Finite-time Tracking Control Method for Lane-changing Warning of Four-wheel Mobile Robots

Abstract

The present invention discloses a finite-time tracking control method applicable to lane-changing warning of a four-wheel mobile robot, constructs a dynamic model of the four-wheel mobile robot; constructs a minimum-distance warning model according to the dynamic model, and uses the machine learning GMM-HMM method, combined with the minimum-distance warning model, to obtain a lane-changing warning safety algorithm for the four-wheel mobile robot, realizing safety warning during the lane-changing process of the mobile four-wheel mobile robot; constructs a finite-time controller for the four-wheel mobile robot with time-varying constraints; determines whether there is danger in lane-changing according to the lane-changing warning safety algorithm of the four-wheel mobile robot, and if so, executes the finite-time controller, and realizes the finite-time stability of the four-wheel mobile robot under this finite-time controller. The present invention realizes that both the sideslip angle of the center of mass and the yaw angular velocity can be constrained in a stable interval during the lane-changing process of the four-wheel mobile robot, and the tracking error of the finite-time controller will not break through the time-varying constraints.

Description

Technical Field

[0001] The present invention relates to the technical field of robot motion control, and particularly relates to a finite-time tracking control method applicable to lane-changing warning of a four-wheel mobile robot. Background Art

[0002] In the past few decades, with the rapid development of fields such as communication and computer networks, related topics of four-wheel mobile robots have become a major research direction in the field of automatic control. Since four-wheel mobile robots are widely used in daily express sorting and special transportation. In order to better utilize mobile robots to assist in completing various tasks and ensure the driving safety of four-wheel mobile robots. More and more researchers are engaged in related research.

[0003] Early warning methods for four-wheel mobile robots include minimum safety distance, machine learning SVM, machine vision, and convolutional neural network. It is mainly used to identify the intentions of surrounding mobile robots for safety warning during lane-changing. Control methods for mobile robots include open-loop control and closed-loop control. Open-loop control is easy to control, but has poor robustness and cannot well suppress interference. Closed-loop control is less affected by its own parameter changes and has strong robustness. Therefore, the closed-loop control of the mobile robot system has important practical application value.

[0004] The lane-changing warning method is based on the operating parameters of the mobile robot's driving behavior. Researchers use the motion data of the mobile robot as the input feature parameters of the classifier, train the support vector machine (SVM) for application to the robot lane recognition and intention change, and also use statistical signal processing and machine learning techniques to model various aspects of the robot's behavior to detect dangerous driving behaviors. There are also researchers who use machine vision to track the motion information and position information of the front robot, use the feature information of SVM for pre-training and recognition of the robot's motion behavior, and additionally consider the angular velocity of the robot's wheel rotation and lateral acceleration as the best observation variables to establish an HMM model for identifying the lane-changing intention of the mobile robot. First, use machine vision to locate the center of the front robot, then use binocular vision to measure the distance between the front robot and the lane, and judge the driving distance of the front robot according to the dispersion. Due to the low recognition efficiency of machine learning, the safety of the current mobile robot warning method based on machine learning needs to be improved.

[0005] Autonomous tracking of a mobile robot means controlling the mobile robot to travel along a planned trajectory, thereby achieving a lane-changing task. Some scholars use the PID algorithm to control the longitudinal headway when a four-wheel robot is following, and some scholars use a control method that combines sliding mode control and a non-linear dynamics model. Under the conditions of initial velocity deviation of interference and adjustment of the speed of the front robot, it can track the speed well. In modern control theory, the model predictive control method is used to control the steering angle of the front wheels of the robot, which can ensure that the four-wheel robot can quickly and accurately track the obstacle avoidance route. Researchers use integral backstepping to derive a lateral lane-changing trajectory tracking controller with a closed-loop structure. In order to achieve the stability constraint control goal, various methods such as model predictive control are proposed and evaluated. In recent years, the finite-time control problem of four-wheel mobile robot systems has received increasing attention from researchers. Compared with asymptotic stable control, finite-time control has the advantages of fast speed, high path tracking accuracy, and strong robustness. Therefore, in order to solve engineering problems, finite-time control is applied to improve the steady-state and dynamic performance of the system. In addition, finite-time control can comply with strict transient response requirements, allowing related industries to improve production efficiency.

[0006] Mobile robot constraints are also issues worthy of study in autonomous tracking control. Mobile robots can usually be described by one or more stability constraints. Some scholars have proposed a lane-changing framework constraint based on a safe driving network to plan the desired robot state. The control barrier function (CBF) has been used to solve the safety control problems of autonomous ground four-wheel mobile robots (AGVs) and other mobile systems (such as lane keeping and adaptive cruise). In addition, in some cases, the time-varying control barrier function has an invariant control of dynamic constraints, and it is used to solve related safety control. With the changes in the longitudinal speed and steering angle of the four-wheel mobile robot, the selection of the lateral stability of the mobile robot is actually time-varying and control-related. To sum up, considering the state constraints of time-varying four-wheel mobile robots is also an area that needs improvement in finite-time trajectory tracking.

