Multi-mobile-robot preset performance formation control method based on communication constraint

Abstract

The invention discloses a multi-mobile-robot preset performance formation control method based on communication constraints. According to the method, firstly, based on a finite time interference observer theory, a finite time convergence interference observer model is established for a system influenced by external interference, and a foundation is laid for subsequent design of an anti-interference controller; secondly, considering the problem of collision avoidance and communication connection maintenance between adjacent mobile robots, introducing a finite time preset performance function, integrating the constraint of collision avoidance and communication connection maintenance into the performance function, and setting an expected formation distance control target; and finally, designing an anti-interference preset performance formation controller by using an asymmetric obstacle Lyapunov function, thereby realizing a control target.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-mobile robot control, and in particular to a multi-mobile robot preset performance formation control method based on communication constraints. Background Art

[0002] Many control methods for multi-mobile robot dynamic models only focus on the study of steady-state performance. In actual multi-mobile robot applications, higher requirements are placed on the system's performance, real-time performance, etc., requiring not only the coordinated control strategy to ensure its steady-state performance, but also the transient performance (such as convergence speed, maximum overshoot, etc.) that meets other practical requirements to ensure the efficiency and reliability of the system. Relevant researchers constrain the transient and steady-state performance of the system by presetting the performance envelope function. However, most of the performance envelope functions used are exponential decay, and the time to converge to the steady state is unknown. In theory, the controlled system needs to spend infinite time to enter the preset steady-state boundary envelope. Therefore, from the perspective of practical application, it is very important to introduce a preset performance function with finite time convergence. In addition, factors such as collisions between robots and communication connections during operation may lead to system performance degradation and the inability to achieve control objectives. Based on the above content, it is necessary and of practical value to incorporate the constraints of collision avoidance and communication connection maintenance into the preset performance function for research.

[0003] It should be noted that any system cannot avoid being affected by disturbances during actual operation, and these disturbances will also have a direct or indirect impact on the transient performance of the system. Therefore, it is particularly important to introduce anti-interference technology and preset performance control technology, and design a control strategy that enhances the robust performance of the system and meets the preset performance indicators. Summary of the invention

[0004] The purpose of the present invention is to propose a preset performance formation control method for multiple mobile robots based on communication constraints, which can effectively improve the robust performance of the robots and ensure that collisions between robots are avoided and communication connections are maintained.

[0005] The specific technical solution of the present invention is as follows: A mobile robot preset performance formation control method based on collision avoidance and connection maintenance, comprising the following steps:

[0006] The mobile robot system model is shown below: Where i∈{1, 2, …, N} represents the number of the mobile robot, Respectively represent the positions on the X and Y axes in the preset coordinate system XOY, represents the azimuth, and Represent the linear velocity and angular velocity control input respectively, li d Represents the position point p i Distance to wheel axle, d i v and d i ω represents disturbance;

[0007] For the above mobile robot, let It can be transformed into the following state space equation form: In the formula, External interference in the system i and its derivatives are bounded;

[0008] For the system affected by disturbance, the following finite-time disturbance observer is constructed: Where γ1 and γ2 represent the observer gain, and Indicates p i and d i The estimated value of U i Represents the known Lipschitz constant. By selecting an appropriate disturbance observer gain, the disturbance observer can effectively estimate the disturbance information in a finite time.

[0009] Next, consider the constraints of collision avoidance and connection maintenance between mobile robots to design a preset performance formation controller. The specific steps are as follows:

[0010] Define the desired formation distance as follows:

[0011] And the relative positions between adjacent mobile robots are expressed as follows:

[0012] Therefore, the distance error is expressed as: in, Indicates the actual distance between adjacent mobile robots. The meanings of collision avoidance and connection maintenance are introduced below;

[0013] Collision avoidance: Avoiding collisions is a key factor in the safe, stable, and efficient operation of each subsystem. Assume that the geometric radius of each subsystem is r i , so we can know that r ij =(r i +r j )>0, obviously, in order to prevent the subsystems from colliding with each other, it is necessary to ensure Introducing the distance error formula mentioned above, the inequality can be transformed into

[0014] Connection maintenance: In practice, the sensing distance of sensors and other mobile devices is limited. Therefore, during the control process, neighboring subsystems must remain within the perception range of their respective neighboring subsystems. Otherwise, once the neighboring agents lose contact, the entire system will become unstable or even collapse. In the present invention, the sufficient condition for connection maintenance is to ensure that the communication between neighboring subsystems will not be interrupted during operation. Assume that the perception radius of each subsystem sensor is R i , while defining R ij =min(R i +r j , R j +r i )>0, it should be noted that the expected formation distance δ ij Must be less than R ij Obviously, in order to maintain connectivity between the subsystems, it is necessary to ensure Introducing the distance error formula mentioned above, the inequality can be transformed into In addition, it should be noted that there is always R i >r i and R ij >r ij Established;

