CN116610119A - Unmanned vehicle formation control method based on new time-varying spacing strategy - Google Patents
Unmanned vehicle formation control method based on new time-varying spacing strategy Download PDFInfo
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- G05D1/02—Control of position or course in two dimensions
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- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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- G05D1/02—Control of position or course in two dimensions
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- G05D1/0287—Control of position or course in two dimensions specially adapted to land vehicles involving a plurality of land vehicles, e.g. fleet or convoy travelling
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Abstract
The application discloses an unmanned vehicle formation control method based on a new time-varying spacing strategy, which is applied to an unmanned vehicle formation control system, wherein the unmanned vehicle formation comprises a lead vehicle and a following vehicle, and the problem that the stability of the whole system is influenced due to unstable queue caused by non-zero initial spacing errors in the prior art is solved by constructing the new time-varying spacing strategy about the spacing errors of two adjacent vehicles so that the initial spacing errors among the vehicles are zero; the self-adaptive update rate and the controller of each following vehicle are designed, the following vehicles pass through preset controller parameters, estimated values and self-motion information obtained by the self-adaptive update rate and the received motion information of the front vehicles and the lead vehicles are calculated in real time, the controller is brought into a longitudinal dynamics model of the following vehicles, the derivative of the acceleration of the following vehicles is obtained, the acceleration change of the following vehicles is controlled according to the derivative of the acceleration, and the control of the vehicle motion in unmanned vehicle formation is realized.
Description
Technical Field
The application belongs to the field of unmanned vehicle formation, and particularly relates to an unmanned vehicle formation control method based on a new time-varying spacing strategy.
Background
With the rapid development of logistics and transportation industry and the rapid increase of the automobile conservation quantity, a road traffic system faces a series of social problems, wherein unmanned vehicle formation control is used as a key link for building an intelligent traffic system, and gradually becomes a research key for building the intelligent traffic system.
Aiming at unmanned vehicles formation control strategies, the unmanned vehicles formation control strategy mainly comprises a fixed-spacing strategy and a time-varying spacing strategy. Most of research results are mainly based on a fixed-spacing strategy, but the spacing strategy is pointed out that the method cannot adapt to complex traffic environments, and the stability of the queue cannot be ensured on the premise that only the information of the speed and the distance between vehicles is obtained. In addition, in practical application, unmanned vehicle formation often needs to adopt different formation forms aiming at different scenes, for example, a formation form with larger spacing is required when traffic complexity is higher, and a formation form with smaller spacing is required when traffic complexity is lower, so that a time-varying spacing strategy has higher practical significance for unmanned vehicle formation control. However, conventional time-varying pitch strategies do not always meet the requirement of zero initial pitch error, especially in heterogeneous formation systems. It is worth noting that non-zero initial pitch error may cause queue instability, thereby affecting overall system stability, and thus solving the non-zero initial pitch error problem of conventional time-varying pitch strategies becomes particularly important.
Disclosure of Invention
The application aims to solve the problems in the background art and provides an unmanned vehicle formation control method based on a new time-varying spacing strategy.
In order to achieve the above purpose, the technical scheme adopted by the application is as follows:
the application provides an unmanned vehicle formation control method based on a new time-varying spacing strategy, which is applied to an unmanned vehicle formation control system, wherein the unmanned vehicle formation comprises a lead vehicle and a following vehicle, each vehicle acquires own motion information through a configured sensor and is in communication interconnection with each other, and the unmanned vehicle formation control method based on the new time-varying spacing strategy comprises the following steps:
and establishing longitudinal dynamics models of the lead car and the following car.
And constructing a new time-varying spacing strategy about the spacing error between the following vehicle and the preceding vehicle, and establishing a proportional-integral-derivative sliding mode function and a coupling sliding mode function which take the spacing error as a control variable.
