Intelligent car formation control method based on random noise damping

Abstract

The application discloses a kind of intelligent car formation control method based on random noise stabilization, utilizes random noise stabilization principle to carry out formation control, different from traditional negative feedback method, the application no longer needs negative feedback, controller parameter range is wider.Value selection.The established first-order and second-order controller has respective advantages, first-order controller convergence speed is fast, and second-order controller control effect is more stable, and user can select appropriate model and controller according to demand.In addition, since the introduction of white noise, the controller is random, and the motion path of the intelligent car is also random.If the multi-intelligent car system is in an antagonistic environment, this random path can better avoid the capture of the intelligent car by the predator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-agent formation control, and particularly relates to a smart car formation control method based on random noise stabilization. BACKGROUND

[0002] The rapid development of mobile intelligent car technology has promoted the progress of human society. At present, intelligent cars have been widely used in various fields, including aerospace, industry and security, etc. However, the ability of a single intelligent car is limited, which cannot fully meet people's needs in some complex environments, such as large-scale environmental map exploration, multi-target rescue and disaster relief, and joint harvesting of crops, etc.

[0003] Multi-agent technology aims to solve the above problems. Formation control technology is an important research direction of multi-agent technology. The formation control goal is to change or maintain the relative position of the multi-agent according to the expectation. At present, there are various multi-agent formation control methods, such as early backstepping method and feedback linearization method, which have preliminarily solved the formation and control problems, and formed various mature and stable formation control strategies represented by follower leader, behavior-based method and virtual structure method. Later, more restrictions were introduced into the multi-agent formation control system, such as considering communication time delay and bandwidth limitation, switching communication topology and obstacle avoidance, etc., so that the control method is closer to the actual situation and has better effect in actual application.

[0004] However, most of the above methods are based on negative feedback, which requires the error system to be fed back to the original system with negative state, and the controller parameters are subject to certain constraints. In fact, introducing a Gaussian white noise into a deterministic system changes its mathematical model into a stochastic differential equation. Under certain conditions, the stability of the stochastic differential equation does not depend on negative feedback. Japanese mathematician Ito Kiyosi made in-depth research on stochastic differential equations and proposed Ito formula for calculating stochastic integrals in 1951. Since then, the theory of stochastic analysis has also been gradually improved. Noise is usually considered to have disadvantages for system stability, but in research it is found that under certain conditions, white noise is beneficial to the stability of the system. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art and provide a smart car formation control method based on random noise stabilization which no longer requires negative feedback and has a wider range of controller parameter values.

[0006] To achieve the above object, the technical solution provided by the present application is as follows:

[0007] A smart car formation control method based on random noise stabilization, including two control modes based on a first-order controller and a second-order controller.

[0008] Based on a first order controller, comprising the following steps:

[0009] S1, a first order intelligent car suitable for unicycle kinematics model and a multi-intelligent car system model composed of n followers and 1 leader are established;

[0010] S2, in the multi-intelligent car system model, the followers are connected with the leader respectively according to the star network topology structure with the leader as the center;

[0011] S3, based on the multi-intelligent car system model, the system error of the multi-intelligent car formation control system is calculated according to the expected formation pose of the user;

[0012] S4, based on the system error, white noise is introduced according to the random noise stabilization principle, and the white noise is coupled to the controller for intelligent car formation control;

[0013] S5, the controller parameters meeting the discrimination condition are determined, under the action of the controller, the system error gradually converges to zero, and the multi-intelligent car formation reaches the stable expected pose;

[0014] Based on a second order controller, comprising the following steps:

[0015] A1, a second order intelligent car suitable for unicycle kinematics model and a multi-intelligent car system model composed of n followers and 1 leader are established;

[0016] A2, in the multi-intelligent car system model, the followers are connected with the leader respectively according to the star network topology structure with the leader as the center;

[0017] A3, based on the multi-intelligent car system model, the system error of the multi-intelligent car formation control system is calculated according to the expected formation pose of the user;

[0018] A4, based on the system error, white noise is introduced according to the random noise stabilization principle, and the white noise is coupled to the controller for intelligent car formation control;

[0019] A5, the controller parameters meeting the discrimination condition are determined, under the action of the controller, the system error gradually converges to zero, and the multi-intelligent car formation reaches the stable expected pose.

