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

Abstract

The invention discloses a collision-free preset time formation control method for a multi-omni-directional mobile robot model with input quantization, which is controlled by a collision-free preset time formation controller and comprises the following steps of: firstly, establishing a multi-omni-directional mobile robot dynamic model with unknown nonlinear terms; by analyzing the kinetic model, a hysteresis quantizer can be constructed to quantize continuous input signals into discrete signals, and a novel artificial potential field function is constructed to realize no collision among a plurality of omnidirectional mobile robots and no collision between the robots and environmental obstacles. An unknown non-linear term is approximated by using a radial basis function neural network so as to establish a Lyapunov function, and a preset time filter is constructed in combination with a dynamic surface control technology. On the basis of the work, the adaptive law of the multi-omni-directional mobile robot model and a collision-free preset time formation controller can be obtained.

Description

Technical Field

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

[0002] In recent years, with the booming development of control technologies such as unmanned aerial vehicle control technology and robot formation control technology, the adaptive control of omnidirectional mobile robots has gradually become a research hotspot. However, with the continuous progress 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 task objectives by itself when facing increasingly complex task requirements. Therefore, the formation control of multi-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 the formation according to task requirements and accurately execute various instructions, which makes omnidirectional mobile robots have broad application prospects in many fields, especially in task environments that require high precision and high flexibility.

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

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

[0005] Second, in the existing control methods for omnidirectional mobile robot formations, although the controlled system can achieve the state that all signals in the closed-loop system are semi-globally ultimately uniformly bounded, their systems are all triggered in real time, which may lead to unnecessary data transmission and waste of communication resources. In practical applications, people usually hope to complete the formation task with fewer resources. Summary of the Invention

[0006] To solve the deficiencies of the existing technology, the present invention designs a collision-free preset-time formation control method for a multi-omnidirectional mobile robot model with input quantization. The method of the present invention quantizes continuous input signals into discrete signals to improve the signal transmission performance of the system, save communication resources, ensure that the controlled system can be stable within a preset time, and at the same time ensure that multiple omnidirectional mobile robots in the system are collision-free throughout the process.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A collision-free preset-time formation control method for a multi-omnidirectional mobile robot model with input quantization, including using a system composed of multiple omnidirectional mobile robots as the control object to establish a dynamic model with unknown non-linear terms;

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

[0009] Use a radial basis function neural network to approximate the unknown non-linear terms in the dynamic model and establish a Lyapunov function;

[0010] Combine the dynamic surface control technology to construct a preset-time filter;

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

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

[0013]

[0014] Among them, represents the pose of the i-th omnidirectional mobile robot, represents the velocity state of the i-th omnidirectional mobile robot,

[0015]

[0016] x wi and y wi respectively represent the coordinate values of the omnidirectional mobile robot in the X w direction and the Y w direction in the world coordinate system;

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

[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, that is, 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 ) respectively represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the $i$-th omnidirectional mobile robot;

[0021] Let and be abbreviated as $f$ i,1 、$f$ i,2 、$g$ i 、$f$ i ; $f$ i,1 and $f$ i,2 represent the unknown nonlinear terms caused by the differences between the actual model establishment and operation scenarios of the omnidirectional mobile robot and the ideal assumptions;

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

[0023]

[0024] 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 kinematic model and the inverse kinematic 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 angular acceleration of the Mecanum wheel;

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

[0034] Furthermore, define the obstacle set of the i-th omnidirectional mobile robot

[0035]

[0036] is the collision detection range;

[0037] z i,1 is the output state tracking error of the i-th omnidirectional mobile robot, and 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, c represents the obstacle in the obstacle set among them,

[0042] d represents the minimum safety distance;

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

[0044] Taking the partial derivative of the artificial potential field function gives:

[0045]

[0046] Furthermore, for the second-order omnidirectional mobile robot model, two Lyapunov functions are constructed;

[0047] The Lyapunov function constructed for the first time is expressed in the following form:

[0048]

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

[0050] is the ideal adjustment scalar of the i-th omnidirectional mobile robot and its estimated value is the estimation error;

[0051] is the ideal adjustment scalar of the j-th omnidirectional mobile robot and its estimated value is the estimation error;

[0052] The Lyapunov function constructed for the second time is expressed in the following form:

[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 constructing the Lyapunov function for the second time for the i-th omnidirectional mobile robot;

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

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

[0059]

[0060] represents the first derivative of the filter, ω i (0) represents the initial value of the filter;

[0061] η ∈ (0, 1), which is a design parameter;

[0062] γ and are design parameters;

[0063] φ is a filter design parameter;

[0064] T d is a predetermined time;

[0065] c i,2 is a positive constant;

[0066] α i,1 is the virtual control variable of the i-th omnidirectional mobile robot.