The method comprises the steps of adopting a neural network to approach a nonlinear function in a longitudinal dynamics model of the following vehicle, adopting an adaptive method to estimate the weight of the neural network, an approximation error and external interference in the longitudinal dynamics model of the following vehicle, and combining a spacing error, a proportional-integral-differential sliding mode function and a coupling sliding mode function to design an adaptive updating rate and a controller of each following vehicle.
Obtaining a neural network weight estimated value and an estimated value of an approximation error and external interference according to the self-adaptive update rate, enabling the following vehicle to pass through preset controller parameters, calculating the size of a controller according to the estimated value and self-adaptive update rate and the received motion information of the preceding vehicle and the lead vehicle, and bringing the size of the controller into a longitudinal dynamics model of the following vehicle to obtain a derivative of acceleration of the following vehicle, and controlling the change of the acceleration of the following vehicle according to the derivative of the acceleration.
Preferably, the building of the longitudinal dynamics model of the lead car and the following car comprises:
each vehicle movement information comprises position, speed and acceleration;
establishing a longitudinal dynamics model of the lead vehicle:
wherein ,x0 and v0 Respectively representing the position and the speed of the lead vehicle, a 0 Representing a desired leader car acceleration function,represents x 0 First derivative of>Representing v 0 Is the first derivative of (a);
establishing a longitudinal dynamics model of an ith following vehicle:
wherein i=1, 2 … N, x i 、v i and ai Respectively representing the position, the speed and the acceleration of the ith following vehicle,represents x i First derivative of>Representing v i First derivative of>Representation a i C i Representing input to the i-th following vehicle engine or brake, w i Indicating external disturbances of the ith following vehicle due to wind or road conditions, and +.> Unknown constant representing external disturbance, f i (v i ,a i ) A nonlinear function is represented, and the nonlinear function is represented as follows:
wherein ,τi Represents the time constant of the ith following vehicle engine, r represents the air mass density, m i 、A i 、C di and dmi Respectively representing the mass, cross-sectional area, drag coefficient and mechanical resistance of the ith follower,represents air resistance;
definition controller u i Is thatSo that the input of the controller is independent of the mass of each vehicle, the longitudinal dynamics model of the ith following vehicle is updated as follows:
preferably, constructing a new time-varying spacing strategy for adjacent two-vehicle spacing errors includes:
constructing a new time-varying spacing strategy:
defining the spacing error between the ith vehicle and the ith-1 vehicle as delta i ：
Wherein, when i is 1, i-1 is equal to 0, the lead car is pi i Represents a positive constant, L i Indicating the length, delta, of the ith vehicle i-1,i The safety distance between the ith vehicle and the (i-1) th vehicle is represented by h, the delay time of the unmanned vehicle formation control system is represented by t, the time is represented by t, the safety coefficient is represented by sigma, and A m Representing the absolute value of the maximum possible deceleration,representation E i First derivative of>Representation E i And (f) second derivative of i Is an exponential term used to satisfy the following equation:
wherein ,representation of delta i First derivative, ->Representation of delta i A second derivative; the first equation in equation (4) represents that the initial pitch error of the new time-varying pitch strategy is in any case zero;
according to formula (3), the desired distance S between the ith vehicle and the (i-1) th vehicle quad,i The method comprises the following steps:
wherein the desired spacing S quad,i When the control system is stable for unmanned vehicles, i.e. spacing error delta i And equal to 0, the minimum distance between two adjacent vehicles is maintained.
Preferably, establishing a proportional-integral-derivative sliding-mode function and a coupling sliding-mode function with a pitch error as a control variable includes:
establishing a proportional-integral-derivative sliding mode function s i The following are provided:
wherein ,Kp 、K i and Kd Respectively representing the proportional, integral and differential coefficients;
according to the error transfer function H i (s)＝δ i+1 (s)/δ i (s) =λ, build δ i and δi+1 The relation between them, thus defining a coupled sliding mode function S i The following are provided:
where λ is a normal number, δ i+1 (s)、δ i (s) represents delta respectively i+1 and δi Is a complex frequency.