[0007] Although many achievements have been made in the lane-changing warning and automatic control of four-wheel mobile robots, no relevant achievements have been made in the finite-time tracking control method for lane-changing warning of four-wheel mobile robots. On the one hand, in practical applications, the control systems of four-wheel mobile robots are subject to various constraints, such as road surface slip rate constraints and speed and acceleration boundary constraints. On the other hand, due to the rapid development of industrial production, higher industrial production indicators and higher safety requirements have forced finite-time control to become an important consideration. Although there are relevant studies on the finite-time control problem under state constraints, there is no relevant research on the finite-time control of safe lane-changing warning under time-varying constraints, which makes the minimum safe lane-changing warning control performance of four-wheel mobile robots have some defects. First, in terms of lane-changing warning, most of the existing safety warning methods are machine learning SVM, which cannot guarantee the safety of four-wheel mobile robots during driving. Second, in terms of controlling speed, the existing control methods have a relatively long control time for mobile robots, which cannot meet higher control requirements. Finally, the existing finite-time controllers do not consider time-varying safety constraints, which poses a hidden danger to the driving stability of the controllers.

[0008] It can be seen that the research on the finite-time tracking control method for lane-changing warning of four-wheel mobile robots still faces many challenges, mainly including the following three technical problems: First, for lane-changing safety warning, how to design a safer lane-changing warning algorithm; second, how to design a finite-time controller under time-varying constraint conditions; third, how to design a controller with a suitable structure based on a complex controller structure. Summary of the Invention

[0009] The present invention aims to solve at least one of the above three technical problems.

[0010] To achieve the above object, the present invention provides a finite-time tracking control method applicable to lane-changing warning of four-wheel mobile robots, specifically including the following steps:

[0011] S1: Construct a dynamic model of a four-wheel mobile robot;

[0012] S2: Construct a minimum distance warning model according to the dynamic model, and use the machine learning GMM-HMM method to combine with the minimum distance warning model to obtain a lane-changing warning safety algorithm for four-wheel mobile robots, so as to realize the safety warning of four-wheel mobile robots during the lane-changing process;

[0013] S3: In order to safely constrain the yaw angular velocity of a four-wheel mobile robot during the lane-changing process, construct a finite-time controller for a four-wheel mobile robot with time-varying constraints;

[0014] S4: Determine whether there is danger in lane change according to the lane change warning safety algorithm for the four-wheel mobile robot. If so, execute the finite-time controller to achieve the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0015] Further, in step S1, the expression of the dynamic model of the four-wheel mobile robot is as follows:

[0016]

[0017]

[0018] where β and ω are the sideslip angle and yaw angular velocity of the center of mass of the four-wheel mobile robot; k f , k r are the front axle tire stiffness and rear axle tire stiffness of the four-wheel mobile robot, l f , l r are the front axle length and rear axle length of the four-wheel mobile robot, m is the mass of the four-wheel mobile robot, v x is the longitudinal velocity of the four-wheel mobile robot, I z is the moment of inertia of the whole vehicle of the four-wheel mobile robot, δ f is the front wheel steering angle, M z is the additional yaw moment of the four-wheel mobile robot, F yf , F yr are the front wheel side force and rear wheel side force of the four-wheel mobile robot;

[0019] By introducing the coordinate transformation u c = M z , y = β, so the above formula can be transformed into the following:

[0020]

[0021]

[0022] y = β

[0023] where the values of each formula are:

[0024]

[0025]

[0026] Further, in step S2, it is set that the minimum distance warning model of the four-wheel mobile robot includes three four-wheel mobile robots, namely the target robot, the first reference robot and the second reference robot. Among them, the target robot and the second reference robot are in the same lane, and the target robot and the first reference robot are in adjacent lanes. The expression of the constructed minimum distance warning model is as follows:

[0027]

[0028] Use lidar to obtain the longitudinal speeds of the target robot, the first reference robot, and the second reference robot; v r = v x - v p is the relative longitudinal speed between the target robot and the second reference robot, v x represents the longitudinal speed of the target robot, v p represents the longitudinal speed of the second reference robot, D r is the minimum safe distance maintained by the target robot from the first reference robot or the second reference robot, D s is the relative distance between the target robot and the second reference robot, D m is the distance traveled by the target robot, D p is the distance traveled by the second reference robot, τ1 + τ2 represents the time taken by the target robot from reaction to starting braking, g is the acceleration due to gravity, is the road surface adhesion coefficient.

