CN116841298B - Finite time tracking control method suitable for four-wheel mobile robot lane change early warning - Google Patents

Abstract

The invention discloses a finite time tracking control method suitable for lane change early warning of a four-wheel mobile robot, which comprises the steps of constructing a dynamics model of the four-wheel mobile robot, constructing a minimum distance early warning model according to the dynamics model, utilizing a machine learning GMM-HMM method and combining the minimum distance early warning model to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, realizing safety early warning of the four-wheel mobile robot in a lane change process, constructing a finite time controller of the four-wheel mobile robot with time-varying constraint, judging whether a lane change is dangerous according to the lane change early warning safety algorithm of the four-wheel mobile robot, if so, executing the finite time controller, and realizing finite time stability of the four-wheel mobile robot under the finite time controller. The invention realizes that the centroid side deflection angle and the yaw rate can be constrained in a stable interval in the lane changing process of the four-wheel mobile robot, and the tracking error of the finite time controller can not break through the time-varying constraint.

Description

Finite time tracking control method suitable for four-wheel mobile robot lane change early warning

Technical Field

The invention relates to the technical field of robot motion control, in particular to a limited time tracking control method suitable for four-wheel mobile robot lane change early warning.

Background

In the past few decades, with the rapid development of fields such as communications and computer networks, the problem associated with four-wheel mobile robots has become a significant research in the field of automatic control. The four-wheel mobile robot is widely applied to daily express sorting and special transportation. In order to better utilize the mobile robot to assist in completing various tasks, the driving safety of the four-wheel mobile robot is ensured. More and more researchers are engaged in related research.

The early warning method of the four-wheel mobile robot has the minimum safety distance, and comprises the steps of machine learning SVM, machine vision and convolutional neural network. The method is mainly used for identifying the intention of surrounding mobile robots and used for safety early warning in the lane changing process. The control method of the mobile robot comprises open loop control and closed loop control. Open loop control is easy to control, but is poor in robustness and does not suppress interference well. The closed loop control is less influenced by the change of the parameter of the closed loop control, and has stronger robustness. Therefore, the closed-loop control of the mobile robot system has important practical application value.

The lane change early warning method is based on the operation parameters of the driving behavior of the mobile robot. Researchers use mobile robot motion data as input characteristic parameters of a classifier, a training Support Vector Machine (SVM) is applied to the lane recognition and change intention of a robot, and statistical signal processing and machine learning technologies are used for modeling all aspects of the robot behavior so as to detect dangerous driving behaviors. The method comprises the steps of firstly, using machine vision to track the motion information and position information of a front robot, using the characteristic information of SVM to train and identify the motion behavior of the robot in advance, and additionally, taking the rotation angular speed and the transverse acceleration of the wheels of the robot as optimal observation variables to establish an HMM model for identifying the lane changing intention of the mobile robot, firstly, using the machine vision to locate the center of the front robot, then using binocular vision to measure the distance between the front robot and a lane, and judging the driving distance of the front robot according to the dispersion. Because the recognition efficiency of machine learning is low, the safety of the mobile robot early warning method based on machine learning at present needs to be improved.

The automatic tracking of the mobile robot means that the mobile robot is controlled to run according to a planned track, so that the lane changing task is realized. The longitudinal head distance of the four-wheel robot at any time is controlled by a learner through a PID algorithm, and the speed of the robot in front can be tracked well under the conditions of interference of initial speed deviation and adjustment of the speed of the robot in front through a control mode of combining sliding mode control with a nonlinear dynamics model. In the modern control theory, the model predictive control method controls the steering front wheel angle of the robot, so that the four-wheel robot can be ensured to track the obstacle avoidance route rapidly and accurately. Researchers use an integral back-stepping method to derive a transverse lane change track tracking controller with a closed-loop structure. In order to achieve the stability constraint control objective, various methods such as model predictive control have been proposed and evaluated. In recent years, the problem of limited time control of four-wheeled mobile robotic systems has been increasingly receiving attention from researchers. Compared with asymptotic stable control, the finite time control has the advantages of high speed, high path tracking precision and strong robustness. Therefore, to address engineering issues, limited time control is applied to improve the steady state and dynamic performance of the system. Furthermore, limited time control may comply with stringent transient response requirements, allowing related industries to increase production efficiency.

Mobile robot restraint is also a worth of research in automatic tracking control. Mobile robots may generally be described in terms of one or more stability constraints. The learner proposes a lane change framework constraint planning expected robot state based on a safe driving network. Control Barrier Functions (CBFs) have been used to address the safety control issues of autonomous ground four-wheel mobile robots (AGVs) and other mobile systems such as lane keeping and adaptive cruise. Furthermore, in some cases, the time-varying control barrier function has a dynamically constrained constant control, which is used to address the associated safety controls. The selection of the lateral stability of the mobile robot is actually time-varying and control-dependent as the longitudinal speed and steering angle of the four-wheeled mobile robot change. In view of the above, considering time-varying four-wheel mobile robot state constraints is also a need for improvement in limited time trajectory tracking.

Although more results on lane change early warning and automatic control of the four-wheel mobile robot are obtained, no related results are obtained in the aspect of a limited time tracking control method of the lane change early warning of the four-wheel mobile robot. On the one hand, in practical application, the four-wheel mobile robot control system is subjected to constraints from various aspects, such as road slip rate constraint and speed acceleration boundary constraint, and on the other hand, due to rapid development of industrial production, higher industrial production indexes and higher safety requirements force limited time control to become an important consideration. Although the related research relates to the problem of limited time control under the state constraint, no related research is designed to the safety lane change early warning limited time control under the time-varying constraint, so that the minimum safety lane change early warning control performance of the four-wheel mobile robot has partial defects. Firstly, in the aspect of lane change early warning, the existing safety early warning method is mainly a machine learning SVM, the running safety of the four-wheel mobile robot cannot be guaranteed, secondly, in the aspect of control speed, the existing control method is relatively long in control time of the mobile robot, the higher control requirement cannot be met, and finally, the existing limited time controller does not consider time-varying safety constraint, and hidden danger is brought to the running stability of the controller.