Preferably, a nonlinear function in a longitudinal dynamics model of the following vehicle is approximated by a neural network, an adaptive method is adopted to estimate the weight of the neural network, an approximation error and external interference in the longitudinal dynamics model of the following vehicle, and an adaptive update rate and a controller of each following vehicle are designed by combining a spacing error, a proportional-integral-derivative sliding mode function and a coupling sliding mode function, and the method comprises the following steps:
mechanical resistance d in equation (1) mi And air resistanceCannot be measured accurately, so f i (v i ,a i ) The function is unknown, and a neural network is adopted to approach a nonlinear function f in a longitudinal dynamics model of the following vehicle i (v i ,a i )：
wherein ,Zi ＝[z 1 ,…,z n ] T ∈R n The input vector is represented as such,represents an ideal weight vector, M represents the number of nodes of the neural network, < +.>Represents an approximation error, and->Unknown constant, ζ, representing approximation error k (Z i )＝[ξ 1 (Z i ),ξ 2 (Z i ),…,ξ M (Z i )] T Represents a radial basis function vector, T represents a transpose, and the radial basis function ζ k (Z i ) Expressed in terms of a gaussian function:
wherein ,φk and Bk The center vector and the width value of the gaussian function are respectively represented;
estimating the weight, approximation error and external interference in a longitudinal dynamics model of the following vehicle of the neural network by adopting an adaptive method:
defining the weight of the neural network, approximation errors and parameter estimation errors of external interference:
wherein ,θi * An unknown constant representing the square of the neural network weight,unknown constants representing approximation error and external disturbance square, +.>Is theta i * Estimated value of ∈10->Is theta i * Error of estimation of ∈10->Is eta i * Estimated value of ∈10->Is->And (2) estimation error of and />The definition is as follows:
designing an adaptive update rate of each following vehicle:
wherein Ξ 1i and Ξ2i Is an arbitrary bounded continuous function, satisfying:
wherein ,is bounded, &>Representation->First derivative of>Representation->Is the first derivative of (a);
the controller of each following vehicle is designed:
wherein ,ki Is the controller gain, θ i A constant greater than 0 and less than 1, lambda, b i ,K p ,K i ,K d ,α i ,β i Is an arbitrary positive constant which is set to be a constant,representing xi i Definition of R i The method comprises the following steps:
wherein ,representation pair Γ i And a second derivative.
Preferably, a neural network weight estimated value and an estimated value of an approximation error and external interference are obtained according to an adaptive update rate, a following vehicle passes through preset controller parameters, the estimated value and self motion information obtained by the adaptive update rate and the received motion information of a front vehicle and a lead vehicle are calculated to obtain the size of the controller, the size of the controller is brought into a longitudinal dynamics model of the following vehicle to obtain a derivative of acceleration of the following vehicle, and the acceleration change of the following vehicle is controlled according to the derivative of the acceleration, and the method comprises the following vehicle comprises the following steps of:
obtaining a neural network weight estimated value and an estimated value of approximation error and external interference according to the self-adaptive update rate of the formula (7), and presetting a controller parameter k i 、λ、π i 、K p 、K i 、K d 、σ、h、A m 、b i and θi Substituting each estimated value obtained according to the formula (7), the motion information of the following vehicle and the received motion information of the preceding vehicle and the lead vehicle into the formula (8) to obtain the controller size of the following vehicle, substituting the controller size of the following vehicle into the formula (2) to obtain the acceleration derivative of the following vehicle, and controlling the acceleration change of the following vehicle according to the acceleration derivative.