[0067] Furthermore, the first constructed adaptation law is expressed in the following form:

[0068]

[0069] where, is the estimated value of the ideal tuning scalar , represents the derivative of the estimated value ;

[0070] is the estimated value of the ideal tuning scalar , represents the derivative of the estimated value ; λ = 2 + η, λ and are both design parameters.

[0071] The second constructed adaptation law is expressed in the following form:

[0072]

[0073]

[0074] is the estimated value of the ideal tuning scalar when constructing the second Lyapunov function , represents the derivative of the estimated value , 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;

[0075] 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;

[0076] Γ i,1 represents the output vector of the radial basis function neural network when constructing the Lyapunov function for the first time of the i-th omnidirectional mobile robot;

[0077] 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;

[0078] 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.

[0079] The virtual control variable and the final collision-free preset time formation controller are expressed by the following formula:

[0080]

[0081] represents the position offset vector of the i-th omnidirectional mobile robot;

[0082] represents the position offset vector of the j-th omnidirectional mobile robot;

[0083] and is the position offset vector and derivative;

[0084] is the estimated value of the ideal adjustment scalar ;

[0085] is the estimated value of the ideal adjustment scalar ;

[0086] c i,1 and c i,c are positive design parameters;

[0087] is the derivative of the reference signal y d ;

[0088]

[0089] τ i represents the input of the hysteresis quantizer;

[0090] δ is a design parameter, and its specific form will be given later;

[0091] The controller design form is as follows:

[0092]

[0093] τ min >0 is the quantization dead zone; 0 < Π < 1 is the quantization density

[0094] is a design parameter.

[0095] Furthermore, the omnidirectional mobile robot is a four-Mecanum-wheel robot.

[0096] Compared with the existing work technologies, the present invention has the following beneficial effects:

[0097] First, in the existing control methods for omnidirectional mobile robot formations, most do not consider the collision-free problem of the system and do not consider the convergence time problem of the omnidirectional mobile robot formation during the control process. Considering that the convergence time is a key index for evaluating the dynamic characteristics of the controlled system, the present invention designs a preset time filter and a preset time formation controller, enabling the multi-omnidirectional mobile robot system to complete the formation task within the optimal time period, and introducing a new artificial potential field function to achieve collision-free formation control of multi-omnidirectional mobile robots. This method can not only stabilize the controlled system within the preset time but also ensure that multiple omnidirectional mobile robots are collision-free throughout the process.

[0098] Second, in the existing control methods for omnidirectional mobile robot formations, although all signals in the closed-loop system of the controlled system can achieve a semi-globally ultimately uniformly bounded state, their systems are all triggered in real time, which may lead to unnecessary data transmission and waste of communication resources. Considering the limited resources, the present invention designs a hysteresis quantizer applicable to the multi-omnidirectional mobile robot model, quantizing the continuous input signal τ i , through the hysteresis quantizer, into a discrete input signal q(τ i ), improving the signal transmission performance of the system, saving communication resources, and providing strong technical support for the high-response-speed, high-precision, and low-resource-consumption control of the multi-omnidirectional mobile robot model formation control. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 is a simplified diagram for the motion analysis of multi-omnidirectional mobile robots.

[0100] Figure 2 is a schematic diagram of the communication topology structure among omnidirectional mobile robots.

[0101] Figure 3 is a formation motion trajectory diagram of omnidirectional mobile robots (OMRs) in the X-Y plane.

[0102] Figure 4 is a position state tracking error diagram of each omnidirectional mobile robot in the X direction.

[0103] Figure 5 is a speed state tracking error diagram of each omnidirectional mobile robot in the X direction.

[0104] Figure 6 It is the position state tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0105] Figure 7 It is the speed state tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0106] Figure 8 It is the output tracking error diagram of each omnidirectional mobile robot in the X direction.

[0107] Figure 9 It is the output tracking error diagram of each omnidirectional mobile robot in the Y direction.

[0108] Figure 10 It is the input torque diagram of the first and second wheels of the first omnidirectional mobile robot.

[0109] Figure 11 It is the input torque diagram of the third and fourth wheels of the first omnidirectional mobile robot.