[0029] Further, in step S2, by using the machine learning GMM-HMM method and combining with the minimum distance warning model, a lane-changing warning safety algorithm for the four-wheel mobile robot is obtained to realize the safety warning during the lane-changing process of the four-wheel mobile robot, including:

[0030] When using the machine learning GMM-HMM method to identify the motion behavior of the four-wheel mobile robot on the basis of establishing the minimum distance warning model, the probability distribution of the GHH-HMM model is described as follows:

[0031]

[0032]

[0033]

[0034] Among them, c im is the mixing weight coefficient of the m-th single Gaussian function of the hidden state s i u im is the weight matrix of the m-th single Gaussian function of the hidden state s i U im is the covariance matrix of the m-th single Gaussian function of the hidden state s i O = (v x , v y , x y ) is the selected observation matrix, v x , v y , x yThey are the longitudinal speed, lateral speed, and lateral displacement of the four-wheel mobile robot respectively; the GMM-HMM parameters are defined as λ = (π, A, c, u, U), where π is the initial state probability distribution vector, A is the state transition probability distribution matrix, c is the mixing weight coefficient, u is the weight matrix, and U is the covariance matrix;

[0035] The mixing weight probability of the GHH-HMM model is b i (O), N(O, u im , U im ); The calculation of the next hidden probability is as follows: It is defined as the probability function that the hidden state at time t is s i and the observation sequence is k;

[0036]

[0037] Among them, Ω i (i) represents the observation value sequence of the previous part up to time t under the GMM-HMM parameters λ = (π, A, c, u, U), and Ξ i (i) represents the observation value sequence of the previous and subsequent parts up to time t under the GMM-HMM parameters λ = (π, A, c, u, U); c ik is the mixing weight coefficient of the k-th single Gaussian function of the hidden state s i , O t is the given observation sequence; u ik is the weight matrix of the k-th single Gaussian function of the hidden state s i , U ik is the covariance matrix of the k-th single Gaussian function of the hidden state s i , l(O t , u ik , U ik ) represents that the hidden state at time t is s i and the probability value of the hidden state sequence formed by the hidden state s i and the previous t - 1 hidden states is the largest;

[0038] The following is the probability estimated by the GMM-HMM model, approximately equal to c ik , u ik , U ik , and can be substituted into the above formula for calculation

[0039]

[0040]

[0041]

[0042] Based on the probability distribution characteristics of the GHH-HMM model for the motion behavior of a four-wheel mobile robot, it is assumed that the transition of the motion behavior from the current state to the next state is random; T is the time series, the number of hidden states is set to N = 3, and the number of Gaussian mixtures is set to M = 3; since the hidden states transfer to any state with the same probability, the initial values π0 and A0 of the parameters π and A are set to be evenly distributed; c, u, and U are automatically initialized by the K-mean clustering algorithm; the corresponding lane-changing warning parameter values are obtained by training the GHH-HMM model. Thereby, the lane-changing behavior of the adjacent four-wheel mobile robot can be identified.

[0043] Furthermore, in step S3, constructing a finite-time controller for a mobile robot with time-varying constraints specifically includes:

[0044] S31: First, define the first error quantity ξ1 = β - y d , where y d is the desired centroid side-slip angle. Then, based on the barrier power integral technique, select an appropriate Lyapunov function to control the centroid side-slip angle during the lane-changing process of the four-wheel mobile robot. Select a Lyapunov function V1 that satisfies the system constraint conditions, then take the first derivative of the selected function, scale and simplify it. At the same time, select an appropriate virtual control law α1 such that where a > 0, 0 < δ < 1, are both constants, that is, the designed virtual control law α1 can constrain the centroid side-slip angle state of the four-wheel mobile robot and achieve finite-time stability.

[0045] S32: First, define the second error quantity where is a constant; then, based on the barrier power integral technique, select an appropriate Lyapunov function to control the yaw rate during the lane-changing process of the four-wheel mobile robot. Similar to S31, select an appropriate Lyapunov function V2, and through derivative simplification and modern control methods, make where c > 0, 0 < δ < 1, are both constants; then use the Backstepping inverse method for inverse design to obtain the actual control input u c , so that the yaw rate ω of the four-wheel mobile robot during the lane-changing process can achieve finite-time stability without breaking through the time-varying constraint conditions.

[0046] In addition, to achieve the above object, the present invention also provides a finite-time tracking control device suitable for lane-changing warning of a four-wheel mobile robot, including the following modules:

[0047] A dynamics modeling module for constructing a dynamics model of the four-wheel mobile robot;

[0048] The lane-changing safety warning module is used to construct a minimum distance warning model based on the dynamic model, and by using the machine learning GMM-HMM method and combining with the minimum distance warning model, obtain a lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning of the four-wheel mobile robot during the lane-changing process;

[0049] The controller construction module is used to construct a finite-time controller for the four-wheel mobile robot with time-varying constraints in order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process;

[0050] The controller execution module is used to judge whether there is danger in the lane change according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller to achieve the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0051] In addition, in order to achieve the above object, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the finite-time tracking control method applicable to the lane-changing warning of the four-wheel mobile robot are realized.

[0052] In addition, in order to achieve the above object, the present invention also provides a storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the finite-time tracking control method applicable to the lane-changing warning of the four-wheel mobile robot are realized.

[0053] The technical solution provided by the present invention has the following beneficial effects:

[0054] 1. The present invention designs a machine learning method for lane-changing warning, combines with the minimum distance warning model, focuses on training the lane-changing parameters of GMM-HMM, and designs an algorithm that better conforms to the lane-changing safety warning in combination with the control requirements of the four-wheel mobile robot system.