Compared with the prior art, the application has the beneficial effects that:
1. the unmanned vehicle formation control method based on the new time-varying spacing strategy enables the initial spacing error between vehicles to be zero by constructing the new time-varying spacing strategy about the spacing error of two adjacent vehicles, and solves the problem that the stability of the whole system is affected due to the fact that the non-zero initial spacing error possibly causes unstable queues in the prior art;
2. according to the unmanned vehicle formation control method based on the new time-varying spacing strategy, the self-adaptive update rate and the controller of each following vehicle are designed, the following vehicles pass through preset controller parameters, the estimated value obtained by the self-adaptive update rate, the self-motion information and the received motion information of the preceding vehicle and the lead vehicle are calculated to obtain the size of the controller, the size of the controller is brought into a longitudinal dynamics model of the following vehicles, so that the derivative of the acceleration of the following vehicles is obtained, the acceleration change of the following vehicles is controlled according to the derivative of the acceleration, and the control of the vehicle motion in unmanned vehicle formation is realized.
Drawings
FIG. 1 is a flow diagram of an unmanned vehicle formation control method based on a new time-varying spacing strategy of the present application;
fig. 2 is a schematic diagram of the unmanned vehicle formation of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It will be understood that when an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
1-2, an unmanned vehicle formation control method based on a new time-varying spacing strategy is applied to an unmanned vehicle formation control system, wherein the unmanned vehicle formation comprises a lead vehicle and a following vehicle, each vehicle acquires own motion information through a configured sensor and is in communication interconnection with each other, as shown in FIG. 2, the vehicles in the unmanned vehicle formation are numbered 0-N from front to back, wherein the 0 th vehicle is the lead vehicle, and the other vehicles are the following vehicles; each vehicle is provided with a GPS, a camera, a laser radar, a millimeter wave radar, an ultrasonic radar and other sensors to acquire own motion information (each vehicle motion information comprises position, speed and acceleration), and a front vehicle-lead vehicle following type communication topological structure is adopted among vehicles, namely, the lead vehicle can send motion information to the following vehicles, and the following vehicles can receive the motion information of the front vehicle and the lead vehicle.
The unmanned vehicle formation control method based on the new time-varying spacing strategy comprises the following steps:
step 1, building a longitudinal dynamics model of a lead car and a following car:
specifically, a longitudinal dynamics model of a lead car is established:
wherein ,x0 and v0 Respectively representing the position and the speed of the lead vehicle, a 0 Representing a desired leader car acceleration function,represents x 0 First derivative of>Representing v 0 Is the first derivative of (a);
establishing a longitudinal dynamics model of an ith following vehicle:
wherein i=1, 2 … N, x i 、v i and ai Respectively representing the position, the speed and the acceleration of the ith following vehicle,represents x i First derivative of>Representing v i One of (2)Order derivative (I)>Representation a i C i Representing input to the i-th following vehicle engine or brake, w i Indicating external disturbances of the ith following vehicle due to wind or road conditions, and +.>Unknown constant representing external disturbance, f i (v i ,a i ) A nonlinear function is represented, and the nonlinear function is represented as follows:
wherein ,τi Represents the time constant of the ith following vehicle engine, r represents the air mass density, m i 、A i 、C di and dmi Respectively representing the mass, cross-sectional area, drag coefficient and mechanical resistance of the ith follower,represents air resistance;
definition controller u i Is thatSo that the input of the controller is independent of the mass of each vehicle, the longitudinal dynamics model of the ith following vehicle is updated as follows:
step 2, constructing a new time-varying distance strategy about the distance error between the following vehicle and the front vehicle, and establishing a proportional-integral-differential sliding mode function and a coupling sliding mode function which take the distance error as a control variable:
specifically, a new time-varying pitch strategy is constructed:
defining the spacing error between the ith vehicle and the ith-1 vehicle as delta i ：
Wherein, when i is 1, i-1 is equal to 0, the lead car is pi i Represents a positive constant, L i Indicating the length, delta, of the ith vehicle i-1,i The safety distance between the ith vehicle and the (i-1) th vehicle is represented by h, the delay time of the unmanned vehicle formation control system is represented by t, the time is represented by t, the safety coefficient is represented by sigma, and A m Representing the absolute value of the maximum possible deceleration,representation E i First derivative of>Representation E i And (f) second derivative of i Is an exponential term used to satisfy the following equation:
wherein ,representation of delta i First derivative, ->Representation of delta i A second derivative; the first equation in equation (4) represents that the initial pitch error of the time-varying pitch strategy is in any case zero;
according to formula (3), the desired distance S between the ith vehicle and the (i-1) th vehicle quad,i The method comprises the following steps:
wherein the desired spacing S quad,i When the control system is stable for unmanned vehicles, i.e. spacing error delta i When equal to 0, the minimum distance between two adjacent vehicles is maintained, and the formula is about v i And thus the desired pitch of the time-varying pitch strategy is time-varying.