Therefore, the research of the limited time tracking control method of the lane change early warning of the four-wheel mobile robot still faces a plurality of challenges, and mainly has three technical problems of how to design a safer lane change early warning algorithm for lane change safety early warning, how to design a limited time controller under a time-varying constraint condition, and how to design a controller with a proper structure based on a complex controller structure.

Disclosure of Invention

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

In order to achieve the above purpose, the present invention provides a finite time tracking control method suitable for four-wheel mobile robot lane change early warning, which specifically comprises the following steps:

S1, constructing a dynamic model of a four-wheel mobile robot;

S2, constructing a minimum distance early warning model according to the dynamics model, combining a machine learning GMM-HMM method with the minimum distance early warning model to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, and realizing safety early warning of the four-wheel mobile robot in the lane change process;

s3, constructing a time-varying constraint-containing finite time controller of the four-wheel mobile robot for safely constraining the yaw rate of the four-wheel mobile robot in the lane changing process;

and S4, judging whether the lane change is dangerous or not according to a lane change early warning safety algorithm of the four-wheel mobile robot, if so, executing a limited time controller, and realizing the limited time stability of the four-wheel mobile robot under the limited time controller.

Further, in step S1, the expression of the kinetic model of the four-wheel mobile robot is as follows:

K_f,k_r is the front axle tire rigidity and the rear axle tire rigidity of the four-wheel mobile robot, l_f,l_r is the front axle length and the rear axle length of the four-wheel mobile robot, M is the mass of the four-wheel mobile robot, v_x is the longitudinal speed of the four-wheel mobile robot, I_z is the moment of inertia of the whole four-wheel mobile robot, delta_f is the front wheel corner, M_z is the additional yaw moment of the four-wheel mobile robot, F_yf,F_yr is the front wheel lateral force and the rear wheel lateral force of the four-wheel mobile robot;

by introducing the coordinate transformation u_c＝M_z, y=β, the above formula can be converted as follows:

y=β

Wherein the values of the formulae are:

further, in step S2, the minimum distance early warning model of the four-wheel mobile robot is set to include three four-wheel mobile robots, which are a target robot, a first reference robot and a second reference robot, wherein the target robot and the second reference robot are located in the same lane, the target robot and the first reference robot are located in adjacent lanes, and the expression of the constructed minimum distance early warning model is as follows:

The longitudinal speed of the target robot, the first reference robot and the second reference robot is obtained by using a laser radar, v_r＝v_x-v_p is the relative longitudinal speed of the target robot and the second reference robot, v_x is the longitudinal speed of the target robot, v_p is the longitudinal speed of the second reference robot, D_r is the minimum safety distance kept between the target robot and 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 moving distance of the target robot, D_p is the moving distance of the second reference robot, tau₁+τ₂ represents the time from the reaction to the starting of braking of the target robot,G is the gravity acceleration rate of the gravity,Is the road adhesion coefficient.

Further, in step S2, the method for applying the machine learning GMM-HMM method and combining with the minimum distance early warning model to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, so as to realize the safety early warning of the four-wheel mobile robot in the lane change process, including:

on the basis of establishing a minimum distance early warning model, when the motion behavior of the four-wheeled mobile robot is identified by using a machine learning GMM-HMM method, the probability distribution of the GHH-HMM model is described as follows:

Wherein c_im is the mixed 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_y is the longitudinal speed, the transverse speed and the transverse displacement of the four-wheeled mobile robot respectively;

GHH-the mixed weight probability of the HMM model is b_i(O),N(O,u_im,U_im), and the hidden probability of the next step is calculated as follows: defining a probability function with a hidden state s_i at the moment t and an observation sequence k;

Wherein Ω_i (i) represents the observation sequence from the previous part to time t under GMM-HMM parameter λ= (pi, a, c, U), Ω_i (i) represents the observation sequence from the previous and subsequent parts to time t under GMM-HMM parameter λ= (pi, a, c, U), c_ik is the mixed weight coefficient of the kth single gaussian function of the hidden state s_i, O_t is the given observation sequence, U_ik is the weight matrix of the kth single gaussian function of the hidden state s_i, U_ik is the covariance matrix of the kth 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 state is the largest;

The following are the followingThe probability estimated for the GMM-HMM model is approximately equal to c_ik,u_ik,U_ik, which can be taken into the above calculation

Setting the transition of the motion behavior from the current state to the next state to be random based on the probability distribution characteristics of GHH-HMM model of the motion behavior of the four-wheel mobile robot, setting T to be a time sequence, setting the number of hidden states to be N=3 and the Gaussian mixture number to be M=3, setting the initial values pi₀、A₀ of parameters pi and A to be evenly distributed due to the fact that the hidden states are transferred to any state with the same probability, automatically initializing c, U and U by a K-mean clustering algorithm, and obtaining corresponding lane change early warning parameter values by training GHH-HMM modelThus, lane change behavior of the adjacent four-wheel mobile robot is recognized.