[0020] Further, the first order unicycle kinematics modeling is represented as:

[0021]

[0022] where x(t) and y(t) are coordinates of the intelligent car in the world coordinate system, and θ(t) is the orientation of the intelligent car; dx(t), dy(t), and dθ(t) are first-order derivatives of the corresponding variables, v(t) and ω(t) are linear velocity and angular velocity of the intelligent car, respectively.

[0023] Further, based on the first-order controller, according to the formation setting parameters (r i , l i ) expected by the user, it means that the i-th follower expects to be at the position with the leader as the coordinate system x = r i , y = l i ; the positions of all follower cars are mathematically transformed according to the set parameters, and the transformed pose is called the virtual pose of the follower car, and the transformation process is:

[0024]

[0025] where X vi (t) is the virtual pose of the follower car, x vi (t) and y vi (t) are virtual positions of the follower car in the world coordinate system, and θ vi (t) is the orientation of the virtual pose of the follower car; x i (t), y i (t), and θ i (t) are the poses of the i-th follower, and l i and r i are expected formation relative position parameters.

[0026] The virtual pose of the follower car is differentiated, and the result is:

[0027] dX vi (t) = H i (t)U i (t)dt,

[0028]

[0029] where U i (t) = [v i (t), ω i (t)] T is the linear velocity and angular velocity of the control object, i.e., the i-th follower.

[0030] Further, step S3 includes:

[0031] According to the unicycle model, the pose X r (t) = [x r (t) y r (t)] of the leader is constructedT and its differential is:

[0032]

[0033] where x r (t), y r (t) and θ r (t) are the position and orientation of the leader vehicle in the world coordinate system, respectively;

[0034] Define the error as:

[0035]

[0036] X vi (t) is the virtual pose of the follower vehicle;

[0037] The error of the multi-robot formation control system is:

[0038]

[0039] where, 1 n×1 is an n-row 1-column matrix with all elements being 1, is the Kronecker product.

[0040] Further, in step S4, the control is performed by the following formula:

[0041]

[0042] where is the inverse matrix of H i (t), is the leader pose derivative, is the controller gain parameter, e i (t) is the defined error, ζ i (t) is the Gaussian white noise introduced to the i-th follower, and the noise is generated by a noise generator.

[0043] Further, in step S5, the judgment process is as follows:

[0044] For the multi-robot formation control system, the formation pose parameters l i , i = 1, 2,..., n and the controller parameters k1, k2 ∈ R satisfy:

[0045] (1) l i < 0 holds for i = 1, 2,..., n;

[0046] (2) k1k2 > 0;

[0047] (3)

[0048] That is, it can be achieved:

[0049]

[0050] The multi-intelligent car formation control system meets the definition of almost sure exponential stability, that is, the system will converge to the desired formation at an exponential rate, and all cars will also be consistent in orientation.

[0051] Further, the second-order unicycle kinematics modeling is expressed as:

[0052]

[0053]

[0054] dθ(t)=ω(t)dt

[0055]

[0056]

[0057] dω(t)=α(t)dt

[0058] where x(t) and y(t) are the coordinates of the unicycle in the world coordinate system, θ(t) is the orientation of the car, dx(t), dy(t), and dθ(t) are the first derivatives of the corresponding variables, is the differential of the first derivative of the corresponding variable, v(t) and ω(t) are the linear and angular velocities of the car, and a(t) and α(t) are the linear and angular accelerations of the car.

