Multi-mobile-robot formation tracking control method and system based on hybrid control

Abstract

The invention discloses a multi-mobile-robot formation tracking control method and system based on hybrid control, and the method comprises the steps: S1, constructing a cooperative formation tracking control system, and setting N mobile robots to carry out the navigation-following formation motion; and S2, designing a hybrid formation tracking controller. And S3, designing parameters and pulse control intervals by the controller. And S4, controlling the multi-mobile robot system to complete the formation task according to the controller in the step S2 and the control parameters and the pulse intervals in the step S3. The problem of formation tracking control of a multi-mobile-robot system is solved, and the method can be suitable for a formation tracking scene in which only part of followers can obtain the information of a navigator, and is more suitable for a mobile robot model containing dynamic influence.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-robot formation control, and in particular to a multi-mobile robot formation tracking control method and system based on hybrid control. Background Art

[0002] As robots develop towards system applications, single robots have single functions and are constrained by information acquisition capabilities, individual capabilities, and system stability. For robot systems, it has many advantages to maintain a certain formation between multiple robots. The multi-mobile robot formation system can utilize local information exchange to enable each robot of the same or different types in the system to cooperate with each other according to the requirements of the task and complete complex tasks that a single robot cannot complete, such as observing and reconnaissance of targets, attacking and capturing targets, and collaborative transportation. At present, traditional solutions to the problem of multi-robot formation control include the leader-follower method, the virtual structure method, the artificial potential field method, and the graph theory method.

[0003] At present, the control framework of multi-mobile robot formation is not universal. Most methods only regard the robot as a mass point, that is, the speed of the system is used as the control input, ignoring the dynamic characteristics of the robot and the individual differences between robots, such as the mass and damping coefficient caused by different loads. Appropriate system description methods need to be developed. In addition, the communication environment and information demand are important factors affecting the formation behavior. How to design a new control strategy to complete the set formation task with less information or reduce the number of communications is also worthy of attention. Summary of the invention

[0004] In view of the above problems, the present invention proposes a multi-mobile robot formation tracking control method and system based on hybrid control, which solves the formation tracking control problem of a multi-mobile robot system.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] The multi-mobile robot formation tracking control method based on hybrid control has the following specific steps:

[0007] S1. Construct a collaborative formation tracking control system and set N mobile robots to perform leader-follower formation movement;

[0008] S2, the design of mixed formation tracking controller;

[0009] S3, controller design parameters and pulse control interval, determine the control parameters and pulse control interval in the controller proposed in S2;

[0010] S4. According to the controller in step S2 and the control parameters and pulse intervals in S3, the multi-mobile robot system is controlled to complete the formation task.

[0011] As a further improvement of the control method of the present invention, step S1 constructs a collaborative formation tracking control system, which is specifically as follows:

[0012] S1-1, build and define multi-mobile robot system and target tracking trajectory;

[0013] Taking into account the differences in mass, damping coefficient and other parameters of the mobile robot due to different loads and individual differences, the dynamics of the robot are constructed as follows:

[0014]

[0015] where p ci =[x ci ,y ci ,θ i ] T is the coordinate system (X i ,Y i ) relative position and relative angle with respect to the reference coordinate system (X0, Y0); Contains the linear velocity and angular velocity information of the i-th mobile robot;

[0016] Through a series of transformation processes, the robot's dynamics can be converted into;

[0017]

[0018] in Design a suitable virtual control input τ i The propulsion force and torque vector of the mobile robot motion can be inferred;

[0019] S1-2, construct the information interaction relationship and target formation tracking task of multiple mobile robot systems;

[0020] Construct a directed graph containing N nodes Used to represent the information interaction relationship of multiple mobile robot systems; introduce constant matrix To describe the geometric configuration;

[0021] S1-3, establish the error dynamics equation of the system;

[0022] Set relative position error and velocity error vector

[0023]

[0024] As a further improvement of the control method of the present invention, the design of S2, the mixed formation tracking controller, is as follows:

[0025] The controller consists of two parts, one is continuous time control and the other is intermittent time pulse control. The proposed mixed formation control strategy can effectively reduce the control energy consumption;

[0026] Introduce δ(·) to represent the δ function used to represent the impulse effect at the pulse moment, and construct auxiliary variables:

[0027]

[0028] Design control algorithm:

[0029]

[0030] in Time series t k Satisfy 0≤t0 <t1<…<t k <…, is a strictly increasing sequence, and The positive constant μ represents the coupling gain, To control the parameter matrix, the coupling gain and control parameters here need to be further designed.