[0110] Figure 12 It is the input torque diagram of the first wheel of the first omnidirectional mobile robot.

[0111] Figure 13 It is the input torque diagram of the first wheel of the second omnidirectional mobile robot.

[0112] Figure 14 It is the input torque diagram of the first wheel of the third omnidirectional mobile robot. Specific implementation manner

[0113] Combining the backstepping method and the dynamic surface control technology, the present invention proposes a collision-free preset-time formation control method for a multi-omnidirectional mobile robot model with input quantization, which is controlled by a collision-free preset-time formation controller. The establishment process of this controller includes the establishment of a multi-omnidirectional mobile robot control model, the establishment of an artificial potential field function, the establishment of a Lyapunov function, the establishment of a preset-time filter, the establishment of an adaptive law, and the establishment of a collision-free preset-time formation controller. By using the control method of the present invention, the preset-time stability of the system is achieved and it is ensured that multiple omnidirectional mobile robots in the system do not collide during the whole process.

[0114] First, a system composed of multiple omnidirectional mobile robots is selected as the control object. All the omnidirectional mobile robots in the control object are followers. A dynamic model of multiple omnidirectional mobile robots with unknown nonlinear terms is constructed. By analyzing this dynamic model, a hysteresis quantizer can be constructed to quantize continuous input signals into discrete signals. An artificial potential field function is also constructed to achieve collision-free among multiple omnidirectional mobile robots and between the robots and environmental obstacles. Under the framework of the backstepping recursive method, a radial basis function neural network is used to approximate the unknown nonlinear terms, and a Lyapunov function is established accordingly. Combining 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.

[0115] The omnidirectional mobile robot is a four-Mecanum-wheel robot;

[0116] The establishment process of the collision-free preset-time formation controller includes the following steps:

[0117] A. Establishment of the control model for multiple omnidirectional mobile robots

[0118] In the multiple omnidirectional mobile robot system, to distinguish multiple omnidirectional mobile robots, each robot is numbered, and the dynamic model of the \(i\)-th omnidirectional mobile robot is given. The dynamic model is described by the following differential equation system:

[0119]

[0120] Among them, represents the pose of the \(i\)-th omnidirectional mobile robot, represents the velocity state of the \(i\)-th omnidirectional mobile robot,

[0121]

[0122] x wi and y wi respectively represent the coordinate values of the \(i\)-th omnidirectional mobile robot in the \(X\) w direction and \(Y\) w direction in the world coordinate system;

[0123] represents the angle between the positive direction of the \(X\) r axis of the robot coordinate system of the \(i\)-th omnidirectional mobile robot and the positive direction of the \(X\) w axis of the world coordinate system;

[0124] y i represents the output state of the \(i\)-th omnidirectional mobile robot;

[0125] 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 ) respectively represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the i-th omnidirectional mobile robot;

[0126] Let and be abbreviated as f i,1 、f i,2 、g i 、f i ; f i,1 and f i,2 represent the unknown non-linear terms caused by the differences between the actual model establishment and operation scenarios of the omnidirectional mobile robot and the ideal assumptions;

[0127] g i represents the inherent non-linear term of the i-th omnidirectional mobile robot itself, and f i represents the inherent control input gain matrix of the i-th omnidirectional mobile robot itself. These characteristics stem from its unique structural features and can be expressed by the following mathematical formula:

[0128]

[0129] is a 3×3 matrix representing the transformation matrix between the world coordinate system and the robot coordinate system;

[0130] represents the static friction force on the Mecanum wheel;

[0131] represents the angular velocity of each wheel of the omnidirectional mobile robot;

[0132] R represents the radius of the Mecanum wheel;

[0133] is a 3×3 matrix representing the derivative of the inverse matrix of;

[0134] B θ represents the viscous friction coefficient of the Mecanum wheel;

[0135] J + is a 3×4 matrix, J is a 4×3 matrix, J +Denote the Jacobian matrix of the forward kinematic model of the omnidirectional mobile robot; J is the Jacobian matrix of the inverse kinematic model of the omnidirectional mobile robot

[0136] represents the angular acceleration of the Mecanum wheel;

[0137] Q is a 4×4 matrix representing the gain matrix of the Mecanum wheel angular acceleration;

[0138] Q -1 is a 4×4 matrix representing the inverse matrix of Q.