[0059] Further, based on the second-order controller, according to the user's desired formation setting parameters (r i , l i ), which means that the i-th follower expects to be in the position of the leader as the coordinate system x=r i , y=l i ; according to the set parameters, the positions of all follower cars are mathematically transformed, and the transformed pose is called the virtual pose of the follower car, and the transformation process is:

[0060]

[0061] where X vi (t) is the virtual pose of the follower car, x vi (t) and y vi (t) are the virtual positions of the follower car in the world coordinate system, and are the corresponding derivatives, and θ vi(t) is the orientation of the virtual pose of the follower vehicle; x i (t), y i (t) and θ i (t) is the pose of the i-th follower, v i (t) and ω i (t) is the linear and angular velocity of the i-th follower, l i and r i are the desired formation relative position parameters;

[0062] Differentiate the virtual pose of the follower vehicle, the result is:

[0063]

[0064] wherein,

[0065]

[0066]

[0067] U i (t) = [a i (t), α i (t)] T is the control object, the linear and angular acceleration of the i-th follower.

[0068] Further, step A3 comprises:

[0069] Construct the pose of the leader according to the unicycle model and differentiate it:

[0070]

[0071]

[0072] wherein, x r (t), y r (t) and θ r (t) are the position and orientation of the leader vehicle in the world coordinate system, v r (t), ω r (t) and a r (t) are the linear, angular and linear acceleration of the leader vehicle, respectively;

[0073] Define the error as:

[0074]

[0075] The n followers are connected with the leader by star topology, i.e. each follower can only communicate with the leader. Each follower can obtain all states of itself by measurement, such as its pose, linear velocity, angular velocity, linear acceleration and angular acceleration, and can obtain all states of the leader by communication, such as the leader's pose, linear velocity, angular velocity, linear acceleration and angular acceleration;

[0076] The error of the multi-intelligent car formation control system is:

[0077]

[0078] wherein, 1 n×1 is a matrix of n rows and 1 column, all of whose elements are 1, is a Kronecker product.

[0079] Further, in step A4, the control is performed by the following formula:

[0080]

[0081] wherein is the inverse matrix of H i (t), E i (t), E r (t) are the matrices defined above, k1 and k2 are controller gain parameters, e im (t) is the mth component of the defined error, ζi i1 (t) and ζ i2 (t) are two independent Gaussian white noises introduced for the ith follower, which are generated by a noise generator;

[0082] In step A5, the judgment process is as follows:

[0083] For the multi-intelligent car formation control system, the formation pose parameters l i i = 1, 2,..., n and the controller parameters k1 and k2 ∈ R satisfy:

[0084] (1) l i < 0 holds for i = 1, 2,..., n;

[0085] (2)

[0086] That is, the following can be achieved:

[0087]

[0088] The multi-intelligent car formation control system satisfies the definition of almost certain exponential stability, i.e. the system will converge to the desired formation at an exponential rate, and all cars will also be consistent in orientation.

[0089] Compared with the prior art, the present application has the following principles and advantages:

[0090] The formation control method designed by using the random noise damping principle is different from the traditional negative feedback method, and the present application no longer needs negative feedback, and the controller parameter value range is wider. The first-order and second-order controllers have respective advantages, the first-order controller has fast convergence speed, and the second-order controller has more stable control effect, and users can select appropriate models and controllers according to requirements. In addition, due to the introduction of white noise, the controller is random, and the motion path of the intelligent car is also random, and if the multi-intelligent car system is in a confrontation environment, the random path can better avoid the capture of the intelligent car by the predator. BRIEF DESCRIPTION OF DRAWINGS

[0091] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the services needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0092] Figure 1 It is a monocycle motion model schematic diagram;

[0093] Figure 2 It is a follower car virtual transformation and formation parameter schematic diagram;

[0094] Figure 3 It is an example simulation result 1 of the first-order controller;

[0095] Figure 4 It is an example simulation result 2 of the first-order controller;

[0096] Figure 5 It is an example simulation result 1 of the second-order controller;

[0097] Figure 6 It is an example simulation result 2 of the second-order controller. DETAILED DESCRIPTION

[0098] The present application will be further described below in combination with specific embodiments:

[0099] The intelligent car formation control method based on random noise damping described in the present embodiment includes two control modes based on a first-order controller and a second-order controller;