[0031] As a further improvement of the control method of the present invention, S3, controller design parameters and pulse control interval are as follows;

[0032] S3-1, combined with the error dynamics equation, simplify the analysis of the closed-loop system under the control algorithm proposed in step S2;

[0033] make The closed loop error system is written as;

[0034]

[0035] S3-2, construct Lyapunov function, analyze the conditions that make the system stable, and determine the appropriate controller parameters and pulse control interval;

[0036] The Lyapunov function is constructed as follows: V(t) = e T (t)Pe(t).

[0037] As a further improvement of the control method of the present invention, the controller parameters and the pulse control interval need to meet the following conditions:

[0038] Condition 1: There exists a constant α>0 such that PA+A T P-αP<0;

[0039] Condition 2: 0<ρ<1,

[0040] Condition 3: α+lnρ / Δ k <0, where

[0041] According to the above three conditions, the appropriate controller parameters and pulse control intervals are determined, and finally it can be proved that the system realizes formation tracking control, maintaining the expected formation configuration while tracking the motion trajectory and posture of the virtual navigator.

[0042] The present invention provides a multi-mobile robot formation tracking control system based on hybrid control, which includes four modules:

[0043] The first module is used to build a collaborative formation tracking control system;

[0044] The second module is used to design a mixed formation tracking controller, wherein the mixed formation tracking controller can perform continuous time control and intermittent time pulse control;

[0045] The third module is used to determine the control parameters and pulse control interval of the mixed formation tracking controller in the second module;

[0046] The fourth module uses the mixed formation tracking controller and the control parameters and pulse control intervals determined by the third module to control the multi-mobile robot system to complete the formation task.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The distributed formation tracking control strategy proposed in the present invention solves the formation tracking control problem of multiple mobile robot systems. The method is applicable to formation tracking scenarios where only some followers can obtain leader information, and is more suitable for mobile robot models that include dynamic effects. The present invention combines the pulse control method and the follower-pilot method, proposes a hybrid formation control algorithm, and correspondingly gives the control gain and pulse interval conditions that make the system stable, driving the follower mobile robot to achieve the formation tracking control goal. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A method flow chart of a preferred embodiment of the present invention;

[0050] Figure 2 A schematic diagram of symbols and coordinate system of a mobile robot according to a preferred embodiment of the present invention;

[0051] Figure 3 A schematic diagram of the multi-mobile robot communication topology and target formation geometry configuration of a preferred embodiment of the present invention;

[0052] Figure 4 Schematic diagram of the formation tracking process of multiple mobile robots according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0054] After research, it was found that the existing multi-robot formation system usually considers the mass point model. This simplified expression cannot reflect the actual situation of mobile robots with different masses, friction, damping, etc. In addition, the existing control algorithms usually use continuous time control, which has limitations such as large communication volume and high control energy consumption.

[0055] To this end, this embodiment aims to provide a distributed formation tracking control method for a multi-mobile robot system based on hybrid control. The implementation method flow chart is as follows: Figure 1 As shown in the figure, it is divided into four steps: construction of collaborative formation tracking control system, design of mixed formation tracking controller, design parameters and pulse control interval of controller, and control of multi-mobile robot system to complete formation task. Try to use less information or reduce the number of communications to complete the set formation task.

[0056] This embodiment proposes a multi-mobile robot formation tracking control method based on hybrid control, the steps are as follows:

[0057] S1: Construction of collaborative formation tracking control system.

[0058] In order to facilitate the design of subsequent controllers, the multi-mobile robot system and target tracking trajectory are first defined; the position and velocity errors based on information interaction are defined, and then the error dynamics equation of the system is established.

[0059] S1.1: Build and define a multi-mobile robot system and target tracking trajectories.

[0060] The navigator can be an actual robot or a virtual target trajectory. To facilitate subsequent analysis and to be more general, the trajectory of the navigator is set to be where q0 and They represent the position and velocity of the navigator respectively, and are continuously differentiable.

