Collision-free preset time formation control method for multiple omnidirectional mobile robots with input quantization

Abstract

The present invention discloses a collision-free preset time formation control method for a multi-omnidirectional mobile robot model with input quantization. Control is performed using a collision-free preset time formation controller. First, a multi-omnidirectional mobile robot dynamics model with unknown nonlinear terms is established. By analyzing the dynamics model, a hysteresis quantizer is constructed to quantize continuous input signals into discrete signals. A novel artificial potential field function is constructed to achieve collision-free control between multiple omnidirectional mobile robots and between robots and environmental obstacles. A radial basis function neural network is used to approximate the unknown nonlinear terms, thereby establishing a Lyapunov function. Combined with dynamic surface control technology, a preset time filter is constructed. Based on the above work, an adaptive law for the multi-omnidirectional mobile robot model and a collision-free preset time formation controller are obtained.

Description

Technical Field

[0001] The present invention belongs to the field of omnidirectional mobile robot control, and in particular relates to a collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization. Background Art

[0002] In recent years, with the rapid development of control technologies such as drone control and robot formation control, the adaptive control of omnidirectional mobile robots has gradually become a research hotspot. However, with the continuous advancement of omnidirectional mobile robot control technology, a single omnidirectional mobile robot is limited by its own resources and capabilities, and it is difficult to complete the mission objectives on its own when faced with increasingly complex mission requirements. Therefore, formation control of multiple omnidirectional mobile robot systems has emerged. With the help of advanced communication technologies and intelligent algorithms, the omnidirectional mobile robots in the formation can maintain or change formation according to mission requirements and accurately execute various commands. This makes omnidirectional mobile robots have broad application prospects in multiple fields, especially in mission environments that require high precision and high flexibility.

[0003] The formation control of omnidirectional mobile robot models aims to develop an adaptive fuzzy control method to achieve stable motion of omnidirectional mobile robot formations and enable them to adapt to changes and uncertainties in the environment. Specifically, the goal of formation control of omnidirectional mobile robot models is to design an adaptive controller to ensure that all signals in the closed-loop system are in a semi-globally eventually uniformly bounded state and that the system output can effectively track the reference signal. Currently, there are many control algorithms and techniques for formation control of omnidirectional mobile robot models. Mainstream control methods include radial basis function neural networks, fuzzy logic systems, and PID controllers. However, the existing technologies still have the following problems:

[0004] First, most of the existing control methods for omnidirectional mobile robot formations do not consider the system's collision-free problem, and do not consider the convergence time problem of omnidirectional mobile robot formations during the control process. Convergence time is a key indicator for evaluating the dynamic characteristics of the controlled system. In actual engineering applications, people usually hope that the controlled system can converge to a stable state quickly.

[0005] Second, existing control methods for omnidirectional mobile robot formations can achieve a semi-globally eventually uniformly bounded state for all signals in the closed-loop system. However, these systems are triggered in real time, which can lead to unnecessary data transmission and waste communication resources. In practical applications, people generally hope to complete formation tasks using fewer resources. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this paper proposes a collision-free, preset-time formation control method for a multi-omnidirectional mobile robot model with input quantization. This method quantizes continuous input signals into discrete signals to improve the system's signal transmission performance, conserve communication resources, and ensure that the controlled system remains stable within a preset time. Furthermore, it ensures that the multiple omnidirectional mobile robots in the system avoid collisions throughout the entire process.

[0007] To achieve the above objectives, the technical solutions of the present invention are as follows: a collision-free preset time formation control method for a multi-omnidirectional mobile robot model with input quantization, comprising: taking a system composed of multiple omnidirectional mobile robots as a control object, and establishing a dynamic model with unknown nonlinear terms;

[0008] Construct an artificial potential field function to achieve collision-free movement between multiple omnidirectional mobile robots and between robots and environmental obstacles;

[0009] Using radial basis function neural network to approximate the unknown nonlinear terms in the dynamic model, and establishing Lyapunov function;

[0010] Combined with dynamic surface control technology, a preset time filter is constructed;

[0011] Design an adaptive law and a collision-free preset time formation controller for multiple omnidirectional mobile robot models.

