing a bipartite consensus error for the rotation task based on the topological relationship of the multi-robot system and the lateral error between the follower and leader robots;

[0031] S420: Substituting the bipartite consistent error and lateral error data models into the designed control input objective function to solve the data-driven bipartite consistent controller;

[0032] S430: Designing a parameter estimation algorithm for estimating unknown parameters in the controller;

[0033] S440: The calculated estimated value participates in the update of the controller under the condition of satisfying the designed reset algorithm, wherein the parameter estimation algorithm, the reset algorithm and the controller together constitute a data-driven bipartite consensus control algorithm for the collaborative rotation of large workpieces by multiple machines.

[0034] Preferably, S410 specifically includes:

[0035] Where, E n (k) represents the bipartite consensus error of the nth follower robot at the kth moment, a i,j is the robot's final adjacency matrix A∈R 3×3 The element in row i and column j, where a 3,j and a i,3 Represents the topological communication relationship between the leader robot and the follower robot, i, j∈{1,2,3}; e * (k) is the expected signal of the lateral error; sign is the sign function, that is:

[0036] Preferably, the control input objective function in S420 is specifically:

[0037] Where J(·) is the nth follower robot’s control input u n (k) objective function; is the penalty factor of the objective function of the nth follower robot;

[0038] For u in the control input objective function n (k) Calculate the partial derivative and obtain the data-driven bipartite consistency controller as follows:

[0039] Where, ρ i is the step size factor, i∈{1,2,…,L u +L e ); It is the element on the main diagonal of the in-degree matrix, that is, D = diag(d1, d2, d3).

[0040] Preferably, the parameter estimation algorithm in S430 is specifically:

[0041] Where η∈(0,2] and μ∈[0,∞) are the corresponding step size factor and penalty factor respectively; is φ n (k) estimated value;

[0042] The reset algorithm in S440 is as follows:

[0043] if or ||ΔH n (k-1)||≤ε or

[0044] Where ε is a very small positive number.

[0045] Preferably, the data-driven binary consensus control algorithm in S500 is specifically:

[0046] This data-driven binary consensus control method for the coordinated rotation of large workpieces by multiple robots employs a data-driven binary consensus controller to achieve the task of rotation by synchronizing follower robots along a reference trajectory in opposite directions, under the guidance of a static leader robot. This data-driven control approach means that the controller design relies solely on the I / O data of the controlled system, without requiring a precise dynamic model. This simplified controller design process, as it eliminates the need for a dynamic model, makes it a user-friendly control design approach. Furthermore, this method ensures the accuracy and safety of multiple robots during the coordinated rotation of large workpieces. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] FIG1 is a flow chart of a data-driven binary consensus control method for a multi-machine coordinated rotation of a large workpiece according to an embodiment of the present invention;

[0048] FIG2 is a schematic diagram of the positions and lateral errors of multiple robots during the collaborative handling and rotation of a large workpiece according to one embodiment of the present invention;

[0049] FIG3 is a schematic diagram of a data-driven binary consensus control method for a multi-machine coordinated rotation of a large workpiece according to an embodiment of the present invention;

[0050] FIG4 is a topological diagram of a multi-robot system according to an embodiment of the present invention;

[0051] FIG5 is a diagram showing the position tracking effect of three robots in the process of collaboratively transporting a large workpiece and rotating it in accordance with an embodiment of the present invention;

[0052] FIG6 is a diagram showing the tracking effect of the x-axis components of two follower robots during the rotation of three robots in one embodiment of the present invention;

[0053] FIG7 is a diagram showing the tracking effect of the y-axis components of two follower robots during the rotation of three robots in one embodiment of the present invention;

[0054] FIG8 is a control input curve of follower robots No. 1 and No. 2 during the rotation of three robots in one embodiment of the present invention;

[0055] FIG9 is a pseudo partial derivative adaptive adjustment curve of follower robot No. 1 during the rotation of three robots in one embodiment of the present invention;

[0056] FIG10 is a pseudo partial derivative adaptive adjustment curve of follower No. 2 during the rotation of three robots in one embodiment of the present invention;

[0057] FIG11 is a rendering of the ratio of the lateral error to the rotation radius of follower robots No. 1 and No. 2 during the rotation of three robots in one embodiment of the present invention;

[0058] FIG12 is a mean square error curve between follower robots No. 1 and No. 2 during the rotation of three robots in one embodiment of the present invention. DETAILED DESCRIPTION

[0059] 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.