[0015] In summary, in order to simultaneously meet the preset performance formation control objectives including collision avoidance and connection maintenance, the following inequality is introduced to constrain the distance error: In the formula, e ij (t)>0 and is the upper and lower performance boundary function and is a monotonically decreasing function; if the initial value e ij (0) and Satisfy e ij (0)≤δ ij -r ij and Then for t ≥ 0, the connection maintenance and collision avoidance between adjacent subsystems can be guaranteed;

[0016] Defining the squared distance error Combination formula The following formula can be obtained: In the formula, if and only if e ij =0, μ ij=0; therefore, the performance boundary constraint imposed on the distance error can be converted into a performance boundary constraint imposed on the distance square error;

[0017] In some practical scenarios such as military reconnaissance or disaster rescue, mobile robots are required to quickly assemble and form an effective combat or rescue formation within a limited time to gain precious time. Therefore, the following continuous and smooth monotonically decreasing finite time preset performance function ψ is selected ij (t): In the formula, and 0 <v ij <1 is the parameter to be selected for the performance function, ψ ij (0) is the initial value of the finite time preset performance function, ψ ijT >0 is the final value of the finite time preset performance function, ψ ij (t) will be Before convergence to ψ ijT . It can be seen from this that the convergence time T can be pre-selected by the user, which is easier to achieve than the exponential decay rate;

[0018] Applying the performance constraint to the squared distance error, we get In the formula, μ ij (t)= d ij ψ ij (t) and d ij and is a positive constant; in addition, μ ij (0)= d ij ψ ij0 and Satisfy the following: Therefore, by choosing the appropriate d ij and The performance boundary constraint of the squared distance error can be achieved, while also meeting the requirements of collision avoidance and communication connection maintenance;

[0019] Calculate the distance error e ij The derivative of is as follows: Will Substitute into μ ij In the process of seeking, we can get:

[0020] Define z ij，1 =μ ij / ψ ij , the system anti-interference preset performance formation controller is designed as: k i >0 indicates controller gain, Represents the formation feedback error, ensuring that the system formation error is constrained within the performance envelope, -z i，2 It represents feedforward disturbance compensation, which is used to weaken or offset the influence of external disturbance on the system in real time;

[0021] C001: For variable z based on formation distance error ij，1 , select the energy function of the following form:

[0022] Generally speaking, it is difficult to directly design a controller for a system with performance constraints. Usually, an error conversion function is introduced to homeomorphically map the original system with constraints to an unconstrained system before designing the controller. Different from the above content, the present invention introduces the barrier Lyapunov function and combines it with It can be seen that when z ij,1 The closer to the border μ ij (t)= d ij ψ ij (t) and The boundary contains the performance function, and the Lyapunov function diverges to infinity. Therefore, it is only necessary to prove that the designed controller can achieve the boundedness of the signal in the closed-loop system, that is, it does not violate the boundary conditions, and then the control objective can be achieved;

[0023] C002: In the formula, log(·) represents the natural logarithm function,

[0024] C003: Calculate V ij，1 The derivative of , we can get:

[0025]

[0026] C004: In the formula,

[0027] C005: For z ij，1 =μ ij / ψ ij Taking the derivation, we can get

[0028]

[0029] C006: Further, substituting C005 into C003 yields

[0030]

[0031] C007: Set the controller u i Substitution In, can be obtained

[0032]

[0033] C008: Further, using the young inequality, we can get

[0034]

[0035] C009: Further scaling, we can get

[0036]

[0037] C010: In the formula,

[0038] C011: According to C010, by selecting an appropriate control gain and a sufficiently small disturbance observer observation error, the entire closed-loop system signal is bounded. Therefore, the preset performance anti-interference formation control of the mobile robot based on collision avoidance and connection maintenance can be achieved under the control law designed by the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A formation diagram of three mobile robots formed under the action of the formation controller designed by the present invention;

[0040] Figure 2 This is a diagram showing the effect of the disturbance observer designed by the present invention estimating the real disturbance;

[0041] Figure 3 It is the formation error diagram of three mobile robots under preset performance constraints;

[0042] Figure 4 The evolution diagram of the mobile robot controller designed by the present invention; DETAILED DESCRIPTION