Further, in step S3, constructing a mobile robot finite time controller including a time-varying constraint specifically includes:

S31, defining a first error amount xi₁＝β-y_d, wherein y_d is a desired centroid slip angle, selecting a proper Lyapunov function based on a barrier exponentiation integral technology to control the centroid slip angle in the four-wheel mobile robot lane changing process, selecting a Lyapunov function V₁ meeting a system constraint condition, then solving a first derivative of the selected function, scaling and simplifying the function, and simultaneously selecting a proper virtual control law alpha₁ to enable the selected function to be in a proper virtual control law alpha₁ to enableWherein a >0,0< delta <1 are constants, namely the designed virtual control law alpha₁ can restrict the centroid slip angle state of the four-wheel mobile robot and achieve limited time stability;

s32, first defining the second error amountWherein the method comprises the steps ofIs constant, then selects proper Lyapunov function based on obstacle exponentiation integral technique to control yaw rate in the course of four-wheel mobile robot lane change, selects proper Lyapunov function V₂ as S31, and makes it through derivative reduction and modern control methodAnd then performing Backstepping back-stepping to obtain an actual control input u_c, so that the yaw rate omega of the four-wheel mobile robot in the course of changing the track can be stable for a limited time under the condition of not breaking through time-changing constraint conditions.

In addition, in order to achieve the above purpose, the invention also provides a finite time tracking control device suitable for the lane change early warning of the four-wheel mobile robot, which comprises the following modules:

the dynamics modeling module is used for constructing a dynamics model of the four-wheel mobile robot;

The lane change safety early warning module is used for constructing a minimum distance early warning model according to the dynamics model, combining the minimum distance early warning model by using a machine learning (GMM-HMM) method to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, and realizing the safety early warning of the four-wheel mobile robot in the lane change process;

The controller construction module is used for constructing a time-varying constraint-containing finite time controller of the four-wheel mobile robot for safely constraining the yaw rate of the four-wheel mobile robot in the lane changing process;

And the controller execution module is used for judging whether the lane change is dangerous or not according to the lane change early warning safety algorithm of the four-wheel mobile robot, if so, executing a limited time controller, and realizing the limited time stability of the four-wheel mobile robot under the limited time controller.

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 in the memory and capable of running on the processor, wherein the processor implements the steps of the finite time tracking control method suitable for lane change early warning of a four-wheel mobile robot when executing the program.

In addition, in order to achieve the above object, the present invention also provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the finite time tracking control method suitable for lane change early warning of a four-wheeled mobile robot.

The technical scheme provided by the invention has the following beneficial effects:

1. the invention designs a machine learning method of lane change early warning, combines a minimum distance early warning model, mainly trains lane change parameters of GMM-HMM, synthesizes control requirements of a four-wheel mobile robot system, and designs an algorithm more in line with lane change safety early warning.

2. The invention performs limited time control on the four-wheel mobile robot lane change early warning, and considers time-varying constraint control, including output constraint limitation and input saturation constraint. By designing the time-varying barrier Lyapunov function, the time-varying constraint is guaranteed not to be destroyed.

3. The controller designed by the invention ensures that the four-wheel mobile robot system is stable for a limited time, and the controller is designed for the state of the system by using a time-varying obstacle power integrator technology, so that the system can reach a stable state for a limited time.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

FIG. 1 is a general flow chart of a finite time tracking control method suitable for lane change pre-warning of a four-wheeled mobile robot according to the present invention;

FIG. 2 is a diagram of a two-degree-of-freedom mobile robot model of the present invention;

FIG. 3 is a graph of a minimum distance warning model of the present invention;

FIG. 4 is a full state constraint map of the four-wheel mobile robot of the present invention, wherein FIG. 4 (a) is a centroid slip angle state tracking error map and FIG. 4 (b) is a yaw rate state tracking error map;

FIG. 5 is a finite time error tracking graph with time varying constraints of the present invention, wherein FIG. 5 (a) is a centroid slip angle control error graph and FIG. 5 (b) is a yaw rate control error graph;

FIG. 6 is an additional yaw moment control input diagram of the present invention;

FIG. 7 is a schematic diagram of a finite time tracking control device suitable for lane change pre-warning of a four-wheeled mobile robot;

fig. 8 is a schematic structural view of an electronic device according to the present invention.

Detailed Description

For a clearer understanding of technical features, objects and effects of the present invention, a detailed description of embodiments of the present invention will be made with reference to the accompanying drawings.

Referring to fig. 1, the invention provides a finite time tracking control method suitable for four-wheel mobile robot lane change early warning, which comprises the following steps:

S1, constructing a dynamic model of a four-wheel mobile robot system;

S2, constructing a minimum distance early warning model according to the dynamics model, combining a machine learning GMM-HMM method with the minimum distance early warning model to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, and realizing safety early warning of the four-wheel mobile robot in the lane change process;

s3, constructing a time-varying constraint-containing finite time controller of the four-wheel mobile robot for safely constraining the yaw rate of the four-wheel mobile robot in the lane changing process;

and S4, judging whether the lane change is dangerous or not according to a lane change early warning safety algorithm of the four-wheel mobile robot, if so, executing a limited time controller, and realizing the limited time stability of the four-wheel mobile robot under the limited time controller.

Based on but not limited to the above method, the implementation procedure of step S1 is as follows:

the problem of kinematic constraint is often encountered in lane change early warning limited time control of a four-wheel mobile robot, and a two-degree-of-freedom mobile robot system shown in fig. 2 is considered, and a kinetic model equation is as follows:

Wherein β, ω is the centroid slip angle and yaw rate of the four-wheel mobile robot, k_f,k_r is the front axle tire stiffness and rear axle tire stiffness of the robot, l_f,l_r is the front axle length and rear axle length of the robot, M is the mass of the mobile robot, v_x is the mobile robot longitudinal speed, I_z is the moment of inertia of the mobile robot in its entirety, δ_f is the front wheel corner, M_z is the additional yaw moment of the four-wheel mobile robot, F_yf,F_yr is the front wheel lateral force and rear wheel lateral force of the mobile robot. By introducing a coordinate transformation, u_c＝M_z, y=β, the above formula can be converted as follows:

y=β

Wherein the values of the formulae are:

based on but not limited to the above method, the specific implementation procedure of step S2 is as follows:

Firstly, setting a minimum distance early warning model of a four-wheel mobile robot to comprise three four-wheel mobile robots, namely a target robot, a first reference robot and a second reference robot, wherein the target robot and the second reference robot are positioned in the same lane, the target robot and the first reference robot are positioned in adjacent lanes, analyzing a lane changing process of the target robot, and predicting the movement behaviors of the first reference robot and the second reference robot by using a machine learning method so as to avoid obstacles and ensure the safety of the lane changing process of the target robot.