[0060] In one embodiment, as shown in FIG1 , a data-driven binary consensus control method for rotating a large workpiece in coordination with multiple machines is provided, the method comprising the following steps:

[0061] S100: Setting a multi-robot system for implementing a rotation task to include a static leader robot that only provides a desired signal and two follower robots.

[0062] In one embodiment, the multi-robot system in S100 includes: a quadrotor representing a leader robot and two robotic arm mobile robots as followers, wherein there is an antagonistic effect between the follower robots, wherein the antagonistic effect means that the running direction is opposite to the direction of the front wheel turning angle.

[0063] S200: Establishing a rotational dynamics model of the follower robot, and then discretizing the rotational dynamics model to obtain a corresponding discrete model, and then constructing a lateral error between the follower and the leader robot based on the position information between the follower and the leader robot.

[0064] Specifically, a schematic diagram of the multi-robot position and lateral error is shown in FIG2 . Before establishing the rotational dynamics model of the follower robot, the prescribed performance and performance function of the robot are set, and the position error of the robot is determined according to the prescribed performance and performance function.

[0065] In one embodiment, S200 includes:

[0066] S210: Establish a rotational dynamics model for a single follower robot, specifically:

[0067] Where n∈{1,2} represents the nth follower robot, x n is the lateral displacement of the nth follower robot, y n is the longitudinal displacement of the nth follower robot system, θ n is the heading angle of the nth follower robot system, v0 is the constant speed of the follower robot system during the rotation process, u n The control input signal represents the front wheel steering angle of the nth follower robot system, L is the wheelbase of the follower robot, and are the lateral displacement x of the nth follower robot system n , longitudinal displacement y n and heading angle θ n The first derivative of ;

[0068] S220: Discretize the rotational dynamics model of the single follower robot to obtain a discrete model of the single follower robot, specifically:

[0069] Where, T s is the sampling time, k∈{1,2,…,∞} is the discrete moment, x n (k+1),yn (k+1) and θ n (k+1) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the k+1th moment, x n (k), y n (k) and θ n (k) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the kth moment, L and v0 are the wheelbase and constant speed, u n (k) is the control input signal of the nth follower robot system at the kth moment, i.e., the front wheel angle;

[0070] S230: Constructing a lateral error between the follower robot and the leader robot based on the position information between the follower robot and the leader robot.

[0071] In one embodiment, the lateral error between the nth follower and the leader robot at the kth moment in S230 is specifically: n (k) = l d ·cos(α n (k))(3)

[0072] Where, in and is the expected signal required by the nth follower provided by the leader; l d is the forward sight distance.

[0073] Furthermore, the foresight distance is an adjustable parameter. The larger the parameter value is, the smoother the tracking curve is. On the contrary, the tracking curve fluctuates frequently.

[0074] S300: Based on the discrete model, an unknown nonlinear function is constructed with the lateral error and the control input as variables, and a lateral error data model of the follower robot is established by applying dynamic linearization technology to the unknown nonlinear function.

[0075] In one embodiment, S300 includes:

[0076] S310: Based on the discrete model, an unknown nonlinear function is constructed with the lateral error and control input as variables, specifically: n (k+1)=f n (u n (k),…,u n (kn u +1),e n (k),…,e n (kn e +1),x n (k),y n (k),θn (k))(4)

[0077] Where, e n (k+1) is the lateral error of the nth follower robot at the k+1th time; f n (…) is an unknown scalar nonlinear function that u +n e All variables are partially derivative and the partial derivatives are continuous, where n u and n e are two unknown positive integers representing the input and output orders of the system; u n (kn u +1) and e n (kn e +1) are the nth follower robot in the knth u The control input at time +1 and the control input at time kn e +1 lateral error at moment.