[0061] Set up N mobile robots to perform leader-follower formation motion. Commonly used mobile robot models are as follows:

[0062]

[0063] In the above formula: q i =[x i ,y i ] T represents the position coordinates of the intersection of the two wheel centers and the axis of the mobile robot i, v i and ω i denote the linear velocity and angular velocity of mobile robot i, θ iRepresents the angle between the mobile robot's forward direction and the x-axis of the global coordinate system. Figure 2 As shown in the figure, the ground coordinate system is (X0, Y0), and the local coordinate system of mobile robot i is (X i ,Y i ).

[0064] However, system (1) does not take into account the differences in mass, damping coefficient and other parameters of the mobile robots due to different loads and individual differences. The patent of the present invention is aimed at a more universal multi-mobile robot system, which is more in line with actual application needs.

[0065] Assuming that the rotational motion of the robot is centered on the mass center, point ci represents the mass center of the i-th mobile robot, and the dynamics of the robot can be expressed as:

[0066]

[0067] where p ci =[x ci ,y ci ,θ i ] T is the coordinate system (X i ,Y i ) relative position and relative angle with respect to the reference coordinate system (X0, Y0); Contains the linear velocity and angular velocity information of the i-th mobile robot;

[0068] In addition, the matrix Contains the angle information of the i-th mobile robot; m i represents the mass of the i-th mobile robot, J i represents the moment of inertia of the ith mobile robot, represents a constant damping matrix.

[0069] Relative to the reference coordinate system (X0, Y0), the position variable q of the i-th mobile robot is i =[x i ,y i ] T The definition is as follows:

[0070] q i =[x ci ,y ci ] T +L i [cosθ i ,sinθ i ] T (3)

[0071] According to (2)(3) and the definition of related variables, we can get:

[0072]

[0073] Multiply both sides of equation (3) by We can get:

[0074]

[0075] Multiply both sides of equation (4) by J T (θ i ) can be obtained:

[0076]

[0077] in Finally, the more general system dynamics of the i-th mobile robot can be expressed as (5). Designing a suitable virtual control input τ i The propulsion force and torque vector of the mobile robot's motion can be inferred.

[0078] S1.2: Constructing information interaction relationships and target formation tracking tasks for multi-mobile robot systems

[0079] Given the internal connection relationship between multiple mobile robot systems, a directed graph containing n nodes is used Indicates. is a node set, The edge set is the edge set. The adjacency matrix of The element a ij is a non-negative constant, Otherwise, a ij =0, in addition a ii =0.

[0080] picture The Laplace matrix of When i≠j, l ij =-a ij , The elements of this matrix can show the connection relationship between the internal AUVs in the multi-AUV system.

[0081] Set a constant matrix To describe the geometric configuration, h ij =h i0 -h j0To anticipate the relative position between the i-th mobile robot and the j-th mobile robot, since the desired formation and controlled variables are specified by the expected displacement of any mobile robot to other mobile robots, a possible H is set to facilitate subsequent analysis.

[0082] by Figure 2 For example, there are 6 mobile robots, that is, N=6, and the red five-pointed star in the figure is the leader. The directed communication topology connection relationship between the mobile robots is also reflected in Figure 3 It can be seen that only robots 1 and 6 can obtain the information of the navigator, and the connection relationship is set to a 10 =a 60 =1,a 20 =a 30 =a 40 =a 50 =0. Figure 2 The Laplacian matrix of the follower robot group can be expressed as

[0083]

[0084] matrix The expected formation set configuration is represented by the matrix H. Figure 2 The regular hexagon in can be represented as:

[0085]

[0086] S1.3: Establish the error dynamics equation of the system.

[0087] Given the expected formation geometry in step S1.2, some variables are defined below to describe the error vector:

[0088]

[0089] The formation control goal is described as follows: accomplish

[0090]

[0091] That is to say, the error system finally realizes that the relative position error and speed error tend to zero: and

[0092] S2: Design of hybrid formation tracking controller.

[0093] In the present invention, it is assumed that the motion trajectory of the leader is known, and the multi-robot system is regarded as followers. Only some followers can obtain the leader's information. They determine the formation framework of the entire system through the relative position constraints between the neighboring robots. The formation framework and the mutual topological connection relationship are given in advance in step S1.2.

[0094] The controller of the present invention is composed of two parts, one part is continuous time control, and the other part is intermittent time pulse control. The proposed mixed formation control strategy can effectively reduce control energy consumption.