The expression of the minimum distance warning model constructed according to fig. 2 is as follows:

The longitudinal speed of the target robot, the first reference robot and the second reference robot is obtained by using a laser radar, v_r＝v_x-v_p is the relative longitudinal speed of the target robot and the second reference robot, v_x is the longitudinal speed of the target robot, v_p is the longitudinal speed of the second reference robot, D_r is the minimum safety distance kept between the target robot and 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 moving distance of the target robot, D_p is the moving distance of the second reference robot, tau₁+τ₂ represents the time from the reaction to the starting of braking of the target robot,G is the gravity acceleration rate of the gravity,Is the road adhesion coefficient.

On the basis of establishing a minimum distance early warning model, when a machine learning (GMM-HMM) method is used for identifying the motion behavior of a mobile robot, the probability distribution of the GHH-HMM model is described as follows:

Wherein c_im is the mixed 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_y is the longitudinal speed, the transverse speed and the transverse displacement of the four-wheeled mobile robot respectively;

GHH-the mixed weight probability of the HMM model is b_i(O),N(O,u_im,U_im), and the hidden probability of the next step is calculated as follows: defining a probability function with a hidden state s_i at the moment t and an observation sequence k;

wherein Ω_i (i) represents the observation sequence from the GMM-HMM parameter λ= (pi, a, c, U) to the front part of time t, Ω_i (i) represents the observation sequence from the GMM-HMM parameter λ= (pi, a, c, U) to the front and rear parts of time t, c_ik is the mixed weight coefficient of the kth single gaussian function of the hidden state s_i, O_t is the given observation sequence, U_ik is the weight matrix of the kth single gaussian function of the hidden state s_i, U_ik is the covariance matrix of the kth 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 state is the largest;

The following are the followingThe probability estimated for the GMM-HMM model is approximately equal to c_ik,u_ik,U_ik, which can be taken into the above calculation

Setting the transition of the motion behavior from the current state to the next state to be random based on the probability distribution characteristics of GHH-HMM model of the motion behavior of the four-wheel mobile robot, setting T to be a time sequence, setting the number of hidden states to be N=3 and the Gaussian mixture number to be M=3, setting the initial values pi₀,A₀ of parameters pi and A to be evenly distributed due to the fact that the hidden states are transferred to any state with the same probability, automatically initializing c, U and U by a K-mean clustering algorithm, and obtaining corresponding lane change early warning parameter values by training GHH-HMM modelThus, lane change behavior of the adjacent four-wheel mobile robot is recognized.

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

Firstly, aiming at time-varying constraint conditions suffered by a four-wheel mobile robot system, a proper obstacle Lyapunov function can be designed through an obstacle Lyapunov exponentiation integration technology, and the centroid slip angle and the yaw rate can be ensured not to break through the upper limit in the whole process through a stability theorem under the time-varying constraint finite time controller.

Secondly, as known from a two-degree-of-freedom mobile robot model, a research object is a second-order nonlinear system, so that a Backstepping back-stepping method can be adopted to design a finite time controller, and meanwhile, a design thought containing time-varying constraints is considered, namely, a barrier-exponentiation integral technology containing time-varying constraints is added in each step of back-stepping design to design a barrier Lyapunov function, the constructed function is led and scaled, a virtual control law alpha₁ is designed, then back-stepping recursion is carried out, and a controller u_c is obtained in the last step, so that the stability of finite time is achieved.

Finally, through the above analysis, the design of virtual control laws and controllers can begin.

The specific implementation procedure of step S3 therefore comprises the following two steps:

Defining a first error quantity xi₁＝β-y_d, wherein y_d is a desired centroid slip angle, selecting a proper Lyapunov function based on a barrier exponentiation integration technology to control a centroid slip angle beta in the four-wheel mobile robot lane changing process, selecting a Lyapunov function V₁ meeting a system constraint condition, then solving a first derivative of the selected function, scaling and simplifying the function, and simultaneously selecting a proper virtual control law alpha₁ to enable the selected function to be in a proper virtual control law alpha₁ to enableWherein a >0,0< delta <1, i.e., the designed virtual control law alpha₁ can constrain the centroid slip angle state of the four-wheeled mobile robot and achieve limited time stability.

In the first step, first let ζ₁＝β-y_d,y_d be the desired centroid yaw angle. The following barrier Lyapunov function V₁ was constructed:

the first derivative of V₁ is known:

Therefore, virtual control alpha₁ is designed to carry out finite time constraint on the state beta of the mass center slip angle:

wherein the relevant numerical parameters areBy designing the virtual control law alpha₁ in this way, the centroid slip angle beta of the four-wheeled mobile robot can be stabilized within a finite time containing time-varying constraints, and then the back-stepping method is used to design the yaw rate state omega of the four-wheeled mobile robot.

Second step, defining a second error amountThen selecting a proper Lyapunov function based on the obstacle exponentiation integration technology to control the yaw rate in the track changing process of the four-wheeled mobile robot, selecting a proper Lyapunov function V₂ as in the first step, and simplifying the derivation and a modern control method to enable the four-wheeled mobile robot to beAnd then performing Backstepping to obtain an actual control input u_c, so that the yaw rate omega of the four-wheel mobile robot in the course of changing the track is stable for a limited time under the condition of not breaking through time-changing constraint.