[0012] Furthermore, in a multi-omnidirectional mobile robot system as the controlled object, the dynamic model of the i-th omnidirectional mobile robot is described as follows:

[0013]

[0014] in, represents the position of the i-th omnidirectional mobile robot, represents the speed state of the i-th omnidirectional mobile robot,

[0015]

[0016] x wi and y wi They represent the X coordinates of the omnidirectional mobile robot in the world coordinate system. w Direction and Y w Coordinate values ​​in the direction;

[0017] represents the robot coordinate system X of the i-th omnidirectional mobile robot r The positive direction of the axis and the world coordinate system X w The angle between the positive directions of the axes;

[0018] y irepresents the output state of the i-th omnidirectional mobile robot;

[0019] q(τ i )=[q(τ i,1 )q(τ i,2 )q(τ i,3 )q(τ i,4 )] T represents the output of the hysteresis quantizer, i.e., the collision-free preset time formation controller of the i-th omnidirectional mobile robot;

[0020] q(τ i,1 ),q(τ i,2 ),q(τ i,3 ),q(τ i,4 ) represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the i-th omnidirectional mobile robot respectively;

[0021] Will and Abbreviated as f i,1 、f i,2 、g i 、f i ;f i,1 and f i,2 Represents the unknown nonlinear term caused by the difference between the actual model establishment and operation scenario of the omnidirectional mobile robot and the ideal assumption;

[0022] g i represents the inherent nonlinear term of the i-th omnidirectional mobile robot, f i It represents the inherent control input gain matrix of the i-th omnidirectional mobile robot and is expressed by the following mathematical formula:

[0023]

[0024] It is a 3×3 matrix representing the transformation matrix between the world coordinate system and the robot coordinate system;

[0025] represents the static friction force on the Mecanum wheel;

[0026] represents the angular velocity of each wheel of the omnidirectional mobile robot;

[0027] R represents the radius of the Mecanum wheel;

[0028] Is a 3×3 matrix, representing The derivative of the inverse matrix of ;

[0029] B θrepresents the viscous friction coefficient of the Mecanum wheel;

[0030] J + is a 3×4 matrix, and J is a 4×3 matrix, representing the Jacobian matrices of the forward kinematics model and inverse kinematics model of the omnidirectional mobile robot respectively;

[0031] represents the angular acceleration of the Mecanum wheel;

[0032] Q is a 4×4 matrix representing the gain matrix of the Mecanum wheel angular acceleration;

[0033] Q -1 It is a 4×4 matrix, representing the inverse matrix of Q.

[0034] Furthermore, the obstacle set of the i-th omnidirectional mobile robot is defined as

[0035]

[0036] is the collision detection range;

[0037] Ω i represents the neighborhood set of the i-th follower;

[0038] is the pose of the i-th omnidirectional mobile robot, is the pose of the environmental obstacle;

[0039] The artificial potential field function is designed as follows:

[0040]

[0041] represents the collision-free distance error, and c represents the obstacle set Obstacles in

[0042] d Represents the minimum safe distance;

[0043] 0 m =[0 0 0] T ;

[0044] Taking the partial derivative of the artificial potential field function, we get:

[0045]

[0046] Furthermore, for the second-order omnidirectional mobile robot model, the Lyapunov function is constructed twice;

[0047] The first constructed Lyapunov function is expressed as follows:

[0048]

[0049] N represents the number of omnidirectional mobile robots;

[0050] is the ideal adjustment scalar of the i-th omnidirectional mobile robot Its estimated value The estimation error of

[0051] is the ideal adjustment scalar for the jth omnidirectional mobile robot Its estimated value The estimation error of

[0052] The second constructed Lyapunov function is expressed as follows:

[0053]

[0054] z i,2 represents the virtual tracking error of the i-th omnidirectional mobile robot;

[0055] s i,2 represents the filtering error of the i-th omnidirectional mobile robot;

[0056] represents the ideal adjustment scalar when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time;

[0057] is the ideal adjustment scalar when constructing the Lyapunov function for the second time Its estimated value The estimation error.

[0058] Furthermore, the preset time filter is expressed by the following differential equation:

[0059]

[0060] ω i (0) = α i,1 (0)

[0061] represents the first-order derivative of the filter, ω i (0) represents the initial value of the filter;

[0062] η∈(0,1), is a design parameter;

[0063] γ and is a design parameter;

[0064] φ is the filter design parameter;

[0065] T d It is a predetermined time;

[0066] c i,2 is a positive constant;

[0067] α i,1 is the virtual control variable of the i-th omnidirectional mobile robot.