[0043] The present invention is further explained below in conjunction with specific implementation processes. It should be understood that these implementations are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0044] A mobile robot preset performance formation control method based on collision avoidance and connection maintenance comprises the following steps:

[0045] Step 1: Set various robot system parameters;

[0046] Step 2: Set various disturbance observer system parameters;

[0047] Step 3: Set various tracking differentiator system parameters;

[0048] Step 4: Set various variable parameters;

[0049] Step 5: Combine steps 1 to 4 to set up the controller;

[0050] Step 6: Use the designed controller to update the dynamic variables inside the robot system until the running time ends;

[0051] Figure 1 The figure is a formation diagram of three mobile robots formed by the formation controller designed by the present invention. It can be seen that the three robots have realized the preset equilateral triangle formation, and the control effect of the proposed controller is good; Figure 2 The effect diagram of the finite time disturbance observer designed by the present invention on estimating the real disturbance is shown. The designed disturbance observer can accurately estimate the disturbance in real time within a finite time, thereby weakening the influence of the disturbance on the system performance and control target and improving the robust performance of the system. Figure 3 The figure is the formation error diagram of three mobile robots under the preset performance constraints. The system formation error has been constrained within the performance function and converged to the preset steady-state boundary within a limited time. This shows that the multi-mobile robot system meets the preset transient and steady-state performance indicators (including convergence speed, overshoot, steady-state error, convergence time, etc.) in the process of realizing formation control, and at the same time meets the constraints of collision avoidance and communication connection maintenance between robots. Figure 4 This is the evolution diagram of the mobile robot controller designed for the present invention. It can be seen from the figure that the controller eventually converges to a constant value.

Claims

1. A method for controlling a multi-mobile robot formation with preset performance based on communication constraints, characterized in that: The following steps are involved: Firstly, for the system affected by external disturbance, the disturbance observer theory is used to establish a finite-time disturbance observer to estimate the external disturbance, which lays a foundation for the subsequent design of the anti-interference formation controller. Secondly, considering the constraints of collision avoidance and communication maintenance between robots, a preset performance function with finite time convergence is designed. Based on this, a distributed preset performance formation control protocol based on interference observer is designed, so that the multi-mobile robot system can achieve the desired formation while satisfying the constraints of collision avoidance and connection maintenance. Finally, an asymmetric barrier Lyapunov function is constructed to deal with the problem that the system constraints are not conducive to the design of the formation controller, and the output of the disturbance observer (disturbance estimate) is used to design a formation controller that meets the performance constraints. At the same time, the goal of the system being unaffected by interference is also achieved.

2. The method for controlling a mobile robot formation with preset performance based on collision avoidance and connection maintenance according to claim 1, characterized in that: First, based on the theory of continuous time differential equations, the following system model affected by disturbance is presented. The specific steps are as follows: For the mobile robot dynamics model: Where i∈{1, 2, …, N} represents the number of the mobile robot, Represents the position on the X and Y axes in the preset coordinate system XoY, represents the azimuth, and Represent the linear velocity and angular velocity control input respectively, l i d Represents the position point p i Distance to wheel axle, d i v and d i ω represents disturbance; For the above mobile robot, it can be analyzed in the form of the following state space equation: In the formula, Assumption 1: There is a disturbance d in the system i and its derivatives are bounded.

3. According to the disturbed system of claim 2 and assumption 1, the following disturbance observer is constructed using the disturbance observer theory, and the specific steps are as follows: Where γ1 and γ2 represent the observer gain, and Indicates p i and d i The estimated value of U i Represents the known Lipschitz constant. By selecting a suitable observer gain, the disturbance observer can be used to estimate the external disturbance better within a finite time.