Establishing a proportional-integral-derivative sliding mode function s i The following are provided:
wherein ,Kp 、K i and Kd Respectively representing the proportional, integral and differential coefficients;
according to the error transfer function H i (s)＝δ i+1 (s)/δ i (s) =λ, build δ i and δi+1 The relation between them, thus defining a coupled sliding mode function S i The following are provided:
where λ is a normal number, δ i+1 (s)、δ i (s) represents delta respectively i+1 and δi Is a complex frequency.
Step 3, adopting a neural network to approach a nonlinear function in a longitudinal dynamics model of the following vehicle, adopting an adaptive method to estimate the weight of the neural network, the approximation error and the external interference in the longitudinal dynamics model of the following vehicle, and combining a spacing error, a proportional-integral-differential sliding mode function and a coupling sliding mode function to design an adaptive update rate and a controller of each following vehicle:
specifically, the mechanical resistance d in equation (1) mi And air resistanceCannot be measured accurately, so f i (v i ,a i ) The function is notIt is known that the neural network is adopted to approach the nonlinear function f in the longitudinal dynamics model of the following vehicle i (v i ,a i )：
wherein ,Zi ＝[z 1 ,…,z n ] T ∈R n The input vector is represented as such,represents an ideal weight vector, M represents the number of nodes of the neural network, < +.>Represents an approximation error, and->Unknown constant, ζ, representing approximation error k (Z i )＝[ξ 1 (Z i ),ξ 2 (Z i ),…,ξ M (Z i )] T Represents a radial basis function vector, T represents a transpose, and the radial basis function ζ k (Z i ) Expressed in terms of a gaussian function:
wherein ,φk and Bk The center vector and the width value of the gaussian function are respectively represented;
estimating the weight, approximation error and external interference in a longitudinal dynamics model of the following vehicle of the neural network by adopting an adaptive method:
defining the weight of the neural network, approximation errors and parameter estimation errors of external interference:
wherein ,θi * An unknown constant representing the square of the neural network weight,unknown constants representing approximation error and external disturbance square, +.>Is theta i * Estimated value of ∈10->Is theta i * Error of estimation of ∈10->Is->Estimated value of ∈10->Is->And (2) estimation error of and />The definition is as follows:
designing an adaptive update rate of each following vehicle:
wherein Ξ 1i and Ξ2i Is an arbitrary bounded continuous function, satisfying:
wherein ,is bounded, &>Representation->First derivative of>Representation->Is the first derivative of (a);
the controller of each following vehicle is designed:
wherein ,ki Is the controller gain, θ i A constant greater than 0 and less than 1, lambda, b i ,K p ,K i ,K d ,α i ,β i Is an arbitrary positive constant which is set to be a constant,representing xi i Definition of R i The method comprises the following steps:
wherein ,representation pair Γ i And a second derivative.