[0068] Furthermore, the adaptive law constructed for the first time is expressed in the following form:

[0069]

[0070] in, Adjust the scalar for ideality The estimated value of Indicates estimated value The derivative of

[0071] Adjust the scalar for ideality The estimated value of Indicates estimated value The derivative of ;λ=2+η,

[0072] λ and These are all design parameters.

[0073] The adaptive law constructed for the second time is expressed in the following form:

[0074]

[0075]

[0076] is the ideal adjustment scalar when constructing the Lyapunov function for the second time The estimated value of Indicates estimated value The derivative of a ij Represents the communication between the i-th omnidirectional mobile robot and the j-th omnidirectional mobile robot. If there is information transmission between the two omnidirectional mobile robots, then a ij =1, otherwise a ij =0;

[0077] b i Represents the communication between the leader and the i-th omnidirectional mobile robot. If there is information transmission, then b i =1, otherwise b i =0;

[0078] Γ i,1represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the first time;

[0079] Γ j,1 represents the output vector of the radial basis function neural network when the j-th omnidirectional mobile robot constructs the Lyapunov function for the first time;

[0080] Γ i,2 Represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time.

[0081] The virtual control variables and the final collision-free preset time formation controller are expressed by the following formula:

[0082]

[0083] represents the position bias vector of the i-th omnidirectional mobile robot;

[0084] represents the position bias vector of the jth omnidirectional mobile robot;

[0085] and is the position bias vector and The derivative of

[0086] is the ideal adjustment scalar estimated value of;

[0087] is the ideal adjustment scalar estimated value of;

[0088] c i,1 and c i,c is a positive design parameter;

[0089] is the reference signal y d The derivative of

[0090]

[0091] τ i represents the input of the hysteresis quantizer;

[0092] δ is a design parameter, and its specific form will be given later;

[0093] The controller design is as follows:

[0094]

[0095] τmin >0 is the quantization dead zone; 0<Π<1 is the quantization density

[0096] is a design parameter.

[0097] Furthermore, the omnidirectional mobile robot is a four-Mecanum wheeled robot.

[0098] Compared with the existing working technology, the present invention has the following beneficial effects:

[0099] First, most existing control methods for omnidirectional mobile robot formations fail to consider the system's collision-free nature and the convergence time required for the control process. However, this invention, recognizing convergence time as a key metric for evaluating the dynamic characteristics of a controlled system, designs a preset time filter and a preset time formation controller to enable the multi-omnidirectional mobile robot system to complete the formation task within an optimal time period. It also introduces a new artificial potential field function to achieve collision-free formation control for multiple omnidirectional mobile robots. This method not only stabilizes the controlled system within a preset timeframe but also ensures that the multiple omnidirectional mobile robots are collision-free throughout the entire process.

[0100] Second, in existing control methods for omnidirectional mobile robot formations, although the controlled system can achieve a semi-globally eventually uniformly bounded state for all signals in the closed-loop system, their systems are triggered in real time, which may lead to unnecessary data transmission and waste communication resources. Taking into account the limited resources, this paper designs a hysteresis quantizer suitable for the multi-omnidirectional mobile robot model, which converts the continuous input signal τ i , quantized into a discrete input signal q(τ i ), which improves the signal transmission performance of the system, saves communication resources, and provides strong technical support for the high-response speed, high-precision, and low-resource consumption control of multi-omnidirectional mobile robot model formation control. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 This is a simplified diagram of the motion analysis of a multi-omnidirectional mobile robot.

[0102] Figure 2 This is a schematic diagram of the communication topology between omnidirectional mobile robots.

[0103] Figure 3 It is the motion trajectory diagram of the omnidirectional mobile robots (OMRs) formation in the XY plane.

[0104] Figure 4 It is the position state tracking error diagram of each omnidirectional mobile robot in the X direction.

[0105] Figure 5It is the velocity state tracking error diagram of each omnidirectional mobile robot in the X direction.

[0106] Figure 6 It is the position state tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0107] Figure 7 It is the velocity state tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0108] Figure 8 is the output tracking error diagram of each omnidirectional mobile robot in the X direction.

[0109] Figure 9 is the output tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0110] Figure 10 This is the input torque diagram of the first and second wheels of the first omnidirectional mobile robot.

[0111] Figure 11 This is the input torque diagram of the third and fourth wheels of the first omnidirectional mobile robot.

[0112] Figure 12 This is the input torque diagram of the first wheel of the first omnidirectional mobile robot.