In the second step, in order to better restrict the yaw rate omega of the four-wheel mobile robot, letSelecting a Lyapunov function V₂ meeting constraint conditions by using a power integrator-based exponentiation integration technology:

Wherein the method comprises the steps of

The first derivative is taken for V₂ and the fuzzy logic and radial basis function network processing is used to know:

meanwhile, the designed finite time controller is as follows:

where v₁₂,v₂₂ is a positive constant and,Is a positive known function.

The control input u_c is thus designed using the above design procedure:

Wherein:

The design of the finite time controller u_c with time-varying constraint is completed, and the control input designed by the control method can enable the four-wheel mobile robot to achieve finite time tracking control within the finite time under the time-varying constraint.

Simulation verification:

In order to verify the effect of the limited time controller of the four-wheel mobile robot designed by the invention on the condition that the system meets time-varying constraint conditions, the change of the state of each centroid side deflection angle and yaw angle speed and the tracking error of the controller, in Matlab software, the following parameters are selected, namely the mass m₁ = 12.5kg of the four-wheel mobile robot, the moment of inertia of the robot is I_z＝2.1kg*m², the front wheelbase l_f = 0.112m, the rear wheelbase l_r = 0.156m, the rigidity k_f = 102N/rad of the front wheels of the robot, the rigidity k_r = 116N/rad of the rear wheels of the robot, the longitudinal speed of the four-wheel mobile robot is v_x = 1.2m/s, and the time-varying upper and lower limit state constraints are as follows: initial states of the four-wheel mobile robot mass yaw angle and yaw rate, β (0) =0.3 rad, ω (0) =0.2 rad/s, the finite time controller parameters are: v₁₁＝3,v₁₂＝1,v₂₁＝5,v₂₂＝4,K₁ = 3, s (·) is composed of a gaussian relation functionAnd θ₁ |=1. The controller is designed and system simulation is performed by using the controller parameter design method. By designing the limited time controller, the centroid slip angle and the yaw rate of the four-wheel mobile robot can be well controlled in a limited time, and time-varying constraint is not broken through.

The following simulation diagrams may effectively demonstrate the effectiveness of the controller of the present design:

In fig. 4 and 5, β, ω represent the system states of the four-wheeled mobile robot, that is, the centroid side deviation angle and the yaw rate of the four-wheeled mobile robot, alpha1 represents the virtual control law in the design process of the controller, eta1, -eta2 represents the upper and lower bounds of the centroid side deviation angle time-varying constraint, u_c represents the additional yaw moment control input, and as can be seen from the simulation results fig. 4 (a) and 4 (b), the centroid side deviation angle and the yaw rate of the four-wheeled mobile robot system in the lane change process can be constrained in a stable interval, and a good effect can be maintained, and as can be seen from the simulation results fig. 5 (a) and 5 (b), the tracking error of the designed time-varying limited time controller does not break through the time-varying constraint. In the simulation result of fig. 6, the designed additional yaw moment controller input can well enable the four-wheel mobile robot system state to be tracked and controlled in a limited time, the convergence speed is high, and the effect in engineering can be achieved.

The limited time tracking control device suitable for the lane change early warning of the four-wheeled mobile robot is described below, and the limited time tracking control device described below and the limited time tracking control method described above can be correspondingly referred to each other.

As shown in fig. 7, a finite time tracking control device suitable for lane change early warning of a four-wheeled mobile robot comprises the following modules:

the dynamics modeling module 710 is configured to construct a dynamics model of the four-wheel mobile robot;

the lane change safety early warning module 720 is used for constructing a minimum distance early warning model according to the dynamics model, combining the minimum distance early warning model by using a machine learning (GMM-HMM) method to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, and realizing the safety early warning of the four-wheel mobile robot in the lane change process;

the controller construction module 730 is configured to construct a finite time controller of the four-wheel mobile robot with time-varying constraints for safely constraining the yaw rate of the four-wheel mobile robot during the lane-changing process;

the controller execution module 740 is configured to determine whether there is a danger in the lane change according to the lane change early warning safety algorithm of the four-wheel mobile robot, if so, execute a limited time controller, and implement limited time stabilization of the four-wheel mobile robot under the limited time controller.

As shown in fig. 8, a physical schematic of an electronic device is illustrated, which may include a processor 810, a communication interface (Communications Interface) 820, a memory 830, and a communication bus 840, where the processor 810, the communication interface 820, and the memory 830 perform communication with each other through the communication bus 840. The processor 810 can call logic instructions in the memory 830 to execute the steps of the finite time tracking control method suitable for the lane change early warning of the four-wheeled mobile robot, which concretely comprises the steps of S1, constructing a dynamics model of the four-wheeled mobile robot, S2, constructing a minimum distance early warning model according to the dynamics model, obtaining a lane change early warning safety algorithm of the four-wheeled mobile robot by combining a machine learning GMM-HMM method with the minimum distance early warning model, realizing the safety early warning of the four-wheeled mobile robot in the lane change process, S3, constructing a finite time controller of the four-wheeled mobile robot with time change constraint for safely constraining the yaw rate of the four-wheeled mobile robot in the lane change process, and S4, judging whether the lane change is dangerous according to the lane change early warning safety algorithm of the four-wheeled mobile robot, if so, executing the finite time controller, and realizing the finite time stability of the four-wheeled mobile robot under the finite time controller.

Further, the logic instructions in the memory 830 described above may be implemented in the form of software functional units and may be stored in a computer-readable storage medium when sold or used as a stand-alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. The storage medium includes various media capable of storing program codes, such as a usb (universal serial bus), a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.