[0078] Specifically, u and n e The value of n depends on the complexity of the nonlinear system. u and n e The larger the value of .

[0079] S320: By using the dynamic linearization technology on the unknown nonlinear system function, a lateral error data model of the follower robot is established, specifically:

[0080] Where, is the pseudo gradient of the nth robot; ΔH n (k)=[Δu n (k),…,Δu n (kL u +1),Δe n (k),…,Δe n (kL e +1)] T is the vector of all control input increments and system output increments of the nth robot; where 1≤L e ≤n e and 0≤L u ≤n u are two positive integers selected according to the complexity of the system, L e , L u are the pseudo-orders of input and output of the multi-robot system respectively; Δu n (k)=u n (k)-u n (k-1); Δe n(k) = e n (k)-e n (k-1).

[0081] Specifically, the general nonlinear system equation is established based on the lateral error, and the process is as follows:

[0082] 1) Substitute the discrete dynamic equation of the follower robot into the lateral error calculation formula to obtain the rewritten error transmission dynamic model:

[0083] Subtract (3) from (6) to get

[0084] Where Δe n (k+1)=e n (k+1)-e n (k) is the lateral error increment of the nth follower robot at the k+1th time.

[0085] According to formula (7), the lateral error e n (k+1) and variable e n (k), x n (k), y n (k), θ n (k) and u n (k) is relevant, so e n (k+1) is the dependent variable, and the remaining variables are independent variables to establish an unknown nonlinear function. The specific formula is as follows: n (k+1)=g n (u n (k),e n (k),x n (k),y n (k),θ n (k)) (8)

[0086] Where g n (…) is an unknown nonlinear function.

[0087] In order to make the nonlinear function more general, g n (…) is rewritten as follows: e n (k+1)=f n (u n (k),…,u n (kn u +1),e n (k),…,e n (kn θ +1),x n (k),y n (k),θn (k)) (9)

[0088] Where, f n (…) is the rewritten general unknown nonlinear system, for the first n u +n e The variables are partially differentiable and the partial derivatives are continuous.

[0089] 2) Combining the rewritten nonlinear system (9), using the Cauchy mean value theorem, we can get:

[0090] Where h n =f n (u n (k-1),…,u n (kn u ),e n (k-1),…,e n (kn θ ),x n (k),y n (k),θ n (k)) -f n (u n (k-1),…,u n (kn u ),e n (k-1),…,e n (kn θ ),x n (k-1),y n (k-1),θ n (k-1)).

[0091] Because h n The variables in are known or can be calculated according to formula (3), so h n There must be a solution that makes the following equation true:

[0092] Where ΔH n (k)=[Δu n (k),…,Δu n (kL u +1),Δe n (k),…,Δe n (kL e +1)] T ,ζ n =[ζ n,1 ,…,ζ n,2 ] T is a constant vector.

[0093] Then, substituting formula (11) into formula (10) we can get

[0094] Finally, let the column vector φ n (k) satisfies the following equation,

[0095] Then formula (12) can be rewritten as That is, formula (5) holds.

[0096] S400: Based on the topological relationship of the multi-robot system and the lateral error between the follower and the leader robot, a bipartite consensus error is constructed for the rotation task. The bipartite consensus error and lateral error data model are substituted into the designed control input objective function to solve the data-driven bipartite consensus controller, and a parameter estimation algorithm is designed to estimate the unknown parameters in the controller. The calculated estimated values ​​participate in the update of the controller under the condition that the designed reset algorithm is satisfied. The parameter estimation algorithm, reset algorithm and controller together constitute a data-driven bipartite consensus control algorithm for the collaborative rotation of large workpieces by multiple machines.

[0097] Specifically, a schematic diagram of a multi-robot data-driven binary consensus control method is shown in Figure 3; the topology diagram of the multi-robot system is shown in Figure 4, where 1 represents follower No. 1, 2 represents follower No. 2, and 3 represents leader No. 3. The weight between follower No. 1 and follower No. 2 is -1, indicating that there is an antagonistic effect between the two. The weight between leader No. 3 and follower No. 1 is 1, indicating that there is no antagonistic effect between the two. The weight between leader No. 3 and follower No. 2 is -1, indicating that there is an antagonistic effect between the two.