[0113] Figure 13 This is the input torque diagram of the first wheel of the second omnidirectional mobile robot.

[0114] Figure 14 This is the input torque diagram of the first wheel of the third omnidirectional mobile robot. DETAILED DESCRIPTION

[0115] The present invention combines the backstepping recursive method and the dynamic surface control technology, and proposes a collision-free preset time formation control method for a multi-omnidirectional mobile robot model with input quantization. The control is performed by a collision-free preset time formation controller. The establishment process of the controller includes the establishment of the multi-omnidirectional mobile robot control model, the establishment of the artificial potential field function, the establishment of the Lyapunov function, the establishment of the preset time filter, the establishment of the adaptive law and the establishment of the collision-free preset time formation controller. The control method of the present invention is used to achieve the preset time stability of the system and ensure that the multiple omnidirectional mobile robots in the system are collision-free throughout the process.

[0116] First, a system consisting of multiple omnidirectional mobile robots is selected as the control object. The omnidirectional mobile robots in the control object are all followers. A dynamic model of multiple omnidirectional mobile robots with unknown nonlinear terms is constructed. By analyzing the dynamic model, a hysteresis quantizer can be constructed to quantize the continuous input signal into a discrete signal; an artificial potential field function is also constructed to achieve collision-free movement between multiple omnidirectional mobile robots and collision-free movement between robots and environmental obstacles; within the framework of the backstepping recursive method, the radial basis function neural network is used to approximate the unknown nonlinear terms to establish the Lyapunov function, and combined with the dynamic surface control technology, a preset time filter is constructed, and finally the adaptive law of the multiple omnidirectional mobile robot model and the collision-free preset time formation controller are obtained.

[0117] The omnidirectional mobile robot is a four-Mecanum wheeled robot;

[0118] The process of establishing the collision-free preset time formation controller includes the following steps:

[0119] A. Establishment of control model for multiple omnidirectional mobile robots

[0120] In a multi-omnidirectional mobile robot system, each robot is numbered to distinguish between them. The dynamic model of the i-th omnidirectional mobile robot is given. The dynamic model is described by the following differential equations:

[0121]

[0122] in, represents the position of the i-th omnidirectional mobile robot, represents the speed state of the i-th omnidirectional mobile robot,

[0123]

[0124] x wi and y wi They represent the X coordinates of the i-th omnidirectional mobile robot in the world coordinate system. w Direction and Y w Coordinate values ​​in the direction;

[0125] represents the robot coordinate system X of the i-th omnidirectional mobile robot r The positive direction of the axis and the world coordinate system X w The angle between the positive directions of the axes;

[0126] y i represents the output state of the i-th omnidirectional mobile robot;

[0127] q(τ i )=[q(τi,1 )q(τ i,2 )q(τ i,3 )q(τ i,4 )] T represents the output of the hysteresis quantizer, i.e., the collision-free preset time formation controller of the i-th omnidirectional mobile robot; q(τ i,1 ),q(τ i,2 ),q(τ i,3 ),q(τ i,4 ) represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the i-th omnidirectional mobile robot respectively;

[0128] Will and Abbreviated as f i,1 、f i,2 、g i 、f i ;f i,1 and f i,2 Represents the unknown nonlinear term caused by the difference between the actual model establishment and operation scenario of the omnidirectional mobile robot and the ideal assumption;

[0129] g i represents the inherent nonlinear term of the i-th omnidirectional mobile robot, f i represents the control input gain matrix inherent to the i-th omnidirectional mobile robot. These characteristics are derived from its unique structural features and can be expressed by the following mathematical formula:

[0130]

[0131] It is a 3×3 matrix representing the transformation matrix between the world coordinate system and the robot coordinate system;

[0132] represents the static friction force on the Mecanum wheel;

[0133] represents the angular velocity of each wheel of the omnidirectional mobile robot;

[0134] R represents the radius of the Mecanum wheel;

[0135] Is a 3×3 matrix, representing The derivative of the inverse matrix of ;

[0136] B θ represents the viscous friction coefficient of the Mecanum wheel;

[0137] J + is a 3×4 matrix, J is a 4×3 matrix, J +The Jacobian matrix of the forward kinematics model of the omnidirectional mobile robot; the Jacobian matrix of the inverse kinematics model of the omnidirectional mobile robot

[0138] represents the angular acceleration of the Mecanum wheel;

[0139] Q is a 4×4 matrix representing the gain matrix of the Mecanum wheel angular acceleration;

[0140] Q -1 It is a 4×4 matrix, representing the inverse matrix of Q.