In still another aspect, the embodiment of the invention further provides a storage medium, wherein a computer program is stored on the storage medium, the computer program is executed by a processor to realize the steps of the finite time tracking control method suitable for the lane change early warning of the four-wheel mobile robot, and the method specifically comprises the steps of S1, constructing a dynamic model of the four-wheel mobile robot, S2, constructing a minimum distance early warning model according to the dynamic model, using a machine learning GMM-HMM method and combining the minimum distance early warning model to obtain a lane change early warning safety algorithm of the four-wheel mobile robot, realizing the safety early warning of the four-wheel mobile robot in the lane change process, S3, constructing a finite time controller of the four-wheel mobile robot with time change constraint for safely constraining the yaw angular velocity of the four-wheel mobile robot in the lane change process, and S4, judging whether the lane change has danger according to the lane change early warning safety algorithm of the four-wheel mobile robot, if so, executing the finite time controller, and realizing the finite time stability of the four-wheel mobile robot under the finite time controller.

It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.

The foregoing embodiment numbers of the present invention are merely for the purpose of description, and do not represent the advantages or disadvantages of the embodiments. In the unit claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third, etc. do not denote any order, but rather the terms first, second, third, etc. are used to interpret the terms as labels.

The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures or equivalent processes disclosed herein or in the alternative, which may be employed directly or indirectly in other related arts.

Claims (7)