[0139] B. Establishment of the artificial potential field function

[0140] To clearly explain the collision-free problem, the obstacle set of the i-th omnidirectional mobile robot is defined

[0141]

[0142] is the collision detection range;

[0143] z i,1 is the output state tracking error of the i-th omnidirectional mobile robot;

[0144] is the pose of the i-th omnidirectional mobile robot, is the pose of the environmental obstacle.

[0145] The artificial potential field function is designed as follows:

[0146]

[0147] represents the collision-free distance error, denotes i,c the transpose of z represents the total obstacle vector;

[0148] d represents the minimum safety distance;

[0149] 0 m =[0 0 0] T .

[0150] Taking the partial derivative of the artificial potential field function gives:

[0151]

[0152] C. Establishment of the Lyapunov function

[0153] For the second-order omnidirectional mobile robot model, we only need to construct the Lyapunov function twice to obtain its adaptive law and controller.

[0154] The first construction of the Lyapunov function can be expressed in the following form:

[0155]

[0156] N represents the number of omnidirectional mobile robots;

[0157] is the ideal adjustment scalar of the i-th omnidirectional mobile robot and its estimated value The estimation error.

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

[0159] The second construction of the Lyapunov function can be expressed in the following form:

[0160]

[0161] z i,2 represents the virtual tracking error of the i-th omnidirectional mobile robot;

[0162] s i,2 represents the filtering error of the i-th omnidirectional mobile robot;

[0163] represents the ideal adjustment scalar of the i-th omnidirectional mobile robot when constructing the Lyapunov function for the second time;

[0164] is the ideal adjustment scalar when constructing the Lyapunov function for the second time and its estimated value The estimation error.

[0165] D. Establishment of the preset time filter

[0166] The preset time filter mentioned above is represented by the following differential equation:

[0167]

[0168] η ∈ (0, 1), is a design parameter;

[0169] γ and are design parameters;

[0170] φ is a filter design parameter;

[0171] T d is a predetermined time;

[0172] c i,2 is a positive constant;

[0173] α i,1 is the virtual control variable of the i-th omnidirectional mobile robot, and its specific form will be given later.

[0174] Establishment of E, adaptation law and controller

[0175] The first construction of the adaptation law can be expressed in the following form:

[0176]

[0177] where is the estimated value of the ideal tuning scalar , represents the derivative of the estimated value ; is the estimated value of the ideal tuning scalar , represents the derivative of the estimated value ; λ = 2 + η, are all design parameters

[0178] The second construction of the adaptation law can be expressed in the following form:

[0179]

[0180] is the estimated value of the ideal tuning scalar when constructing the Lyapunov function for the second time , represents the derivative of the estimated value , 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;

[0181] 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;

[0182] Γ i,1 represents the output vector of the radial basis function neural network when constructing the Lyapunov function for the first time for the i-th omnidirectional mobile robot;

[0183] Γ j,1Denote 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;

[0184] Γ i,2 Denote 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.

[0185] Based on the previous work, we can obtain the virtual control variable and the final collision-free preset-time formation controller, which can be expressed by the following formula:

[0186]

[0187] and is the position offset vector and 's derivative;

[0188] is the estimated value of the ideal adjustment scalar ;

[0189] is the estimated value of the ideal adjustment scalar ;

[0190] c i,1 and c i,c are positive design parameters;

[0191] is the derivative of the reference signal y d .

[0192]

[0193] δ is a design parameter, and its specific form will be given later;

[0194] is the estimated value of the ideal adjustment scalar .

[0195] The actual controller will be designed in the following form:

[0196]

[0197] τ min >0 is the quantization dead zone; 0 < Π < 1 is the quantization density;

[0198] is a design parameter.

[0199] τ i represents the input of the hysteresis quantizer.

[0200] The motion analysis diagram of the multi-omnidirectional mobile robot involved in the present invention is as shown in Figure 1 . The schematic diagram of the communication topology structure among the omnidirectional mobile robots involved in the present invention is as shown in Figure 2 . 0 represents the reference signal, that is, the leader, and 1, 2, and 3 represent three follower omnidirectional mobile robots. Figure 2 Among them, the controlled objects are three followers.