[0141] B. Establishment of artificial potential field function

[0142] In order to clearly explain the collision-free problem, the obstacle set of the i-th omnidirectional mobile robot is defined as

[0143]

[0144] is the collision detection range;

[0145] is the pose of the i-th omnidirectional mobile robot, is the pose of the environmental obstacle.

[0146] The artificial potential field function is designed as follows:

[0147]

[0148] represents the collision-free distance error, represents z i,c The transpose of represents the total obstacle vector;

[0149] d Represents the minimum safe distance;

[0150] 0 m =[0 0 0] T .

[0151] Taking the partial derivative of the artificial potential field function, we get:

[0152]

[0153] C. Establishment of Lyapunov function

[0154] For the second-order omnidirectional mobile robot model, we only need to construct the Lyapunov function twice to obtain its adaptive law and controller.

[0155] The first construction of the Lyapunov function can be expressed in the following form:

[0156]

[0157] N represents the number of omnidirectional mobile robots;

[0158] is the ideal adjustment scalar of the i-th omnidirectional mobile robot Its estimated value The estimation error.

[0159] is the ideal adjustment scalar for the jth omnidirectional mobile robot Its estimated value The estimation error.

[0160] The second construction of the Lyapunov function can be expressed as follows:

[0161]

[0162] z i,2 represents the virtual tracking error of the i-th omnidirectional mobile robot;

[0163] s i,2 represents the filtering error of the i-th omnidirectional mobile robot;

[0164] represents the ideal adjustment scalar when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time;

[0165] is the ideal adjustment scalar when constructing the Lyapunov function for the second time Its estimated value The estimation error.

[0166] D. Preset time filter establishment

[0167] The preset time filter is expressed by the following differential equation:

[0168]

[0169] ω i (0) = α i,1 (0)

[0170] η∈(0,1), is a design parameter;

[0171] γ and is a design parameter;

[0172] φ is the filter design parameter;

[0173] T d It is a predetermined time;

[0174] c i,2 is a positive constant;

[0175] α i,1 is the virtual control variable of the i-th omnidirectional mobile robot, and its specific form will be given later.

[0176] E. Adaptive Law and Controller Establishment

[0177] The first construction of the adaptive law can be expressed in the following form:

[0178]

[0179] in, Adjust the scalar for ideality The estimated value of Indicates estimated value The derivative of Adjust the scalar for ideality The estimated value of Indicates estimated value The derivative of ;λ=2+η, All are design parameters

[0180] The second construction of the adaptive law can be expressed in the following form:

[0181]

[0182] is the ideal adjustment scalar when constructing the Lyapunov function for the second time The estimated value of Indicates estimated value The derivative of a ij Represents the communication between the i-th omnidirectional mobile robot and the j-th omnidirectional mobile robot. If there is information transmission between the two omnidirectional mobile robots, then a ij =1, otherwise a ij =0;

[0183] b i Represents the communication between the leader and the i-th omnidirectional mobile robot. If there is information transmission, then b i =1, otherwise b i =0;

[0184] Γ i,1 represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the first time;

[0185] Γ j,1represents the output vector of the radial basis function neural network when the j-th omnidirectional mobile robot constructs the Lyapunov function for the first time;

[0186] Γ i,2 Represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time.

[0187] Based on the previous work, we can obtain the virtual control variables and the final collision-free preset time formation controller, which can be expressed by the following formula:

[0188]

[0189] and is the position bias vector and The derivative of

[0190] is the ideal adjustment scalar estimated value of;

[0191] is the ideal adjustment scalar estimated value of;

[0192] c i,1 and c i,c is a positive design parameter;

[0193] is the reference signal y d The derivative of .

[0194]

[0195] δ is a design parameter, and its specific form will be given later;

[0196] is the ideal adjustment scalar estimated value.

[0197] The actual controller will be designed as follows:

[0198]

[0199] τ min >0 is the quantization dead zone; 0<Π<1 is the quantization density;

[0200] is a design parameter.

[0201] τ i Represents the input to the hysteresis quantizer.

[0202] The schematic diagram of the motion analysis of the multi-omnidirectional mobile robot according to the present invention is as follows Figure 1 The schematic diagram of the communication topology structure between the omnidirectional mobile robots involved in the present invention is shown in FIG. Figure 2 As shown, 0 represents the reference signal, i.e. the leader, 1, 2, 3 represent the three follower omnidirectional mobile robots, Figure 2 There are three followers in the control object.