[0055] 2. The present invention performs finite-time control on the lane-changing warning of the four-wheel mobile robot, considering time-varying constraint control, including output constraint limitation and input saturation constraint. By designing a time-varying barrier Lyapunov function, it is ensured that the time-varying constraints are not violated.

[0056] 3. The controller designed by the present invention enables the four-wheel mobile robot system to achieve finite-time stability. The time-varying barrier power integrator technology is used to design the controller for the state of the system, so that the system can reach the stable state in a relatively short finite time. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0058] Figure 1It is the overall flowchart of a finite-time tracking control method for lane-changing warning of a four-wheel mobile robot according to the present invention;

[0059] Figure 2 It is the model diagram of a two-degree-of-freedom mobile robot according to the present invention;

[0060] Figure 3 It is the model diagram of the minimum distance warning according to the present invention;

[0061] Figure 4 It is the full-state constraint diagram of the four-wheel mobile robot according to the present invention, where Figure 4 (a) is the state tracking error diagram of the sideslip angle of the center of mass, Figure 4 (b) is the state tracking error diagram of the yaw angular velocity;

[0062] Figure 5 It is the finite-time error tracking diagram with time-varying constraints according to the present invention, where Figure 5 (a) is the control error diagram of the sideslip angle of the center of mass, Figure 5 (b) is the control error diagram of the yaw angular velocity;

[0063] Figure 6 It is the additional yaw moment control input diagram according to the present invention;

[0064] Figure 7 It is the structural schematic diagram of a finite-time tracking control device for lane-changing warning of a four-wheel mobile robot according to the present invention;

[0065] Figure 8 It is the structural schematic diagram of an electronic device according to the present invention. Specific embodiments

[0066] For a clearer understanding of the technical features, objectives, and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0067] Refer to Figure 1 , the present invention provides a finite-time tracking control method for lane-changing warning of a four-wheel mobile robot, including the following steps:

[0068] S1: Construct the dynamic model of the four-wheel mobile robot system;

[0069] S2: Construct the minimum distance warning model according to the dynamic model, and use the machine learning GMM-HMM method to combine with the minimum distance warning model to obtain the lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning during the lane-changing process of the four-wheel mobile robot;

[0070] S3: In order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process, construct a finite-time controller for the four-wheel mobile robot with time-varying constraints;

[0071] S4: Determine whether there is danger in lane change according to the lane change warning safety algorithm for four-wheel mobile robots. If so, execute the finite-time controller, and achieve the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0072] Based on but not limited to the above method, the implementation process of step S1 is as follows:

[0073] In the finite-time control of lane change warning for four-wheel mobile robots, the problem of kinematic constraints is often encountered. Consider the two-degree-of-freedom mobile robot system as Figure 2 shown, and its dynamic model equation is as follows:

[0074]

[0075]

[0076] where β and ω are the sideslip angle of the center of mass and the yaw angular velocity of the four-wheel mobile robot; k f , k r are the front axle tire stiffness and the rear axle tire stiffness of the robot, l f , l r are the front axle length and the rear axle length of the robot, m is the mass of the mobile robot, v x is the longitudinal velocity of the mobile robot, I z is the moment of inertia of the whole vehicle of the mobile robot, δ f is the front wheel steering angle, M z is the additional yaw moment of the four-wheel mobile robot, F yf , F yr are the front wheel lateral force and the rear wheel lateral force of the mobile robot. By introducing coordinate transformation, it can be known that u c = M z , y = β, so the above formula can be transformed into the following:

[0077]

[0078]

[0079] y = β

[0080] The values of each formula are as follows:

[0081]

[0082]

[0083] Based on but not limited to the above method, the specific implementation process of step S2 is as follows:

[0084] First, assume that the minimum distance warning model of the four-wheel mobile robot includes three four-wheel mobile robots, namely the target robot, the first reference robot, and the second reference robot. The target robot and the second reference robot are in the same lane, and the target robot and the first reference robot are in adjacent lanes. Analyze the lane-changing process of the target robot, and then use machine learning methods to predict the motion behaviors of the first reference robot and the second reference robot, so as to avoid obstacles and ensure the safety of the target robot during the lane-changing process.

[0085] According to Figure 2 The expression of the constructed minimum distance warning model is as follows:

[0086]

[0087] Use lidar to obtain the longitudinal speeds of the target robot, the first reference robot, and the second reference robot; v r = v x - v p is the relative longitudinal speed between the target robot and the second reference robot, v x represents the longitudinal speed of the target robot, v p represents the longitudinal speed of the second reference robot, D r is the minimum safe distance maintained by the target robot from the first reference robot or the second reference robot, D s is the relative distance between the target robot and the second reference robot, D m is the distance traveled by the target robot, D p is the distance traveled by the second reference robot, τ1 + τ2 represents the time it takes for the target robot to react and start braking, g is the acceleration due to gravity, is the road surface adhesion coefficient.