[0100] Among them,

[0101] Based on the first-order controller, the following steps are included:

[0102] S1, establish a first-order intelligent car suitable for unicycle kinematics model and a multi-intelligent car system model composed of n followers and 1 leader;

[0103] As shown in Figure 1 , the first-order unicycle kinematics modeling is expressed as:

[0104]

[0105] Where x(t) and y(t) are the coordinates of the intelligent car in the world coordinate system, and θ(t) is the orientation of the intelligent car; dx(t), dy(t), and dθ(t) are the first-order derivatives of the corresponding variables, and v(t) and ω(t) are the linear and angular velocities of the intelligent car, respectively.

[0106] S2, in the multi-intelligent car system model, the followers are connected to the leader in a star network topology;

[0107] As shown in Figure 2 , based on the first-order controller, the desired formation setting parameters (r i ,l i ) are set by the user, which means that the i-th follower is expected to be at the position with the leader as the coordinate system x=r i , y=l i ; according to the set parameters, the positions of all follower cars are mathematically transformed, and the transformed pose is called the virtual pose of the follower car, and the transformation process is:

[0108]

[0109] Where X vi (t) is the virtual pose of the follower car, x vi (t) and y vi (t) are the virtual positions of the follower car in the world coordinate system, and θ vi (t) is the orientation of the virtual pose of the follower car; x i (t), y i (t), and θ i (t) are the poses of the i-th follower, and l i and r i are the desired formation relative position parameters.

[0110] The virtual pose of the follower car is differentiated, and the result is:

[0111] dX vi (t)=H i (t)U i (t)dt,

[0112]

[0113] wherein U i (t) = [v i (t), ω i (t)] T are the linear and angular velocities of the controlled object, the i-th follower.

[0114] S3, based on the multi-intelligent car system model, the system error of the multi-intelligent car formation control system is obtained according to the formation pose expected by the user;

[0115] Firstly, the pose X r (t) = [x r (t), y r (t)] T of the leader is constructed according to the unicycle model, and the differential thereof is solved:

[0116]

[0117] wherein x r (t), y r (t) and θ r (t) are the position and orientation of the leader car in the world coordinate system, respectively;

[0118] The error is defined as:

[0119]

[0120] X vi (t) is the virtual pose of the follower car;

[0121] The error of the final multi-intelligent car formation control system is:

[0122]

[0123] wherein, 1 n×1 is a matrix with n rows and 1 column, all elements of which are 1, is the Kronecker product.

[0124] S4, based on the system error, white noise is introduced according to the random noise stabilization principle, and the white noise is coupled to the controller for intelligent car formation control;

[0125] The control is specifically performed through the following formula:

[0126]

[0127] wherein is the inverse matrix of H i (t), is the leader pose derivative, For the controller gain parameters, e i (t) is the defined error, ζ i (t) is the Gaussian white noise introduced by the i-th follower, and the noise is generated by a noise generator.

[0128] S5, determine the controller parameters that satisfy the discriminant condition, under the action of the controller, the system error gradually converges to zero, and the multi-intelligent car formation reaches the stable expected pose;

[0129] The discrimination process is as follows:

[0130] For the multi-intelligent car formation control system, the formation pose parameters l i , i = 1, 2,..., n and the controller parameters k1, k2 ∈ R satisfy:

[0131] (1) l i <0 for i = 1, 2,..., n;

[0132] (2) k1k2 > 0;

[0133] (3)

[0134] That is, it can be realized:

[0135]

[0136] The multi-intelligent car formation control system satisfies the definition of almost certain exponential stability, that is, the system will converge to the expected formation at an exponential rate, and all cars will also be consistent.