Translated fromChinese

1.一种适用于四轮移动机器人变道预警的有限时间跟踪控制方法，其特征在于，包括以下步骤：1. A limited time tracking control method for lane change warning of a four-wheeled mobile robot, characterized in that it comprises the following steps:S1：构建四轮移动机器人的动力学模型；S1: Construct the dynamic model of the four-wheeled mobile robot;S2：根据动力学模型构建最小距离预警模型，运用机器学习GMM-HMM方法，结合最小距离预警模型，得到四轮移动机器人变道预警安全算法，实现移四轮移动机器人在变道过程中的安全预警；S2: Based on the dynamics model, a minimum distance warning model is constructed. The machine learning GMM-HMM method is used in combination with the minimum distance warning model to obtain a lane change warning safety algorithm for the four-wheeled mobile robot, thus realizing a safety warning for the four-wheeled mobile robot during lane change.S3：为了安全约束四轮移动机器人在变道过程中的横摆角速度，构建一种含时变约束的四轮移动机器人有限时间控制器；S3: In order to safely constrain the yaw angular velocity of the four-wheeled mobile robot during lane change, a finite-time controller for the four-wheeled mobile robot with time-varying constraints is constructed;S4：根据四轮移动机器人变道预警安全算法判断变道是否存在危险，若是，则执行有限时间控制器，在该有限时间控制器下实现四轮移动机器人的有限时间稳定；S4: judging whether there is a danger in changing lanes according to the lane change warning safety algorithm of the four-wheeled mobile robot, and if so, executing a finite time controller to achieve finite time stability of the four-wheeled mobile robot under the finite time controller;步骤S3中，构建一种含时变约束的移动机器人有限时间控制器具体包括：In step S3, constructing a mobile robot finite time controller with time-varying constraints specifically includes:S31：首先定义第一误差量，其中y_d为期望质心侧偏角，然后基于障碍加幂积分技术选择合适的Lyapunov函数控制四轮移动机器人变道过程中的质心侧偏角，选择满足系统约束条件的Lyapunov函数，然后对该选取的函数求一阶导数，并缩放和简化，同时选取合适的虚拟控制律，使得，其中，均为常数，也即所设计的虚拟控制律能使四轮移动机器人的质心侧偏角状态约束并达到有限时间稳定；S31: First define the first error amount , wherey_d is the desired center of mass sideslip angle, and then select the appropriate Lyapunov function based on the obstacle plus power integration technology to control the center of mass sideslip angle of the four-wheeled mobile robot during the lane change process, and select the Lyapunov function that meets the system constraints , then find the first-order derivative of the selected function, scale and simplify it, and select the appropriate virtual control law , so that ,in , are all constants, that is, the designed virtual control law It can constrain the sideslip angle state of the center of mass of the four-wheeled mobile robot and achieve finite-time stability;S32：首先定义第二误差量，其中，为常数；然后基于障碍加幂积分技术去选择合适的Lyapunov函数控制四轮移动机器人变道过程中的横摆角速度，与S31一样选取适当的Lyapunov函数，通过求导化简和现代控制方法使得，其中，均为常数；然后运用Backstepping反步法进行反步设计从而得到实际控制输入，使得四轮移动机器人在变道过程中的横摆角速度在不突破时变约束条件下实现有限时间稳定。S32: First define the second error amount ,in , is a constant; then based on the obstacle plus power integration technology, a suitable Lyapunov function is selected to control the yaw angular velocity of the four-wheeled mobile robot during the lane change process. The appropriate Lyapunov function is selected as in S31 , through derivation simplification and modern control methods, ,in , are all constants; then the Backstepping method is used to perform backstepping design to obtain the actual control input , which makes the yaw angular velocity of the four-wheeled mobile robot during lane change Achieve finite-time stability without violating time-varying constraints.2.根据权利要求1所述的适用于四轮移动机器人变道预警的有限时间跟踪控制方法，其特征在于，步骤S1中，所述四轮移动机器人的动力学模型的表达式如下：2. The finite time tracking control method for lane change warning of a four-wheeled mobile robot according to claim 1, characterized in that in step S1, the expression of the dynamic model of the four-wheeled mobile robot is as follows:其中，是四轮移动机器人的质心侧偏角和横摆角速度；是四轮移动机器人的前轴轮胎刚度和后轴轮胎刚度，是四轮移动机器人的前轴长度和后轴长度，是四轮移动机器人的质量，是四轮移动机器人纵向速度，是四轮移动机器人整车的转动惯量，是前轮转角，是四轮移动机器人的附加横摆力矩，是四轮移动机器人的前轮侧向力和后轮侧向力；in, are the sideslip angle and yaw velocity of the center of mass of the four-wheeled mobile robot; is the front axle tire stiffness and rear axle tire stiffness of the four-wheel mobile robot, is the length of the front and rear axles of the four-wheeled mobile robot, is the mass of the four-wheeled mobile robot, is the longitudinal speed of the four-wheeled mobile robot, is the moment of inertia of the four-wheel mobile robot, is the front wheel turning angle, is the additional yaw torque of the four-wheel mobile robot, are the lateral forces of the front and rear wheels of the four-wheeled mobile robot;通过引入坐标变换，故上式可以转化为如下：By introducing coordinate transformation , so the above formula can be transformed into the following:其中各式的值为：The values of each formula are:。 .3.根据权利要求1所述的适用于四轮移动机器人变道预警的有限时间跟踪控制方法，其特征在于，步骤S2中，设定四轮移动机器人的最小距离预警模型中包括三个四轮移动机器人，分别为目标机器人、第一参考机器人和第二参考机器人，其中目标机器人与第二参考机器人处于同一车道，目标机器人与第一参考机器人处于相邻车道，构建的最小距离预警模型的表达式如下：3. The limited time tracking control method for lane change warning of a four-wheeled mobile robot according to claim 1 is characterized in that, in step S2, the minimum distance warning model of the four-wheeled mobile robot is set to include three four-wheeled mobile robots, namely a target robot, a first reference robot and a second reference robot, wherein 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, and the expression of the constructed minimum distance warning model is as follows:运用激光雷达获取目标机器人、第一参考机器、第二参考机器人的纵向速度；为目标机器人与第二参考机器人的相对纵向速度，v_x表示目标机器人的纵向速度，v_p表示第二参考机器人的纵向速度，为目标机器人与第一参考机器人或第二参考机器人保持的最小安全距离，为目标机器人与第二参考机器人之间的相对距离，为目标机器人移动的距离，为第二参考机器人移动的距离，代表目标机器人从反应到启动制动所用的时间，，为重力加速度，为路面附着系数。Using laser radar to obtain the longitudinal speed of the target robot, the first reference robot, and the second reference robot; is the relative_longitudinal velocity between the target robot and the second reference robot,vx_represents the longitudinal velocity of the target robot,vp represents the longitudinal velocity of the second reference robot, is the minimum safety distance between the target robot and 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 the target robot moves, is the distance moved by the second reference robot, Represents the time taken by the target robot from reaction to braking. , is the acceleration due to gravity, is the road adhesion coefficient.4.