[0098] In one embodiment, S400 includes:

[0099] S410: Constructing a bipartite consensus error for the rotation task based on the topological relationship of the multi-robot system and the lateral error between the follower and leader robots;

[0100] S420: Substituting the bipartite consistent error and lateral error data models into the designed control input objective function to solve the data-driven bipartite consistent controller;

[0101] S430: Designing a parameter estimation algorithm for estimating unknown parameters in the controller;

[0102] S440: The calculated estimated value participates in the update of the controller under the condition of satisfying the designed reset algorithm, wherein the parameter estimation algorithm, the reset algorithm and the controller together constitute a data-driven bipartite consensus control algorithm for the collaborative rotation of large workpieces by multiple machines.

[0103] In one embodiment, S410 specifically includes:

[0104] Where, E n (k) represents the bipartite consensus error of the nth follower robot at the kth moment, a i,j is the robot's final adjacency matrix A∈R 3×3 The element in row i and column j, where a 3,j and a i,3 Represents the topological communication relationship between the leader robot and the follower robot, i, j∈{1,2,3}; e * (k) is the expected signal of the lateral error; sign is the sign function, that is:

[0105] In one embodiment, the control input objective function in S420 is specifically:

[0106] Where J(·) is the nth follower robot’s control input u n (k) objective function; is the penalty factor of the objective function of the nth follower robot;

[0107] For u in the control input objective function n (k) Calculate the partial derivative and obtain the data-driven bipartite consistency controller as follows:

[0108] Where, ρ i is the step size factor, i∈{1,2,…,L u +L e}; It is the element on the main diagonal of the in-degree matrix, that is, D = diag(d1, d2, d3).

[0109] Specifically, the penalty factor is mainly used to limit the change of the control input to ensure the smoothness of the control input signal. n,i (k),i=1,2,,L u +L e is unknown, so a parameter estimation algorithm is designed to estimate the unknown parameter.

[0110] In one embodiment, the parameter estimation algorithm in S430 is specifically:

[0111] Where η∈(0,2] and μ∈[0,∞) are the corresponding step size factor and penalty factor respectively; is φ n (k) is the estimated value.

[0112] In order to enhance the tracking capability of the time-varying parameters of the data-driven bipartite consensus control algorithm, a reset algorithm is designed.

[0113] The reset algorithm in S440 is as follows:

[0114] Where ε is a very small positive constant.

[0115] Specifically, ε is a very small positive constant, usually set to 10 -5 ; yes The initial value of .

[0116] S500: Calculate the front wheel angle control signal based on the data-driven binary consensus control algorithm and input it to the multi-robot system to complete the rotation control of the large workpiece.

[0117] In one embodiment, the data-driven binary consensus control algorithm in S500 is specifically as follows:

[0118] Where, the unknown parameter φ in the controller (16) is n (k) Estimated value obtained by the parameter estimation algorithm (17) and the reset algorithm (18) replace.

[0119] Finally, the control input signal of the robot system calculated by the data-driven bipartite consensus control algorithm is input into the constructed simulation model to verify the effectiveness of the data-driven bipartite consensus control method for the multi-robot system. The main steps are:

[0120] During the free motion of the robot, the lateral error e of each robot is calculated from the reference position and the actual position of the robot. n (k) By combining the lateral error of each follower, the expectation and the Laplace matrix describing the topological relationship, the robot lateral error is transformed to obtain the bipartite consensus error for the rotation task; based on the bipartite consensus error of the multi-robot system, the controller is designed and the unknown parameter φ in the controller is calculated. n (k) Identify and then identify the estimated value The input is sent to the controller to generate control input signals, enabling multiple robots to achieve state tasks.