[0088] On the basis of establishing the minimum distance warning model, when using the machine learning GMM - HMM method to identify the motion behavior of the mobile robot, the probability distribution of the GHH - HMM model is described as follows:

[0089]

[0090]

[0091]

[0092] Among them, c im is the mixing weight coefficient of the m-th single Gaussian function of the hidden state s i u im is the weight matrix of the m-th single Gaussian function of the hidden state s i U imFor the hidden state s i The covariance matrix of the m-th single Gaussian function, O = (v x , v y , x y ) is the selected observation matrix, v x , v y , x y are respectively the longitudinal speed, lateral speed, and lateral displacement of the four-wheel mobile robot; The GMM-HMM parameters are defined as λ = (π, A, c, u, U), where π is the initial state probability distribution vector, A is the state transition probability distribution matrix, c is the mixing weight coefficient, u is the weight matrix, and U is the covariance matrix;

[0093] The mixing weight probability of the GHH-HMM model is b i (O), N(O, u im , U im ); The next hidden probability is calculated as follows: Defined as the probability function that the hidden state at time t is s i and the observation sequence is k;

[0094]

[0095] where, Ω i (i) represents the observation value sequence of the previous part up to time t under the GMM-HMM parameters λ = (π, A, c, u, U), and Ξ i (i) represents the observation value sequence of the previous and subsequent parts up to time t under the GMM-HMM parameters λ = (π, A, c, u, U); c ik is the mixing weight coefficient of the k-th single Gaussian function of the hidden state s i , O t is the given observation sequence; u ik is the weight matrix of the k-th single Gaussian function of the hidden state s i , and U ik is the covariance matrix of the k-th single Gaussian function of the hidden state s i , and l(O t , u ik , U ik ) represents that the probability value of the hidden state at time t being s i and the hidden state sequence formed by the hidden state s i and the previous t - 1 hidden states is the largest;

[0096] The following is the probability estimated by the GMM-HMM model, approximately equal to c ik , u ik , U ik , and can be substituted into the above formula for calculation

[0097]

[0098]

[0099]

[0100] Based on the probability distribution characteristics of the GHH-HMM model for the motion behavior of a four-wheel mobile robot, it is assumed that the transition of the motion behavior from the current state to the next state is random; T is the time series, the number of hidden states is set to N = 3, and the number of Gaussian mixtures is set to M = 3; since the hidden state transfers to any state with the same probability, the initial values π0 and A0 of the parameters π and A are set to be evenly distributed; c, u, and U are automatically initialized by the K-mean clustering algorithm; the corresponding lane-changing warning parameter values are obtained by training the GHH-HMM model. Thus, the lane-changing behavior of adjacent four-wheel mobile robots can be identified.

[0101] Based on but not limited to the above method, the specific implementation idea of step S3 is as follows:

[0102] First, for the time-varying constraint conditions suffered by the four-wheel mobile robot system, through the barrier Lyapunov power integral technique, a suitable barrier Lyapunov function can be designed, and it can be guaranteed by the stability theorem that the sideslip angle and yaw rate of the center of mass will not break through the upper limit in the entire process of the time-varying constraint finite-time controller.

[0103] Secondly, from the two-degree-of-freedom mobile robot model, it can be seen that the research object is a second-order nonlinear system. Therefore, the Backstepping method can be used to design a finite-time controller. Considering the design idea with time-varying constraints, this method can be used for both high-order non-holonomic systems and third-order systems, that is, the barrier Lyapunov function is designed by adding the barrier power integral technique with time-varying constraints in each step of the backstepping design. By differentiating and scaling the constructed function and designing the virtual control law α1, and then performing backstepping recursion, the controller u is obtained in the last step. c , so as to achieve finite-time stability.

[0104] Finally, through the above analysis, the virtual control law and the controller can be designed.

[0105] Therefore, the specific implementation process of step S3 includes the following two steps:

[0106] The first step: Define the first error quantity ξ1 = β - y d , where y dis the desired centroid sideslip angle; then, based on the barrier power integral technique, a suitable Lyapunov function is selected to control the centroid sideslip angle β during the lane-changing process of the four-wheel mobile robot. A Lyapunov function V1 that satisfies the system constraint conditions is selected, and then the first derivative of the selected function is calculated, scaled, and simplified. At the same time, a suitable virtual control law α1 is selected such that where a > 0, 0 < δ < 1, that is, the designed virtual control law α1 can constrain the centroid sideslip angle state of the four-wheel mobile robot and achieve finite-time stability.

[0107] In the first step, first let ξ1 = β - y d , y d is the desired centroid yaw angle. Construct the following barrier Lyapunov function V1:

[0108]

[0109] Calculating the first derivative of V1 shows that:

[0110]

[0111] Therefore, design the virtual control α1 to perform finite-time constraint on the centroid sideslip angle state β:

[0112]

[0113] where the relevant numerical parameters are By designing the virtual control law α1 in this way, the centroid sideslip angle β of the four-wheel mobile robot can be stabilized within a finite time with time-varying constraints. Next, the Backstepping inverse method is used to design the yaw angular velocity state ω of the four-wheel mobile robot.