根据权利要求1所述的适用于四轮移动机器人变道预警的有限时间跟踪控制方法，其特征在于，步骤S2中，所述运用机器学习GMM-HMM方法，结合最小距离预警模型，得到四轮移动机器人变道预警安全算法，实现四轮移动机器人在变道过程中的安全预警，包括：4. The finite time tracking control method for lane change warning of a four-wheeled mobile robot according to claim 1 is characterized in that, in step S2, the machine learning GMM-HMM method is used in combination with a minimum distance warning model to obtain a lane change warning safety algorithm for the four-wheeled mobile robot, so as to realize a safety warning of the four-wheeled mobile robot during the lane change process, including:在建立最小距离预警模型的基础上，运用机器学习GMM-HMM方法识别四轮移动机器人的运动行为时，GHH-HMM模型的概率分布描述如下：On the basis of establishing the minimum distance warning model, the machine learning GMM-HMM method is used to identify the motion behavior of the four-wheeled mobile robot. The probability distribution of the GHH-HMM model is described as follows:其中，为隐藏状态的第个单高斯函数的混合权重系数，是隐藏状态的第单高斯函数的权重矩阵，为隐藏状态的第个单高斯函数的协方差矩阵，是选取的观测矩阵，分别是四轮移动机器人的纵向速度、横向速度、横向位移；GMM-HMM参数被定义为，为初始状态概率分布向量，为状态转移概率分布矩阵，为混合权重系数，为权重矩阵，为协方差矩阵；in, Hidden state No. The mixing weight coefficients of a single Gaussian function, Is a hidden state No. The weight matrix of a single Gaussian function, Hidden state No. The covariance matrix of a single Gaussian function, is the selected observation matrix, They are the longitudinal velocity, lateral velocity, and lateral displacement of the four-wheeled 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;GHH-HMM模型的混合权重概率为；下一步的隐藏概率计算如下式：定义为时刻隐藏状态为且观测序列是的概率函数；The mixed weight probability of the GHH-HMM model is ; The hidden probability of the next step is calculated as follows: Defined as The hidden state at the moment is And the observation sequence is The probability function of其中，代表在GMM-HMM参数下，到时刻前部分的观测值序列，代表在GMM-HMM参数下，到时刻前后部分的观测值序列；为隐藏状态的第个单高斯函数的混合权重系数，为给定观测序列；是隐藏状态的第单高斯函数的权重矩阵，为隐藏状态的第个单高斯函数的协方差矩阵，表示时刻隐藏状态为且隐藏状态与前面个隐藏状态构成的隐藏状态序列的概率值最大；in, Represents the parameters in GMM-HMM Next, to The sequence of observations before the moment, Represents the parameters in GMM-HMM Next, to The sequence of observations before and after the moment; Hidden state No. The mixing weight coefficients of a single Gaussian function, For a given observation sequence; Is a hidden state No. The weight matrix of a single Gaussian function, Hidden state No. The covariance matrix of a single Gaussian function, express The hidden state at the moment is And hidden state With the front The probability value of the hidden state sequence composed of hidden states is the largest;以下，，为GMM-HMM模型所估计的概率，另其等于，，，可带入上式计算；the following , , is the probability estimated by the GMM-HMM model, and , , , can be substituted into the above formula to calculate ;基于四轮移动机器人运动行为的GHH-HMM模型的概率分布特征，设定运动行为从当前状态到下一状态的转变是随机的；为时间序列，隐藏状态数目设置为，并且高斯混合数设置为；由于隐藏状态以相同的概率转移到任何状态，参数、的初始值、设置为平均分配；由K-mean聚类算法自动初始化；通过训练GHH-HMM模型得到对应的变道预警参数值，从而辨识出相邻四轮移动机器人的变道行为。Based on the probability distribution characteristics of the GHH-HMM model of the motion behavior of the four-wheeled mobile robot, the transition of the motion behavior from the current state to the next state is set to be random; For time series, the number of hidden states is set to , and the Gaussian mixture number is set to ; Since the hidden state is transferred to any state with the same probability, the parameter , Initial value of , Set to even distribution; Automatically initialized by K-mean clustering algorithm; the corresponding lane change warning parameter value is obtained by training the GHH-HMM model , thereby identifying the lane-changing behavior of adjacent four-wheeled mobile robots.5.一种适用于四轮移动机器人变道预警的有限时间跟踪控制装置，其特征在于，包括以下模块：5. A limited time tracking control device for lane change warning of a four-wheeled mobile robot, characterized in that it includes the following modules:动力学建模模块，用于构建四轮移动机器人的动力学模型；Dynamics modeling module, used to build the dynamics model of the four-wheeled mobile robot;变道安全预警模块，用于根据动力学模型构建最小距离预警模型，运用机器学习GMM-HMM方法，结合最小距离预警模型，得到四轮移动机器人变道预警安全算法，实现移四轮移动机器人在变道过程中的安全预警；The lane change safety warning module is used to build a minimum distance warning model based on the dynamics model, and use the machine learning GMM-HMM method in combination with the minimum distance warning model to obtain a lane change warning safety algorithm for the four-wheeled mobile robot, thereby realizing a safety warning for the four-wheeled mobile robot during the lane change process;控制器构建模块，用于为了安全约束四轮移动机器人在变道过程中的横摆角速度，构建一种含时变约束的四轮移动机器人有限时间控制器；A controller building module is used to build a finite-time controller for a four-wheeled mobile robot with time-varying constraints in order to safely constrain the yaw angular velocity of the four-wheeled mobile robot during lane change;控制器执行模块，用于根据四轮移动机器人变道预警安全算法判断变道是否存在危险，若是，则执行有限时间控制器，在该有限时间控制器下实现四轮移动机器人的有限时间稳定；A controller execution module is used to determine whether there is a danger in changing lanes according to the lane change warning safety algorithm of the four-wheeled mobile robot, and if so, to execute a finite time controller to achieve finite time stability of the four-wheeled mobile robot under the finite time controller;控制器构建模块具体配置为：The controller building module is specifically configured as follows:首先定义第一误差量，其中y_d为期望质心侧偏角，然后基于障碍加幂积分技术选择合适的Lyapunov函数控制四轮移动机器人变道过程中的质心侧偏角，选择满足系统约束条件的Lyapunov函数，然后对该选取的函数求一阶导数，并缩放和简化，同时选取合适的虚拟控制律，使得，其中，均为常数，也即所设计的虚拟控制律能使四轮移动机器人的质心侧偏角状态约束并达到有限时间稳定；First, define the first error , wherey_d is the desired center of mass sideslip angle, and then select the appropriate Lyapunov function based on the obstacle plus power integration technology to control the center of mass sideslip angle of the four-wheeled mobile robot during the lane change process, and select the Lyapunov function that meets the system constraints , then find the first-order derivative of the selected function, scale and simplify it, and select the appropriate virtual control law , so that ,in , are all constants, that is, the designed virtual control law It can constrain the sideslip angle state of the center of mass of the four-wheeled mobile robot and achieve finite-time stability;首先定义第二误差量，其中，为常数；然后基于障碍加幂积分技术去选择合适的Lyapunov函数控制四轮移动机器人变道过程中的横摆角速度，与S31一样选取适当的Lyapunov函数，通过求导化简和现代控制方法使得，其中，均为常数；然后运用Backstepping反步法进行反步设计从而得到实际控制输入，使得四轮移动机器人在变道过程中的横摆角速度在不突破时变约束条件下实现有限时间稳定。First, define the second error ,in , is a constant; then based on the obstacle plus power integration technology, a suitable Lyapunov function is selected to control the yaw angular velocity of the four-wheeled mobile robot during the lane change process. The appropriate Lyapunov function is selected as in S31 , through derivation simplification and modern control methods, ,in , are all constants; then the Backstepping method is used to perform backstepping design to obtain the actual control input , which makes the yaw angular velocity of the four-wheeled mobile robot during lane change Achieve finite-time stability without violating time-varying constraints.6.一种电子设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述程序时实现如权利要求1-4中任一项所述的适用于四轮移动机器人变道预警的有限时间跟踪控制方法的步骤。6. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the limited-time tracking control method for lane change warning for a four-wheeled mobile robot as described in any one of claims 1 to 4 are implemented.7.一种存储介质，其上存储有计算机程序，其特征在于，该计算机程序被处理器执行时实现如权利要求1-4中任一项所述的适用于四轮移动机器人变道预警的有限时间跟踪控制方法的步骤。7. A storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the limited time tracking control method for lane change warning of a four-wheeled mobile robot as described in any one of claims 1 to 4 are implemented.