[0121] Specifically, simulation curves validate the position tracking performance. Referring to Figures 5 to 12, Figure 5 shows that the follower robot is able to effectively track the desired trajectory provided by the leader during the rotation process. Figures 6 and 7 show the tracking effects of the x-axis and y-axis components of the follower robot during the rotation, respectively. Figures 6 and 7 show that the trajectories of the two follower robots are essentially symmetrical along the x-axis, consistent with the effect of bipartite consensus control. Figure 8 shows the control input signals calculated by the data-driven bipartite consensus control algorithm. Figures 9 and 10 show the adaptive adjustment curves of the pseudo-partial derivatives of Followers 1 and 2. Figure 11 shows the effect of the ratio of the lateral error to the rotation radius of Followers 1 and 2. It can be seen that the ratio of the lateral error to the rotation radius of both follower robots is stable at around 1%, which also reflects the good tracking effect of the proposed data-driven bipartite consensus control algorithm under this rotation radius (R = 25). Finally, Figure 12 shows the mean square error curve between the two follower robots, where the mean square error indicator function is defined as MSE(E1(k),E2(k))=(|E1(k)| 2 +|E2(k)| 2 ) / 2. As can be seen from Figure 12, under the control input signal generated by the designed data-driven bipartite consensus control algorithm, the mean square error and the bipartite consensus error converge gradually along the time axis.

[0122] The above data-driven binary consensus control method has the following advantages:

[0123] 1. By designing a data-driven bipartite consensus controller, the follower robots can move synchronously along a reference trajectory in opposite directions under the leadership of a static leader robot, thus achieving the rotation task.

[0124] 2. Data-driven control: Controller design relies solely on the I / O data of the controlled system, eliminating the need for a precise dynamics model. This simplifies the controller design process, making it a user-friendly control design approach.

[0125] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A data-driven binary consensus control method for multi-machine collaborative rotation of large workpieces, characterized in that: The method comprises the following steps: S100: setting a multi-robot system for implementing a rotation task to include a static leader robot that only provides a desired signal and two follower robots; S200: establishing a rotational dynamics model of the follower robot, and then discretizing the rotational dynamics model to obtain a corresponding discrete model, and then constructing a lateral error between the follower and the leader robot according to position information between the follower and the leader robot; S300: According to the discrete model, an unknown nonlinear function is constructed with the lateral error and the control input as variables, and a lateral error data model of the follower robot is established by using a dynamic linearization technique for the unknown nonlinear function; S400: According to the topological relationship of the multi-robot system and the lateral error between the follower and the leader robot, a bipartite consensus error for the rotation task is constructed, and the bipartite consensus error and lateral error data model are substituted into the designed control input objective function to solve the data-driven bipartite consensus controller, and a parameter estimation algorithm is designed to estimate the unknown parameters in the controller. The calculated estimated values ​​participate in the update of the controller under the condition that the designed reset algorithm is satisfied, wherein the parameter estimation algorithm, the reset algorithm and the controller together constitute a data-driven bipartite consensus control algorithm for the coordinated rotation of large workpieces by multiple machines; S500: Calculate the front wheel angle control signal according to the data-driven binary consensus control algorithm and input it into the multi-robot system to complete the rotation control of the large workpiece.

2. The method according to claim 1, characterized in that The multi-robot system in S100 includes: a quadrotor aircraft representing a leader robot and two robotic arm mobile robots as followers, wherein there is an antagonistic effect between the follower robots, wherein the antagonistic effect means that the running direction is opposite to the direction of the front wheel turning angle.

3. The method according to claim 2, characterized in that S200 includes: S210: Establish a rotation dynamics model of a single follower robot, specifically: Where n∈{1,2} represents the nth follower robot, x n is the lateral displacement of the nth follower robot, y n is the longitudinal displacement of the nth follower robot system, θ n is the heading angle of the nth follower robot system, v0 is the constant speed of the follower robot system during the rotation process, u n As the control input signal, it represents the front wheel steering angle of the nth follower robot system, L is the wheelbase of the follower robot, and are the lateral displacement x of the nth follower robot system respectively. n , longitudinal displacement y n and heading angle θ n The first derivative of ; S220: discretizing the rotational dynamics model of a single follower robot to obtain a discrete model of the single follower robot, specifically: Where, T s is the sampling time, k∈{1,2,...,∞} is the discrete time, x n (k+1),y n (k+1) and θ n (k+1) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the k+1th moment, x n (k), y n (k) and θ n (k) are the lateral displacement, longitudinal displacement and heading angle of the nth follower robot system at the kth moment, L and v0 are the wheelbase and constant speed, u n (k) is the control input signal of the nth follower robot system at the kth moment, i.e., the front wheel steering angle; S230: Constructing a lateral error between the follower robot and the leader robot according to the position information between the follower robot and the leader robot.