[0201] The simulation results are as shown in Figures 3 - 14 . Figure 3 It shows the formation motion trajectory of the multi-omnidirectional mobile robots. It can be seen that the followers OMR1, OMR2, and OMR3 track the motion trajectory generated by the leader Leader with a certain position offset, and there is no collision from beginning to end;

[0202] Figure 4 It shows the position state tracking effect of each omnidirectional robot in the X direction; Figure 5 It shows the speed state tracking effect of each omnidirectional mobile robot in the X direction; Figure 6 It shows the position state tracking effect of each omnidirectional mobile robot in the Y direction; Figure 7 It shows the speed state tracking effect of each omnidirectional mobile robot in the Y direction; Figure 8 It shows the output state tracking effect of each omnidirectional mobile robot in the X direction; Figure 9 It shows the output state tracking effect of each omnidirectional mobile robot in the Y direction;

[0203] Figures 4 - 9 It can be seen that the tracking errors of each state of each omnidirectional mobile robot in the X direction and the Y direction gradually converge after 5 s, but there will be small fluctuations when avoiding obstacles in the environment, and then it quickly stabilizes, realizing the preset time stability of each state of each omnidirectional robot in the X direction and the Y direction.

[0204] Figure 10 And Figure 11 show the input torques of the 4 wheels of the first omnidirectional mobile robot; q(τ 1,1 ), q(τ 1,2 ), q(τ 1,3 ), q(τ 1,2 ) respectively represent the input torques of the 1st, 2nd, 3rd, and 4th Mecanum wheels of the first omnidirectional mobile robot.

[0205] Figure 12 , Figure 13 And Figure 14 show the input torques of the wheels at the same position of the 3 omnidirectional mobile robots.

[0206] Figures 10 - 14It can be seen that the input torque of each wheel of each omnidirectional mobile robot is extremely large in the initial stage of formation movement, and then tends to be stable. However, when avoiding environmental obstacles, there will be small fluctuations, and then it quickly stabilizes again, and good quantization effects are achieved. From the perspective of force, it shows that through the controller designed by the present invention, the multi-omnidirectional mobile robot system can achieve the expected formation control within the preset time.

[0207] It can be seen from the above simulation result diagrams that the multi-omnidirectional mobile robot system can complete the formation task within the preset time, and can achieve no collision between multiple omnidirectional mobile robots and no collision between the omnidirectional mobile robot and environmental obstacles. The quantization effect of the system input state is very good, and the tracking errors of the position states, velocity states in the X and Y directions, and the overall output state of each omnidirectional mobile robot in the system reach stability within the preset time, achieving the expected collision-free preset time formation control.

[0208] The present invention is not limited to this embodiment, and any equivalent conceptions or changes 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 taken as the control object, and a dynamic model with unknown nonlinear terms is established; Construct artificial potential field function; 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 is characterized in that: In a multi-omnidirectional mobile robot system, the dynamic model of the i-th omnidirectional mobile robot is described as follows: in, represents the position and posture of the i-th omnidirectional mobile robot, represents the speed state of the i-th omnidirectional mobile robot, x wi and wi They represent the X coordinates of the omnidirectional mobile robot in the world coordinate system. w Direction and Y w Coordinate values ​​in direction; represents the robot coordinate system X of the i-th omnidirectional mobile robot r The positive direction of the axis is the same as 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 It 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 control input gain matrix inherent to 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, which represent 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.

3. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 2 is characterized in that: Define the obstacle set for the i-th omnidirectional mobile robot is the collision detection range; z i,1 is the output state tracking error of the i-th omnidirectional mobile robot, Ω i represents the neighborhood set of the i-th follower; is the pose of the i-th omnidirectional mobile robot, is the position of environmental obstacles; The artificial potential field function is designed 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 partial derivative of the artificial potential field function, we get:

4. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 3 is characterized in that: For the second-order omnidirectional mobile robot model, the Lyapunov function is constructed twice; The first constructed Lyapunov function is expressed in the following form: N represents the number of omnidirectional mobile robots; is the ideal adjustment scalar for the i-th omnidirectional mobile robot With its estimated value The estimation error of is the ideal adjustment scalar for the jth omnidirectional mobile robot With 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 for the second construction of the Lyapunov function With its estimated value The estimation error.

5. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 4, characterized in that: The preset time filter is expressed by the following differential equation: oh i (0)=a i,1 (0) 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 the 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.

6. The collision-free preset time formation control method of a multi-omnidirectional mobile robot model with input quantization according to claim 5, 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: The ideal adjustment scalar for the second construction of the Lyapunov function The estimated value of Indicates estimated value The derivative of 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 It 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 offset vector and The derivative of is the ideal adjustment scalar An estimated value of is the ideal adjustment scalar An 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 form is as follows: t iβ =P 1-β t min ,β=1,2,..., τ min >0 is the quantization dead zone; 0<Π<1 is the quantization density is a design parameter.

7. 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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