[0137] Based on the second-order controller, the following steps are included:

[0138] A1, establish a second-order intelligent car suitable for the kinematic model of a unicycle and a multi-intelligent car system model composed of n followers and 1 leader;

[0139] The second-order unicycle kinematic modeling is expressed as:

[0140]

[0141]

[0142] dθ(t) = ω(t)dt

[0143]

[0144]

[0145] dω(t) = α(t)dt

[0146] where x(t) and y(t) are coordinates of the unicycle in the world coordinate system, θ(t) is the orientation of the unicycle, dx(t), dy(t) and dθ(t) are first derivatives of corresponding variables, are differentials of first derivatives of corresponding variables, v(t) and ω(t) are linear and angular velocities of the unicycle, a(t) and α(t) are linear and angular accelerations of the unicycle.

[0147] A2, in the multi-intelligent unicycle system model, according to the star network topology, the follower is centered on the leader and connected with the leader respectively;

[0148] Based on the second-order controller, according to the user's desired formation setting parameters (r i , l i ), the meaning is that the i-th follower is expected to be in the position with the leader as the coordinate system x = r i , y = l i ; according to the set parameters, the positions of all follower unicycles are mathematically transformed, and the transformed poses are called virtual poses of the follower unicycles, and the transformation process is:

[0149]

[0150] where X vi (t) is the virtual pose of the follower unicycle, x vi (t) and y vi (t) are virtual positions of the follower unicycle in the world coordinate system, and are corresponding derivatives, θ vi (t) is the orientation of the virtual pose of the follower unicycle; x i (t), y i (t) and θ i (t) are the pose of the i-th follower, v i (t) and ω i (t) are linear and angular velocities of the i-th follower, l i and r i are expected formation relative position parameters;

[0151] The virtual pose of the follower unicycle is differentiated, and the result is:

[0152]

[0153] where,

[0154]

[0155]

[0156] Ui (t) = [a i (t), a i (t)] T are the linear and angular accelerations of the control object, the i-th follower.

[0157] A3, based on the multi-intelligent car system model, the system error of the multi-intelligent car formation control system is obtained according to the formation pose expected by the user;

[0158] According to the unicycle model, the pose of the leader is constructed and its differential is obtained:

[0159]

[0160]

[0161] where x r (t), y r (t) and θ r (t) are the position and orientation of the leader car in the world coordinate system, v r (t), ω r (t) and a r (t) are the linear velocity, angular velocity and linear acceleration of the leader car, respectively.

[0162] Define the error as:

[0163]

[0164] The star topology is used to connect n followers with the leader, i.e. each follower can only communicate with the leader, and each follower can only obtain the pose, linear velocity, angular velocity, linear acceleration and angular acceleration of the leader through communication in addition to measuring its own pose, linear velocity, angular velocity, linear acceleration and angular acceleration.

[0165] The error of the final multi-intelligent car formation control system is:

[0166]

[0167] where, 1 n×1 is a matrix of n rows and 1 column, all elements of which are 1, is the Kronecker product.

[0168] A4, based on the system error, according to the random noise stabilization principle, white noise is introduced, and the white noise is coupled to the controller for intelligent car formation control.

[0169] The control is specifically performed by the following formula:

[0170]

[0171] wherein is H i the inverse matrix of E i (t), E r (t) is the matrix defined above, k1, k2 are controller gain parameters, e im (t) is the mth component of the defined error, ζ i1 (t) and ζ i2 (t) are two independent Gaussian white noises introduced for the ith follower, the noises are generated by a noise generator.

[0172] A5, determining the controller parameters satisfying the discrimination condition, under the action of the controller, the system error gradually converges to zero, and the formation of the intelligent car reaches the stable expected pose.

[0173] The discrimination process is as follows:

[0174] For the formation control system of the intelligent car, the formation pose parameters l i , i = 1, 2,..., n and the controller parameters k1, k2 ∈ R satisfy:

[0175] (1) l i < 0 holds for i = 1, 2,..., n;

[0176] (2)

[0177] That is, the following can be achieved:

[0178]

[0179] The formation control system of the intelligent car satisfies the definition of almost certain exponential stability, that is, the system will converge to the expected formation at an exponential rate, and all the cars will also be consistent in direction.