Step 4, obtaining a neural network weight estimated value and an estimated value of an approximation error and external interference according to the self-adaptive update rate, enabling the following vehicle to pass through preset controller parameters, calculating the size of a controller according to the estimated value and self-adaptive update rate and the received motion information of the preceding vehicle and the lead vehicle, and bringing the size of the controller into a longitudinal dynamics model of the following vehicle to obtain a derivative of the acceleration of the following vehicle, and controlling the acceleration change of the following vehicle according to the derivative of the acceleration:
specifically, the neural network weight estimated value, the approximation error and the estimated value of external interference are obtained according to the self-adaptive update rate of the formula (7), and the controller parameter k is preset i 、λ、π i 、K p 、K i 、K d 、σ、h、A m 、b i and θi Substituting each estimated value obtained according to the formula (7), the motion information of the following vehicle and the received motion information of the preceding vehicle and the lead vehicle into the formula (8) to obtain the controller size of the following vehicle, substituting the controller size of the following vehicle into the formula (2) to obtain the acceleration derivative of the following vehicle, and controlling the acceleration change of the following vehicle according to the acceleration derivative.
And constructing a Lyapunov function to prove the stability of the unmanned vehicle formation control system:
constructing a Lyapunov function:
deriving the above formula can obtain:
wherein ,represents V i First derivative of>Represent S i First derivative of ζ 1 and ζ2 Representing the relevant parameters;
defining a global lyapunov function as:
from equation (9), it can be obtained:
wherein ,representing the first derivative of V;
wherein ：
according to the lyapunov stability theory, it can be obtained:
wherein ,
if V (0) is greater than or equal to 0, S can be obtained i ,Is bounded by, inter alia,
by adjusting zeta 1 and ζ2 Related parameter k in (a) i 、λ、K d So that S i Converging near the origin, delta, as can be seen from equations (5) and (6) i Can also converge near the origin to meet the bicycle stability because of S i ＝λs i -s i+1 Can converge near the origin, so:
the Laplace transform is performed on equation (10) to obtain:
thus, the error transfer function H i (s)＝δ i+1 (s)/δ i (s) =λ, when 0 < λ+.ltoreq.1, the queue is made stable.
Wherein V (0), S i (0)、 and />Representing the respective initial values.
The unmanned vehicle formation control method based on the new time-varying spacing strategy enables the initial spacing error between vehicles to be zero by constructing the new time-varying spacing strategy about the spacing error of two adjacent vehicles, and solves the problem that the stability of the whole system is affected due to the fact that the non-zero initial spacing error possibly causes unstable queues in the prior art; according to the unmanned vehicle formation control method based on the new time-varying spacing strategy, the self-adaptive update rate and the controller of each following vehicle are designed, the following vehicles pass through preset controller parameters, the estimated value obtained by the self-adaptive update rate, the self-motion information and the received motion information of the preceding vehicle and the lead vehicle are calculated to obtain the size of the controller, the size of the controller is brought into a longitudinal dynamics model of the following vehicles, so that the derivative of the acceleration of the following vehicles is obtained, the acceleration change of the following vehicles is controlled according to the derivative of the acceleration, and the control of the vehicle motion in unmanned vehicle formation is realized.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above-described embodiments represent only the more specific and detailed embodiments of the present application, but are not to be construed as limiting the claims. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (6)
1. An unmanned vehicle formation control method based on a new time-varying spacing strategy is applied to an unmanned vehicle formation control system, and is characterized in that: the unmanned vehicle formation control method based on the new time-varying spacing strategy comprises the following steps of:
establishing longitudinal dynamics models of a lead car and a following car;
constructing a new time-varying distance strategy about the distance error between the following vehicle and the front vehicle, and establishing a proportional-integral-differential sliding mode function and a coupling sliding mode function which take the distance error as a control variable;
adopting a neural network to approach a nonlinear function in a longitudinal dynamics model of the following vehicle, adopting an adaptive method to estimate the weight of the neural network, an approximation error and external interference in the longitudinal dynamics model of the following vehicle, and combining a spacing error, a proportional-integral-differential sliding mode function and a coupling sliding mode function to design an adaptive updating rate and a controller of each following vehicle;
obtaining a neural network weight estimated value and an estimated value of an approximation error and external interference according to the self-adaptive update rate, enabling the following vehicle to pass through preset controller parameters, calculating the size of a controller according to the estimated value and self-adaptive update rate and the received motion information of the preceding vehicle and the lead vehicle, and bringing the size of the controller into a longitudinal dynamics model of the following vehicle to obtain a derivative of acceleration of the following vehicle, and controlling the change of the acceleration of the following vehicle according to the derivative of the acceleration.