[0095] Introduce δ(·) to represent the δ function, which is equal to zero at all points except zero, and its integral over the entire domain is equal to 1. The mathematical expression is: At the same time, it satisfies the identity

[0096] For the i-th mobile robot, construct the following auxiliary variables:

[0097]

[0098] where a ij It is a directed graph The adjacency matrix of The i-th row and j-th column element of a i0 is the connection weight between the ith follower and the leader.

[0099] The designed control algorithm is:

[0100]

[0101] in Time series t k Satisfy 0≤t0 <t1<…<t k <…, is a strictly increasing sequence, and The positive constant μ represents the coupling gain, is the control parameter matrix. The coupling gain and control parameters here need to be further designed.

[0102] S3: Controller design parameters and pulse control interval

[0103] After completing the controller design, it is also necessary to clarify how to select reasonable control parameters. In the mixed formation control strategy adopted by the present invention, there is a pulse formation control item, and the influence of the time interval of the pulse sequence on the stability of the system also needs to be analyzed comprehensively in the continuous time state. How to select the pulse control interval that makes the system stable is also one of the important problems solved by the present invention.

[0104] S3.1 combines the error dynamics equation to simplify the closed-loop system under the control algorithm (6).

[0105] make The closed-loop error system can be written as

[0106]

[0107] in definition System (7) can be written as:

[0108]

[0109] in

[0110] S3.2 constructs the Lyapunov function, analyzes the conditions that make the system stable, and determines the appropriate controller parameters and pulse control interval.

[0111] The Lyapunov function is constructed as follows: V(t) = e T (t)Pe(t), where P>0 is a diagonal matrix of suitable dimension.

[0112] For t∈[t k ,t k+1 ), k≥0, condition 1 must be met: there exists a constant α>0 such that PA+A T P-αP<0.

[0113] If condition 1 is met, the Dini derivative of the function V(t) satisfies:

[0114]

[0115] That is to say

[0116] make where λ max (·), λ min (·) represent the maximum and minimum eigenvalues ​​of the matrix, respectively, and λ max (B e K e )≤κ M ,

[0117] For t = t k , condition 2 needs to be satisfied: 0<ρ<1.

[0118] At pulse time t = t k ,have It can be introduced:

[0119]

[0120] If condition 2 is true, Then for t∈[t k-1 ,t k ),have

[0121] Combining continuous time and pulse time,

[0122]

[0123] Given condition 3: α+lnρ / Δ k <0, where

[0124] If condition 3 is met, combining the continuous time and pulse time, we can get In other words, the closed-loop system (8) is exponentially stable, and the system achieves formation tracking control, maintaining the expected formation configuration while tracking the motion trajectory and posture of the virtual navigator.

[0125] S4: According to the controller in step S2 and the control parameters and pulse intervals in S3, the multi-mobile robot system is controlled to complete the formation task.

[0126] by Figure 2 Taking the topological connection and target formation configuration as an example, an implementation example of a system consisting of 6 multi-mobile robots tracking the movement of a single leader is given.

[0127] The dynamic settings of the navigator are

[0128] q0(t)=[50cos(0.018πt)50sin(0.018πt)] T ,

[0129]

[0130] The initial position of the follower mobile robot is randomly selected in the range [-15,15], and the initial velocity is randomly selected in the range [-5,5]. The model coefficients are chosen as θ i =π / 12, L i =0.15m.

[0131] The control algorithm is (6) in step S2, and the control coefficient is selected as μ = 0.9 according to the conditions in step S3.2, K x =diag(1,1),K v =diag(2,2), the pulse interval is selected as 0.8s≤t according to the condition in step S3.2 k+1 -t k ≤1.8s.

[0132] The simulation results of the formation tracking motion trajectory are shown in the figure below: Figure 4 .

[0133] As a preferred embodiment, a multi-mobile robot formation tracking control system is proposed, which includes a first module, a second module, a third module, and a fourth module. The first module is used to construct a collaborative formation tracking control system; the second module is used to design a mixed formation tracking controller, and the mixed formation tracking controller can perform continuous time control and intermittent time pulse control; the third module is used to determine the control parameters and pulse control interval of the mixed formation tracking controller in the second module; the fourth module uses the mixed formation tracking controller and the control parameters and pulse control interval determined by the third module to control the multi-mobile robot system to complete the formation task.