[0203] The simulation results are as follows Figure 3-14 shown. Figure 3 The figure shows the trajectory of a multi-omnidirectional mobile robot formation. It can be seen that followers OMR1, OMR2, and OMR3 track the trajectory generated by the leader with a certain position offset, and there is no collision from beginning to end.

[0204] Figure 4 The position status tracking effect of each omnidirectional robot in the X direction is shown; Figure 5 The speed state tracking effect of each omnidirectional mobile robot in the X direction is shown; Figure 6 The position state tracking effect of each omnidirectional mobile robot in the Y direction is shown; Figure 7 The speed state tracking effect of each omnidirectional mobile robot in the Y direction is shown; Figure 8 The output state tracking effect of each omnidirectional mobile robot in the X direction is shown; Figure 9 The output state tracking effect of each omnidirectional mobile robot in the Y direction is shown;

[0205] Figure 4-Figure 9 It can be seen that the tracking errors of each state in the X and Y directions of each omnidirectional mobile robot gradually converge after 5 seconds, but there will be slight fluctuations when avoiding environmental obstacles, and then it will quickly stabilize, achieving the preset time stability of each state of each omnidirectional robot in the X and Y directions.

[0206] Figure 10 and Figure 11 The input torque of the four wheels of the first omnidirectional mobile robot is shown; q(τ 1,1 ),q(τ 1,2 ),q(τ 1,3 ),q(τ 1,2 ) represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the first omnidirectional mobile robot, respectively.

[0207] Figure 12 , Figure 13 and Figure 14 Shows the input torque of the wheels at the same position of three omnidirectional mobile robots.

[0208] Figure 10-14As can be seen, the input torque to each wheel of each omnidirectional mobile robot is extremely high at the beginning of the formation motion, then stabilizes. However, slight fluctuations occur during obstacle avoidance, before quickly stabilizing. This demonstrates the ability of the controller designed in this invention to achieve the desired timed formation control for a multi-omnidirectional mobile robot system.

[0209] The simulation results above demonstrate that the multi-omnidirectional mobile robot system can complete the formation task within the preset time, without collisions between the robots or with environmental obstacles. The system's input states are quantized effectively, and the tracking errors of the X- and Y-direction positions and velocities of each robot, as well as the overall output state, all stabilize within the preset time, achieving the desired collision-free, preset-time formation control.

[0210] The present invention is not limited to this embodiment, and any equivalent concepts or modifications within the technical scope disclosed by the present invention are included in the protection scope of the present invention.

Claims

1. A collision-free preset time formation control method for a multi-omnidirectional mobile robot model with input quantization, characterized in that: A system consisting of multiple omnidirectional mobile robots is used as the control object, and a dynamic model with unknown nonlinear terms is established. In the multi-omnidirectional mobile robot system, the dynamic model of the i-th omnidirectional mobile robot is described as follows: in, represents the position of the i-th omnidirectional mobile robot, represents the speed state of the i-th omnidirectional mobile robot, x wi and y wi They represent the X coordinates of the omnidirectional mobile robot in the world coordinate system. w Direction and Y w Coordinate values ​​in the direction; represents the robot coordinate system X of the i-th omnidirectional mobile robot r The positive direction of the axis and the world coordinate system X w The angle between the positive directions of the axes; y i represents the output state of the i-th omnidirectional mobile robot; q(τ i )=[q(τ i,1 )q(τ i,2 )q(τ i,3 )q(τ i,4 )] T represents the output of the hysteresis quantizer, i.e., the collision-free preset time formation controller of the i-th omnidirectional mobile robot; q(τ i,1 ),q(τ i,2 ),q(τ i,3 ),q(τ i,4 ) represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the i-th omnidirectional mobile robot respectively; Will and Abbreviated as f i,1 、f i,2 、g i 、f i ;f i,1 and f i,2 Represents the unknown nonlinear term caused by the difference between the actual model establishment and operation scenario of the omnidirectional mobile robot and the ideal assumption; g i represents the inherent nonlinear term of the i-th omnidirectional mobile robot, f i It represents the inherent control input gain matrix of the i-th omnidirectional mobile robot and is expressed by the following mathematical formula: It is a 3×3 matrix representing the transformation matrix between the world coordinate system and the robot coordinate system; represents the static friction force on the Mecanum wheel; represents the angular velocity of each wheel of the omnidirectional mobile robot; R represents the radius of the Mecanum wheel; Is a 3×3 matrix, representing The derivative of the inverse matrix of ; B θ represents the viscous friction coefficient of the Mecanum wheel; J + is a 3×4 matrix, and J is a 4×3 matrix, representing the Jacobian matrices of the forward kinematics model and inverse kinematics model of the omnidirectional mobile robot respectively; represents the angular acceleration of the Mecanum wheel; Q is a 4×4 matrix representing the gain matrix of the Mecanum wheel angular acceleration; Q -1 Is a 4×4 matrix, representing the inverse matrix of Q; Define the obstacle set for the i-th omnidirectional mobile robot is the collision detection range; Ω i represents the neighborhood set of the i-th follower; is the pose of the i-th omnidirectional mobile robot, is the pose of the environmental obstacle; The artificial potential field function is constructed as follows: represents the collision-free distance error, and c represents the obstacle set Obstacles in d Represents the minimum safe distance; 0 m ＝[0 0 0] T ； Taking the partial derivative of the artificial potential field function, we get: Using radial basis function neural network to approximate the unknown nonlinear terms in the dynamic model, and establishing Lyapunov function; Combined with dynamic surface control technology, a preset time filter is constructed; Design an adaptive law and a collision-free preset time formation controller for multiple omnidirectional mobile robot models.

2. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 1, characterized in that: For the second-order omnidirectional mobile robot model, the Lyapunov function is constructed twice; The first constructed Lyapunov function is expressed as follows: N represents the number of omnidirectional mobile robots; is the ideal adjustment scalar of the i-th omnidirectional mobile robot Its estimated value The estimation error of is the ideal adjustment scalar for the jth omnidirectional mobile robot Its estimated value The estimation error of The second constructed Lyapunov function is expressed as follows: z i,2 represents the virtual tracking error of the i-th omnidirectional mobile robot; s i,2 represents the filtering error of the i-th omnidirectional mobile robot; represents the ideal adjustment scalar when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time; is the ideal adjustment scalar when constructing the Lyapunov function for the second time Its estimated value The estimation error.

3. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 2, characterized in that: The preset time filter is expressed by the following differential equation: represents the first-order derivative of the filter, ω i (0) represents the initial value of the filter; η∈(0,1), is a design parameter; γ and is a design parameter; φ is the filter design parameter; T d It is a predetermined time; c i,2 is a positive constant; α i,1 is the virtual control variable of the i-th omnidirectional mobile robot.

4. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 3, characterized in that: The first constructed adaptive law is expressed in the following form: in, Adjust the scalar for ideal The estimated value of Indicates estimated value The derivative of Adjust the scalar for ideal The estimated value of Indicates estimated value The derivative of ;λ=2+η, λ and All are design parameters; The adaptive law constructed for the second time is expressed in the following form: Ideal adjustment scalar for the second construction of the Lyapunov function The estimated value of Indicates estimated value The derivative of a ij Represents the communication between the i-th omnidirectional mobile robot and the j-th omnidirectional mobile robot. If there is information transmission between the two omnidirectional mobile robots, then a ij =1, otherwise a ij =0; b i Represents the communication between the leader and the i-th omnidirectional mobile robot. If there is information transmission, then b i =1, otherwise b i =0; Γ i,1 represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the first time; Γ j,1 represents the output vector of the radial basis function neural network when the j-th omnidirectional mobile robot constructs the Lyapunov function for the first time; Γ i,2 represents the output vector of the radial basis function neural network when the i-th omnidirectional mobile robot constructs the Lyapunov function for the second time; The virtual control variables and the final collision-free preset time formation controller are expressed by the following formula: represents the position bias vector of the i-th omnidirectional mobile robot; represents the position bias vector of the jth omnidirectional mobile robot; and is the position bias vector and The derivative of is the ideal adjustment scalar estimated value of; is the ideal adjustment scalar estimated value of; c i,1 and c i,c is a positive design parameter; is the reference signal y d The derivative of τ i represents the input of the hysteresis quantizer; δ is a design parameter, and its specific form will be given later; The controller design is as follows: τ min >0 is the quantization dead zone; 0<Π<1 is the quantization density is a design parameter.

5. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 1, characterized in that: The omnidirectional mobile robot is a four-Mecanum wheeled robot.

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