2. The unmanned vehicle formation control method based on the new time-varying spacing strategy as claimed in claim 1, wherein: the building of the longitudinal dynamics model of the lead car and the following car comprises the following steps:
each vehicle movement information comprises position, speed and acceleration;
establishing a longitudinal dynamics model of the lead vehicle:
wherein ,x0 and v0 Respectively representing the position and the speed of the lead vehicle, a 0 Representing a desired leader car acceleration function,represents x 0 First derivative of>Representing v 0 Is the first derivative of (a);
establishing a longitudinal dynamics model of an ith following vehicle:
wherein i=1, 2 … N, x i 、v i and ai Respectively representing the position, the speed and the acceleration of the ith following vehicle,represents x i First derivative of>Representing v i First derivative of>Representation a i C i Representing input to the i-th following vehicle engine or brake, w i Indicating external disturbances of the ith following vehicle due to wind or road conditions, and +.> Unknown constant representing external disturbance, f i (v i ,a i ) A nonlinear function is represented, and the nonlinear function is represented as follows:
wherein ,τi Represents the time constant of the ith following vehicle engine, r represents the air mass density, m i 、A i 、C di and dmi Respectively representing the mass, cross-sectional area, drag coefficient and mechanical resistance of the ith follower,represents air resistance;
definition controller u i Is thatSo that the input of the controller is independent of the mass of each vehicle, the longitudinal dynamics model of the ith following vehicle is updated as follows:
3. the unmanned vehicle formation control method based on the new time-varying spacing strategy as claimed in claim 2, wherein: the construction of a new time-varying spacing strategy for adjacent two-vehicle spacing errors includes:
constructing a new time-varying spacing strategy:
defining the spacing error between the ith vehicle and the ith-1 vehicle as delta i ：
Wherein, when i is 1, i-1 is equal to 0, the lead car is pi i Represents a positive constant, L i Indicating the length, delta, of the ith vehicle i-1,i The safety distance between the ith vehicle and the (i-1) th vehicle is represented by h, the delay time of the unmanned vehicle formation control system is represented by t, the time is represented by t, the safety coefficient is represented by sigma, and A m Representing the absolute value of the maximum possible deceleration,representation E i First derivative of>Representation E i And (f) second derivative of i Is an exponential term used to satisfy the following equation:
wherein ,representation of delta i First derivative, ->Representation of delta i A second derivative; the first equation in equation (4) represents that the initial pitch error of the new time-varying pitch strategy is in any case zero;
according to formula (3), the desired distance S between the ith vehicle and the (i-1) th vehicle quad,i The method comprises the following steps:
wherein the desired spacing S quad,i When the control system is stable for unmanned vehicles, i.e. spacing error delta i And equal to 0, the minimum distance between two adjacent vehicles is maintained.
4. A method of unmanned vehicle formation control based on a new time-varying pitch strategy as claimed in claim 3, wherein: the establishing a proportional-integral-derivative sliding mode function and a coupling sliding mode function which take the space error as a control variable comprises the following steps:
establishing a proportional-integral-derivative sliding mode function s i The following are provided:
wherein ,Kp 、K i and Kd Respectively representing the proportional, integral and differential coefficients;
according to the error transfer function H i (s)＝δ i+1 (s)/δ i (s) =λ, build δ i and δi+1 The relation between them, thus defining a coupled sliding mode function S i The following are provided:
where λ is a normal number, δ i+1 (s)、δ i (s) represents delta respectively i+1 and δi Is a complex frequency.