[0114] Second step: Define the second error quantity Then, based on the barrier power integral technique, a suitable Lyapunov function is selected to control the yaw angular velocity during the lane-changing process of the four-wheel mobile robot. Similar to the first step, an appropriate Lyapunov function V2 is selected. Through derivative calculation, simplification, and modern control methods, where c > 0, 0 < δ < 1; then the Backstepping inverse method is used for backstepping design to obtain the actual control input u c , such that the yaw angular velocity ω of the four-wheel mobile robot achieves finite-time stability without breaking through the time-varying constraint conditions during the lane-changing process.

[0115] In the second step, in order to better constrain the yaw angular velocity ω of the four-wheel mobile robot, let Using the power integration technique based on a power integrator, select the Lyapunov function V2 that satisfies the constraint conditions:

[0116]

[0117] where

[0118]

[0119] Take the first derivative of V2 and use fuzzy logic and radial basis neural networks to obtain:

[0120]

[0121] Meanwhile, the designed finite-time controller is:

[0122]

[0123] where v 12 , v 22 are positive constants, is a positive known function.

[0124] Using the above design process, thus design the control input u c :

[0125]

[0126] where:

[0127]

[0128] Thus, the finite-time controller u c with time-varying constraints is designed. The control input designed by this control method can enable the four-wheel mobile robot to achieve finite-time tracking control within a finite time under time-varying constraints.

[0129] Simulation verification:

[0130] To verify the changes in the sideslip angle and yaw rate states of the system and the effect of the controller tracking error when the finite-time controller of the four-wheel mobile robot designed by the present invention satisfies the time-varying constraint conditions, in the Matlab software, select the following parameters: the mass of the four-wheel mobile robot m1 = 12.5 kg, the moment of inertia of the robot is I z = 2.1 kg·m 2 , the front wheelbase of the robot l f = 0.112 m, the rear wheelbase of the robot l r = 0.156 m, the stiffness of the front wheel tires of the robot k f = 102 N / rad, the stiffness of the rear wheel tires of the robot k r= 116 N / rad, the longitudinal speed of the four-wheel mobile robot is v x = 1.2 m / s, and the time-varying upper and lower state constraints are as follows: The initial states of the sideslip angle and yaw rate of the center of mass of the four-wheel mobile robot: β(0) = 0.3 rad, ω(0) = 0.2 rad / s, and the parameters of the finite-time controller are: v 11 = 3, v 12 = 1, v 21 = 5, v 22 = 4, K1 = 3, S(·) is composed of Gaussian relation functions and ||θ1|| = 1. The controller is designed using the above controller parameter design method and system simulation is carried out. By designing this finite-time controller, the sideslip angle and yaw rate of the center of mass of the four-wheel mobile robot can be well controlled in finite time without breaking through the time-varying constraints.

[0131] The following simulation diagrams can effectively prove the effectiveness of the controller designed by the present invention:

[0132] Figure 4 and Figure 5 In, β and ω respectively represent the system states of the four-wheel mobile robot, that is, the sideslip angle and yaw rate of the center of mass of the four-wheel mobile robot, alpha1 represents the virtual control law in the controller design process, eta1 and -eta1 represent the upper and lower bounds of the time-varying constraints of the sideslip angle, eta2 and -eta2 represent the upper and lower bounds of the time-varying constraints of the yaw rate, and u c represents the additional yaw moment control input. From the simulation results Figure 4 (a) and Figure 4 (b), it can be seen that the sideslip angle and yaw rate of the four-wheel mobile robot system during the lane-changing process can be constrained in a stable interval and maintain good results. From the simulation results Figure 5 (a) and Figure 5 (b), it can be seen that the tracking error of the designed time-varying finite-time controller will not break through the time-varying constraints. From the simulation results Figure 6 in, the designed additional yaw moment controller input can well make the system state of the four-wheel mobile robot track and control in finite time, and the convergence speed is relatively fast, and it can achieve the effect in engineering.

[0133] Next, a finite-time tracking control device applicable to lane-changing warning of four-wheel mobile robots provided by the present invention will be described. The finite-time tracking control device described below can be mutually corresponding and referred to with the finite-time tracking control method described above.

[0134] As Figure 7As shown, a finite-time tracking control device applicable to lane-changing warning of a four-wheel mobile robot includes the following modules:

[0135] A dynamic modeling module 710 for constructing a dynamic model of the four-wheel mobile robot;

[0136] A lane-changing safety warning module 720 for constructing a minimum distance warning model based on the dynamic model, applying the machine learning GMM-HMM method, and combining with the minimum distance warning model to obtain a lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning of the four-wheel mobile robot during the lane-changing process;

[0137] A controller construction module 730 for constructing a finite-time controller for the four-wheel mobile robot with time-varying constraints in order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process;