4. According to the interference estimation value output by the interference observer described in claim 3, the interference is directly compensated or offset in the feedforward channel; it paves the way for the subsequent design of the anti-interference formation controller to eliminate the negative impact of interference on the system. On this basis, considering the constraints of system collision avoidance and connection maintenance, the information of the intelligent agent and the neighbors is used to design a preset performance controller containing collision avoidance and communication connection maintenance constraints, and combined with the constructed interference observer to form a feedforward-feedback composite controller. The specific steps are as follows: Define the desired formation distance as follows: And the relative positions between adjacent systems are expressed as follows: Therefore, the distance error is expressed as follows: in, Indicates the actual distance between adjacent systems; Collision avoidance and connection maintenance are described as follows: Collision avoidance: Avoiding collisions is a key factor in the safe, stable, and efficient operation of each subsystem. Assume that the geometric radius of each subsystem is r i , so we know that r ij =(r i +r j )>0, obviously, in order to prevent the subsystems from colliding with each other, it is necessary to ensure Introducing the distance error formula mentioned above, the inequality can be transformed into Connection maintenance: In practice, the sensing distance of sensors and other mobile devices is limited. Therefore, during the control process, neighboring subsystems must remain within the sensing range of their respective neighboring subsystems. Otherwise, once the neighboring robots lose contact, the entire system will become unstable or even crash. In the present invention, the sufficient condition for connection maintenance is to ensure that the communication between neighboring subsystems will not be interrupted during operation. Assume that the sensing radius of each subsystem sensor is R i , while defining R ij =min(R i +r j , R j +r i )>0, it should be noted that the expected formation distance δ ij Must be less than R ij Obviously, in order to maintain connectivity between the subsystems, it is necessary to ensure Introducing the distance error formula mentioned above, the inequality can be transformed into In addition, it should be noted that there is always R i >r i and R ij >r ij Established; In summary, in order to simultaneously meet the formation control objectives of collision avoidance and connection maintenance, the following inequality is introduced to constrain the distance error: In the formula, e ij (t)>0 and is the upper and lower performance boundary function and is a monotonically decreasing function; if the initial value e ij (0) and Satisfy e ij (0)≤δ ij -r ij and Then for t ≥ 0, the connection maintenance and collision avoidance between adjacent subsystems can be guaranteed; Defining the squared distance error Combination formula The following formula can be obtained: In the formula, if and only if e ij =0, μ ij =0; therefore, the performance boundary constraint imposed on the distance error can be converted into a performance boundary constraint imposed on the distance square error; Choose the following continuous and smooth monotonically decreasing finite-time preset performance function ψ ij (t): In the formula, and 0<v ij <1 is the parameter to be selected for the performance function, ψ ij (0) is the initial value of the finite time preset performance function, ψ ijT >0 is the final value of the finite time preset performance function, ψ ij (t) will be Before convergence to ψ ijT . It can be seen from this that the convergence time T can be pre-selected by the user, which is easier to achieve than the exponential decay rate; Next, a performance constraint is applied to the squared distance error: In the formula, μ ij (t)= d ij ψ ij (t) and d ij and is a positive constant; in addition, μ ij (0)= d ij ψ ij0 and satisfy: Therefore, by choosing the appropriate d ij and The performance boundary constraint of the squared distance error can be achieved, while also meeting the requirements of collision avoidance and communication connection maintenance; Calculate the distance error e ij The derivative of is as follows: Will Substitute into μ ij In the process of seeking, we can get: Define z ij，1 =μ ij / ψ ij , the system anti-interference preset performance formation controller is designed as follows: In the formula, k i >0 indicates controller gain, Represents the formation feedback error, ensuring that the system formation error is constrained within the performance envelope, -z i，2 It represents feedforward disturbance compensation, which is used to weaken or offset the impact of external disturbance on the system in real time.

5. According to the preset performance formation controller based on the interference observer designed in claim 4, the multi-mobile robot system can realize anti-interference formation control, and the formation control error can be limited within the preset performance boundary, while meeting the requirements of system collision avoidance and connection maintenance. The specific steps of theoretical analysis are as follows: B001: For variable z based on formation distance error ij，1 , construct the following asymmetric obstacle Lyapunov function Where log(·) represents the natural logarithm function, Generally speaking, it is difficult to directly design a controller for a system with performance constraints. Usually, an error conversion function is introduced to homeomorphically map the original system with constraints to an unconstrained system before designing the controller. Different from the above content, the present invention introduces the barrier Lyapunov function and combines it with It can be seen that when z ij，1 The closer to the border μ ij (t)= d ij ψ ij (t) and The boundary contains the performance function, and the Lyapunov function diverges to infinity. Therefore, it is only necessary to prove that the designed controller can achieve the boundedness of the signal in the closed-loop system, that is, it does not violate the boundary conditions, and then the control objective can be achieved; B002: For z ij，1 =μ ij / ψ ij Taking the derivation, we can get B003: Substituting into B002, we get B004: V ij，1 Taking the derivation, we can get In the formula, B005: Combined with B003, we get B006: Set the controller u i Substitution In, can be obtained B007: Using Young's inequality, we can get B008: By further scaling B007, we can get In the formula, B009: According to B008, appropriate control gain and sufficiently small disturbance observer observation error are selected so that the signal in the entire closed-loop system is bounded. Therefore, the mobile robot can achieve anti-interference formation control under the action of the designed controller and at the same time meet the system collision avoidance and connection maintenance requirements.

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