4. The method according to claim 3, characterized in that The lateral error between the nth follower and the leader robot at the kth moment in S230 is specifically: n (k) = l d ·cos(α n (k)) In the formula, in and is the expected signal required by the nth follower provided by the leader; l d is the forward sight distance.

5. The method according to claim 4, characterized in that The S300 includes: S310: According to the discrete model, an unknown nonlinear function is constructed with the lateral error and the control input as variables, specifically: e n (k+1)=f n (u n (k),…,u n (kn u +1),e n (k),…,e n (kn e +1), x n ( k ), y n ( k ), θ n (k)) In the formula, e n (k+1) is the lateral error of the nth follower robot at the k+1th time; f n (…) is an unknown scalar nonlinear function that u +n e All variables are partially differentiable and the partial derivatives are continuous, where n u and n e are two unknown positive integers, used to represent the input and output orders of the system; u n (kn u +1) and e n (kn e +1) respectively for the nth follower robot in the knth u The control input at time +1 and at kn e +1 lateral error at moment; S320: By using the dynamic linearization technology on the unknown nonlinear system function, a lateral error data model of the follower robot is established, specifically: In the formula, is the pseudo gradient of the nth robot; ΔH n (k)=[Δu n (k),...,Δu n (kL u +1),Δe n (k),...,Δe n (kL e +1)] T is the vector of all control input increments and system output increments of the nth robot; where 1≤L e ≤n e and 0≤L u ≤n u are two positive integers selected according to the complexity of the system, L e , L u are the pseudo-orders of the input and output of the multi-robot system respectively; Δu n (k) = u n (k)-u n (k-1); Δe n (k) = e n (k)-e n (k-1).

6. The method according to claim 5, characterized in that S400 includes: S410: constructing a bipartite consensus error for the rotation task based on the multi-robot system topology and the lateral error between the follower and leader robots; S420: Substituting the bisection consistent error and lateral error data model into the designed control input objective function to solve the data driven bisection consistent controller; S430: Designing a parameter estimation algorithm for estimating unknown parameters in the controller; S440: The calculated estimated value participates in the update of the controller under the condition that the designed reset algorithm is satisfied, wherein the parameter estimation algorithm, the reset algorithm and the controller together constitute a data-driven binary consensus control algorithm for the collaborative rotation of large workpieces by multiple machines.

7. The method according to claim 6, characterized in that S410 is specifically: In the formula, E n (k) represents the bisection agreement error of the nth follower robot at the kth moment, a i,j is the robot's final adjacency matrix A∈R 3×3 The element in row i and column j, where a 3,j and a i,3 represents the topological communication relationship between the leader robot and the follower robot, i,j∈{1,2,3}; e * (k) is the expected signal of the lateral error; sign is the sign function, that is:

8. The method according to claim 7, characterized in that The control input objective function in S420 is specifically: Where J(·) is the nth follower robot’s control input u n (k) objective function; is the penalty factor of the objective function of the nth follower robot; For the control input objective function u n (k) Obtain the partial derivative and obtain the data-driven bisection consistent controller as follows: In the formula, ρ i is the step size factor, i∈{1,2,...,L u +L e }; It is the element on the main diagonal of the in-degree matrix, that is, D = diag(d1, d2, d3).

9. The method according to claim 8, characterized in that The parameter estimation algorithm in S430 is specifically: Where η∈(0,2] and μ∈[0,∞) are the corresponding step size factor and penalty factor respectively; Yes n (k) estimated value; The reset algorithm in S440 is as follows: if or ||ΔH n (k-1)||≤ε or In the formula, ε is a very small positive number.

10. The method according to claim 9, characterized in that The data-driven binary consensus control algorithm in S500 is as follows:

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