[0138] A controller execution module 740 for judging whether there is danger in lane-changing according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller to achieve the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0139] As Figure 8 shown, a schematic diagram of the physical structure of an electronic device is exemplified. The electronic device may include: a processor 810, a communication interface 820, a memory 830, and a communication bus 840. Among them, the processor 810, the communication interface 820, and the memory 830 complete mutual communication through the communication bus 840. The processor 810 can call the logical instructions in the memory 830 to execute the steps of the above finite-time tracking control method applicable to lane-changing warning of a four-wheel mobile robot, specifically including: S1: constructing a dynamic model of the four-wheel mobile robot; S2: constructing a minimum distance warning model according to the dynamic model, applying the machine learning GMM-HMM method, and combining with the minimum distance warning model to obtain a lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning of the four-wheel mobile robot during the lane-changing process; S3: constructing a finite-time controller for the four-wheel mobile robot with time-varying constraints in order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process; S4: judging whether there is danger in lane-changing according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller to achieve the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0140] In addition, when the logical instructions in the above-mentioned memory 830 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0141] In another aspect, an embodiment of the present invention further provides a storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the above-mentioned finite-time tracking control method applicable to lane-changing warning of a four-wheel mobile robot, specifically including: S1: Construct a dynamic model of the four-wheel mobile robot; S2: Construct a minimum-distance warning model according to the dynamic model, and use the machine learning GMM-HMM method to combine with the minimum-distance warning model to obtain a lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning during the lane-changing process of the four-wheel mobile robot; S3: In order to safely constrain the yaw rate of the four-wheel mobile robot during the lane-changing process, construct a finite-time controller for the four-wheel mobile robot with time-varying constraints; S4: Judge whether there is danger in the lane change according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller, and realize the finite-time stability of the four-wheel mobile robot under this finite-time controller.

[0142] It should be noted that in this article, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or system including that element.

[0143] The serial numbers of the above-mentioned embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments. Among the unit claims listing several devices, several of these devices may be specifically embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order, and these words can be interpreted as identifiers.

[0144] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A finite-time tracking control method applicable to lane-changing warning of a four-wheel mobile robot, characterized in that It includes the following steps: S1: Construct the dynamic model of a four-wheel mobile robot; S2: Construct a minimum distance warning model based on the dynamic model, use the machine learning GMM-HMM method, and combine it with the minimum distance warning model to obtain the lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning during the lane-changing process of the four-wheel mobile robot; S3: In order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process, construct a finite-time controller for the four-wheel mobile robot with time-varying constraints; S4: Judge whether there is danger in lane-changing according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller, and realize the finite-time stability of the four-wheel mobile robot under this finite-time controller; In step S3, constructing a finite-time controller for a mobile robot with time-varying constraints specifically includes: S31: First, define the first error quantity , where y d is the desired centroidal sideslip angle. Then, based on the obstacle augmented power integral technique, select an appropriate Lyapunov function to control the centroidal sideslip angle during the lane-changing process of the four-wheel mobile robot, and select a Lyapunov function that satisfies the system constraint conditions . Then, take the first derivative of the selected function, scale and simplify it. At the same time, select an appropriate virtual control law such that , where are all constants. That is, the designed virtual control law can constrain the centroidal sideslip angle state of the four-wheel mobile robot and achieve finite-time stability; S32: First, define the second error quantity , where is a constant; then, based on the barrier power integral technique, select an appropriate Lyapunov function to control the yaw rate during the lane-changing process of the four-wheel mobile robot. Select an appropriate Lyapunov function as in S31, and through derivative simplification and modern control methods, make , where are all constants; then use the Backstepping inverse method for inverse design to obtain the actual control input such that the yaw rate of the four-wheel mobile robot achieves finite-time stability without breaking through the time-varying constraint conditions during the lane-changing process.

2. The finite-time tracking control method for lane-changing warning applicable to a four-wheel mobile robot according to claim 1, characterized in that In step S1, the expression of the dynamic model of the four-wheel mobile robot is as follows: wherein, is the sideslip angle and yaw rate of the centroid of the four-wheel mobile robot; are the front axle tire stiffness and rear axle tire stiffness of the four-wheel mobile robot, are the front axle length and rear axle length of the four-wheel mobile robot, is the mass of the four-wheel mobile robot, is the longitudinal speed of the four-wheel mobile robot, is the moment of inertia of the whole vehicle of the four-wheel mobile robot, is the front wheel steering angle, is the additional yaw moment of the four-wheel mobile robot, are the front wheel side force and rear wheel side force of the four-wheel mobile robot; By introducing a coordinate transformation , the above equation can be transformed as follows: Where the values of each formula are: 。 3. The finite-time tracking control method for lane-changing warning applicable to a four-wheel mobile robot according to claim 1, wherein In step S2, it is set that the minimum distance warning model of the four-wheel mobile robot includes three four-wheel mobile robots, namely the target robot, the first reference robot, and the second reference robot. Among them, the target robot and the second reference robot are in the same lane, and the target robot and the first reference robot are in adjacent lanes. The expression of the constructed minimum distance warning model is as follows: Use lidar to obtain the longitudinal speeds of the target robot, the first reference robot, and the second reference robot; is the relative longitudinal speed between the target robot and the second reference robot, v x represents the longitudinal speed of the target robot, v p represents the longitudinal speed of the second reference robot, is the minimum safe distance maintained by the target robot from the first reference robot or the second reference robot, is the relative distance between the target robot and the second reference robot, is the distance traveled by the target robot, is the distance traveled by the second reference robot, represents the time taken by the target robot from reaction to starting braking, , is the acceleration due to gravity, is the road surface adhesion coefficient.