[0134] As a preferred embodiment, a computer-readable storage medium is proposed, wherein at least one executable instruction is stored in the storage medium, and when the executable instruction is run on an electronic device, the electronic device executes the multi-mobile robot formation tracking control method based on hybrid control as disclosed in the above embodiment. The above-mentioned integrated unit implemented in the form of a software functional unit can be stored in a computer-readable storage medium. The above-mentioned software functional unit is stored in a storage medium, including a number of instructions for a computer device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0135] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A multi-mobile robot formation tracking control method based on hybrid control, characterized in that: The specific steps are as follows: S1. Construct a collaborative formation tracking control system and set N mobile robots to perform leader-follower formation movement; S2, the design of mixed formation tracking controller; S3, controller design parameters and pulse control interval, determine the control parameters and pulse control interval in the controller proposed in S2; S4. According to the controller in step S2 and the control parameters and pulse intervals in S3, the multi-mobile robot system is controlled to complete the formation task.

2. The multi-mobile robot formation tracking control method based on hybrid control according to claim 1 is characterized by: Step S1 constructs a collaborative formation tracking control system, as follows: S1-1, build and define multi-mobile robot system and target tracking trajectory; Taking into account the differences in mass, damping coefficient and other parameters of the mobile robot due to different loads and individual differences, the dynamics of the robot are constructed as follows: where p ci =[x ci ,y ci ,θ i ] T is the coordinate system (X i ,Y i ) relative position and relative angle with respect to the reference coordinate system (X0, Y0); Contains the linear velocity and angular velocity information of the i-th mobile robot; Through a series of transformation processes, the robot's dynamics can be converted into; in Design a suitable virtual control input τ i The propulsion force and torque vector of the mobile robot motion can be inferred; S1-2, construct the information interaction relationship and target formation tracking task of multiple mobile robot systems; Construct a directed graph containing N nodes Used to represent the information interaction relationship of multiple mobile robot systems; introduce constant matrix To describe the geometric configuration; S1-3, establish the error dynamics equation of the system; Set relative position error and velocity error vector 3. The multi-mobile robot formation tracking control method based on hybrid control according to claim 1 is characterized by: S2. The design of the mixed formation tracking controller is as follows: The controller consists of two parts, one is continuous time control and the other is intermittent time pulse control. The proposed mixed formation control strategy can effectively reduce the control energy consumption; Introduce δ(·) to represent the δ function used to represent the impulse effect at the pulse moment, and construct auxiliary variables: Design control algorithm: in Time series t k Satisfy 0≤t0 <t1<…<t k <…, is a strictly increasing sequence, and The positive constant μ represents the coupling gain, To control the parameter matrix, the coupling gain and control parameters here need to be further designed.

4. The multi-mobile robot formation tracking control method based on hybrid control according to claim 1, characterized in that: S3, controller design parameters and pulse control interval, as follows; S3-1, combined with the error dynamics equation, simplify and analyze the closed-loop system under the control algorithm proposed in step S2; make The closed loop error system is written as; S3-2, construct Lyapunov function, analyze the conditions that make the system stable, and determine the appropriate controller parameters and pulse control interval; The Lyapunov function is constructed as follows: V(t) = e T (t)Pe(t).

5. The multi-mobile robot formation tracking control method based on hybrid control according to claim 4 is characterized in that: The controller parameters and pulse control intervals must meet the following conditions: Condition 1: There exists a constant α>0 such that PA+A T P-ΔP<0; Condition 2: 0<ρ<1, Condition 3: α+lnρ / Δ k <0, among them According to the above three conditions, the appropriate controller parameters and pulse control intervals are determined, and finally it can be proved that the system realizes formation tracking control, maintaining the expected formation configuration while tracking the motion trajectory and posture of the virtual navigator.

6. The multi-mobile robot formation tracking control system based on hybrid control according to claims 1-5, characterized in that: It consists of four modules: The first module is used to build a collaborative formation tracking control system; The second module is used to design a mixed formation tracking controller, wherein the mixed formation tracking controller can perform continuous time control and intermittent time pulse control; The third module is used to determine the control parameters and pulse control interval of the mixed formation tracking controller in the second module; The fourth module uses the mixed formation tracking controller and the control parameters and pulse control intervals determined by the third module to control the multi-mobile robot system to complete the formation task.

Images