5. The unmanned vehicle formation control method based on the new time-varying spacing strategy according to claim 4, wherein: the method adopts a neural network to approach a nonlinear function in a longitudinal dynamics model of the following vehicle, adopts an adaptive method to estimate the weight of the neural network, the approximation error and the external interference in the longitudinal dynamics model of the following vehicle, combines a spacing error, a proportional-integral-differential sliding mode function and a coupling sliding mode function, designs an adaptive update rate and a controller of each following vehicle, and comprises the following steps:
mechanical resistance d in equation (1) mi And air resistanceCannot be measured accurately, so f i (v i ,a i ) The function is unknown, and a neural network is adopted to approach a nonlinear function f in a longitudinal dynamics model of the following vehicle i (v i ,a i )：
wherein ,Zi ＝[z 1 ,…,z n ] T ∈R n The input vector is represented as such,represents an ideal weight vector, M represents the number of nodes of the neural network, < +.>Represents an approximation error, and-> Unknown constant, ζ, representing approximation error k (Z i )＝[ξ 1 (Z i ),ξ 2 (Z i ),…,ξ M (Z i )] T Represents a radial basis function vector, T represents a transpose, and the radial basis function ζ k (Z i ) Expressed in terms of a gaussian function:
wherein ,φk and Bk The center vector and the width value of the gaussian function are respectively represented;
estimating the weight, approximation error and external interference in a longitudinal dynamics model of the following vehicle of the neural network by adopting an adaptive method:
defining the weight of the neural network, approximation errors and parameter estimation errors of external interference:
wherein ,unknown constant representing the square of the weights of the neural network, +.>Unknown constants representing approximation error and external disturbance square, +.>Is->Estimated value of ∈10->Is->Error of estimation of ∈10->Is->Estimated value of ∈10->Is->And> and />The definition is as follows:
designing an adaptive update rate of each following vehicle:
wherein Ξ 1i and Ξ2i Is an arbitrary bounded continuous function, satisfying:
wherein ,is bounded, &>Representation->First derivative of>Representation->Is the first derivative of (a);
the controller of each following vehicle is designed:
wherein ,ki Is the gain of the controller and,a constant greater than 0 and less than 1, lambda, b i ,K p ,K i ,K d ,α i ,β i Is an arbitrary positive constant which is set to be a constant,representing xi i Definition of R i The method comprises the following steps:
wherein ,representation pair Γ i And a second derivative.
6. The unmanned vehicle formation control method based on the new time-varying spacing strategy according to claim 5, wherein: the method comprises the steps that a neural network weight estimated value and an estimated value of an approximation error and external interference are obtained according to an adaptive update rate, a following vehicle passes through preset controller parameters, the estimated value and self-motion information obtained by the adaptive update rate and the received motion information of a front vehicle and a lead vehicle are calculated to obtain the size of a controller, the size of the controller is brought into a longitudinal dynamics model of the following vehicle to obtain a derivative of acceleration of the following vehicle, and the acceleration change of the following vehicle is controlled according to the derivative of the acceleration, and the method comprises the following steps of:
obtaining a neural network weight estimated value and an estimated value of approximation error and external interference according to the self-adaptive update rate of the formula (7), and presetting a controller parameter k i 、λ、π i 、K p 、K i 、K d 、σ、h、A m 、b i Andsubstituting each estimated value obtained according to the formula (7), the motion information of the following vehicle and the received motion information of the preceding vehicle and the lead vehicle into the formula (8) to obtain the controller size of the following vehicle, substituting the controller size of the following vehicle into the formula (2) to obtain the acceleration derivative of the following vehicle, and controlling the acceleration change of the following vehicle according to the acceleration derivative.
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