4. The finite-time tracking control method for lane-changing warning applicable to a four-wheel mobile robot according to claim 1, characterized in that In step S2, the method of using machine learning GMM-HMM, combining with the minimum distance warning model, to obtain the lane-changing warning safety algorithm for the four-wheel mobile robot and realize the safety warning during the lane-changing process of the four-wheel mobile robot includes: When using the machine learning GMM-HMM method to identify the motion behavior of the four-wheel mobile robot on the basis of establishing the minimum distance warning model, the probability distribution of the GHH-HMM model is described as follows: Among them, is in the hidden state of the th mixing weight coefficient of a single Gaussian function, is the weight matrix of the th single Gaussian function of the hidden state , is the covariance matrix of the th single Gaussian function of the hidden state , is the selected observation matrix, are respectively the longitudinal speed, lateral speed, and lateral displacement of a four-wheel mobile robot; the GMM-HMM parameters are defined as , is the initial state probability distribution vector, is the state transition probability distribution matrix, is the mixing weight coefficient, is the weight matrix, is the covariance matrix; The mixing weight probability of the GHH-HMM model is ; The next hidden probability is calculated as follows: Defined as The hidden state at time And the observation sequence is The probability function of; Among them, represents the observation value sequence of the first part up to the time under the GMM-HMM parameters, and represents the observation value sequence of the front and back parts up to the time under the GMM-HMM parameters; is the mixing weight coefficient of the th single Gaussian function of the hidden state , is the given observation sequence; is the weight matrix of the th single Gaussian function of the hidden state , is the covariance matrix of the th single Gaussian function of the hidden state , represents that the probability value of the hidden state being at the time and the hidden state forming the hidden state sequence with the previous hidden states is the largest;​​​​​ The following , , is the probability estimated by the GMM-HMM model, and let it be equal to , , , which can be substituted into the above formula for calculation ; Based on the probability distribution characteristics of the GHH-HMM model for the motion behavior of a four-wheel mobile robot, it is assumed that the transition of the motion behavior from the current state to the next state is random; is a time series, and the number of hidden states is set to , and the number of Gaussian mixtures is set to ; Since the hidden state transfers to any state with the same probability, the parameters , initial values , are set to be evenly distributed; is automatically initialized by the K-mean clustering algorithm; The corresponding lane-changing warning parameter values are obtained by training the GHH-HMM model, so as to identify the lane-changing behavior of adjacent four-wheel mobile robots.

5. A finite-time tracking control device applicable to lane-changing warning of a four-wheel mobile robot, characterized in that, It includes the following modules: A dynamic modeling module, used to construct the dynamic model of a four-wheel mobile robot; A lane-changing safety warning module, used to construct a minimum distance warning model according to the dynamic model, use the machine learning GMM-HMM method, and combine it with the minimum distance warning model to obtain the lane-changing warning safety algorithm for the four-wheel mobile robot, so as to realize the safety warning during the lane-changing process of the four-wheel mobile robot; A controller construction module, used to construct a finite-time controller for a four-wheel mobile robot with time-varying constraints in order to safely constrain the yaw angular velocity of the four-wheel mobile robot during the lane-changing process; A controller execution module, used to judge whether there is danger in lane-changing according to the lane-changing warning safety algorithm of the four-wheel mobile robot. If so, execute the finite-time controller, and realize the finite-time stability of the four-wheel mobile robot under this finite-time controller; The controller construction module is specifically configured as: First, define the first error quantity , where y d is the desired centroid sideslip angle. Then, based on the obstacle augmented power integral technique, select an appropriate Lyapunov function to control the centroid sideslip angle during the lane-changing process of the four-wheel mobile robot, and select a Lyapunov function that satisfies the system constraint conditions . Then, take the first derivative of the selected function, scale and simplify it, and at the same time select an appropriate virtual control law such that , where are all constants, that is, the designed virtual control law can constrain the centroid sideslip angle state of the four-wheel mobile robot and achieve finite-time stability; First, define the second error quantity , where is a constant; then, based on the barrier plus power integral technique, select an appropriate Lyapunov function to control the yaw rate during the lane-changing process of the four-wheel mobile robot. Select an appropriate Lyapunov function as in S31. Through derivative simplification and modern control methods, make , where are all constants; then use the Backstepping inverse method for inverse design to obtain the actual control input such that the yaw rate of the four-wheel mobile robot achieves finite-time stability without breaking through the time-varying constraint conditions during the lane-changing process.

6. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that When the processor executes the program, it realizes the steps of the finite-time tracking control method for lane-changing warning applicable to a four-wheel mobile robot according to any one of claims 1-4.

7. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it realizes the steps of the finite-time tracking control method for lane-changing warning applicable to a four-wheel mobile robot according to any one of claims 1-4.

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