[0180] In practical applications, for a formation of n followers and 1 leader of intelligent cars, first, a first-order or second-order model is selected through S1; then the formation parameters r i , l i are set through S2, and a virtual car of the follower is constructed; then the leader state is calculated according to S3 and the error is constructed; the appropriate linear velocity and angular velocity or linear acceleration and angular acceleration are given to the controlled car according to the controller designed by S4; according to the discrimination condition given by S5, the stability of the formation system can be achieved.

[0181] In order to prove the effectiveness of the method described in the application, the following simulation experiments are made:

[0182] As Figures 3-6Given an instance under the action of first-order and second-order noise controller simulation, initial state bits:

[0183]

[0184]

[0185]

[0186]

[0187] The desired formation is r1=-2, l1=-2, r2=0, l2=-1, r3=2, l3=2; the selected controller parameters are k1=1, k2=4, and all parameters satisfy the discrimination condition.

[0188] Figure 3 The motion path of each car under the first-order noise controller.

[0189] Figure 4 The system error convergence under the first-order noise controller.

[0190] Figure 5 The motion path of each car under the second-order noise controller.

[0191] Figure 6 The system error convergence under the second-order noise controller.

[0192] The simulation results show that the control method of the application can effectively realize the formation control of the multi-intelligent car, and does not need negative feedback, and the controller parameter value range is larger. The simulation shows that the car motion path is random, and this random path can better avoid the capture of the intelligent car by the predator. The superiority of the control method is embodied. The first-order noise controller has faster convergence speed, and the car motion under the second-order controller is more stable.

[0193] The above-described embodiments are only the preferred embodiments of the application, and do not limit the implementation range of the application, so that any changes made according to the shape and principle of the application should be covered in the protection scope of the application.

Claims

1. A smart car formation control method based on random noise damping, characterized in that, Both a first-order controller and a second-order controller are included; The first-order controller includes the following steps: S1, a first-order multi-intelligent car system model composed of n followers and one leader is established, wherein the followers and the leader are first-order intelligent cars applicable to a first-order monocular kinematics model; S2, in the first-order multi-intelligent car system model, the followers are connected with the leader according to a star network topology structure; S3, based on the first-order multi-intelligent car system model, system errors of the multi-intelligent car formation control system are calculated according to a desired formation pose of a user; S4, based on the system errors, white noise is introduced according to a random noise stabilization principle, and the white noise is coupled to the controller for intelligent car formation control; S5, controller parameters meeting a discrimination condition are determined, under the action of the controller, the system errors gradually converge to zero, and the multi-intelligent car formation reaches a stable desired pose; The second-order controller includes the following steps: A1, a second-order multi-intelligent car system model composed of N followers and one leader is established, wherein the followers and the leader are second-order intelligent cars applicable to a second-order monocular kinematics model; A2, in the second-order multi-intelligent car system model, the followers are connected with the leader according to a star network topology structure; A3, based on the second-order multi-intelligent car system model, system errors of the multi-intelligent car formation control system are calculated according to a desired formation pose of a user; A4, based on the system errors, white noise is introduced according to a random noise stabilization principle, and the white noise is coupled to the controller for intelligent car formation control; A5, controller parameters meeting a discrimination condition are determined, under the action of the controller, the system errors gradually converge to zero, and the multi-intelligent car formation reaches a stable desired pose; According to the user's desired platoon setting parameters , the meaning is the desired position of the th follower in the leader's coordinate system; according to the set parameters, the positions of all follower carts are mathematically transformed, and the transformed pose is called the virtual pose of the follower cart, and the transformation process is: ； wherein, is a virtual pose of the follower vehicle, and is a virtual position of the follower vehicle in the world coordinate system, is an orientation of the virtual pose of the follower vehicle; , and is a pose of the th follower. The virtual pose of the follower car is differentiated, and the result is: ， ； wherein, , is the control input quantity for the th follower, and are the linear and angular velocities, respectively, of the th follower; In step S4, control is performed through the following formula: ; wherein is the inverse matrix of , is the leader pose derivative, is the controller gain parameter, is the defined error, is a Gaussian white noise introducing the th follower, the noise being generated by a noise generator; In step S5, the discrimination process is as follows: For the multi-intelligent car formation control system, is the first axis coordinate of the leader in the leader coordinate system, and the controller gain coefficient , satisfies: (1) For holds; （2） ； （3） ； That is, the following is achieved: The multi-intelligent car platoon control system meets the definition of almost sure exponential stability, that is, the system will converge to the desired platoon at an exponential rate, and all the cars will also be consistent in orientation. 2.The intelligent vehicle formation control method based on random noise damping according to claim 1, wherein, The first-order monocular kinematics model of the first-order intelligent car is represented as: ， wherein and are the coordinates of the first-order smart car in the world coordinate system, is the orientation of the first-order smart car; , , are the first-order derivatives of the corresponding variables, and are the linear and angular velocities of the first-order smart car. 3.The intelligent vehicle formation control method based on random noise damping according to claim 1, wherein, Step S3 includes: According to a first unicycle kinematics model to build the leader's pose And find its differential: ， wherein, , and are the position and orientation of the leader cart in the world coordinate system, respectively; The error is defined as: , virtual pose for the follower cart; The error of the final multi-intelligent car formation control system is: ， wherein , , is row column matrix, is the Kronecker product.

4. The intelligent vehicle formation control method based on random noise damping according to claim 1, wherein, The second-order monocular kinematics model of the second-order intelligent car is represented as: ， wherein and are coordinates of the second-order intelligent car in the world coordinate system, is the orientation of the second-order intelligent car, , , are first derivatives of the corresponding variables, , are differentials of the first derivatives of the corresponding variables, and are linear and angular velocities of the second-order intelligent car, and are linear and angular accelerations of the second-order intelligent car.

5. The intelligent vehicle formation control method based on random noise damping according to claim 4, characterized in that, when based on a second order controller, the formation set parameters desired by the user , which means the desired position of the th follower in the leader coordinate system; the positions of all follower carts are mathematically transformed according to the set parameters, and the transformed pose is called the virtual pose of the follower cart, and the transformation process is: ， wherein, is the virtual pose of the follower vehicle, and is the virtual position of the follower vehicle in the world coordinate system, and is the corresponding derivative, , and is the pose of the th follower, and is the linear and angular velocity of the th follower; The virtual pose of the follower car is differentiated, and the result is: ， Wherein, ， , For the first The control input of a follower. and The first The linear and angular accelerations of the followers.

6. The intelligent vehicle formation control method based on random noise damping according to claim 5, characterized in that, Step A3 includes: According to the second-order monocular kinematics model, the pose of the leader is constructed and the differential thereof is found: ， ； wherein, , and are the position and orientation of the leader car in the world coordinate system, respectively, , and are the linear velocity, angular velocity and linear acceleration of the leader car, respectively. The error is defined as: ； The N followers are connected with the leader by using the star topology structure, that is, each follower can only communicate with the leader, and each follower can only obtain all states of the leader such as the pose, linear velocity, angular velocity, linear acceleration and angular acceleration of the leader through communication, in addition to all states of itself such as the pose, linear velocity, angular velocity, linear acceleration and angular acceleration of the follower obtained by measurement; The error of the final multi-intelligent car formation control system is: ， wherein , , is row column elements of matrix, is the Kronecker product.

7. The intelligent vehicle formation control method based on random noise damping according to claim 6, characterized in that, In step A4, control is performed through the following formula: ， wherein is the inverse matrix of , is the matrix defined above, , is a controller gain parameter, is the first component of the defined error, and are two independent Gaussian white noises introduced for the first follower, the noises being generated by a noise generator; In step A5, the discrimination process is as follows: For the multi-intelligent car formation control system, is the axis coordinate of the th follower in the leader coordinate system, and the controller gain coefficient , satisfy: (1) For holds; （2） ； That is, the following is achieved: ， The multi-intelligent car formation control system meets the definition of almost certain exponential stability, that is, the system will converge to the desired formation at an exponential rate, and all cars will also be consistent in direction.

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