CN109885883B - Unmanned vehicle transverse motion control method based on GK clustering algorithm model prediction - Google Patents
Unmanned vehicle transverse motion control method based on GK clustering algorithm model prediction Download PDFInfo
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Abstract
The invention discloses a control method of transverse motion of an unmanned vehicle based on GK clustering algorithm model prediction, which comprises the following steps of 1, acquiring the current state of the vehicle in real time; 2, collecting the surrounding environment of the vehicle and planning the expected path in real time; 3, establishing a single-track whole vehicle model by using a GK clustering algorithm; 4, converting the monorail vehicle model obtained in the step 3 into a state space equation of a linear error model, and performing discretization processing; 5, establishing a linear time-varying model prediction controller by using a linear time-varying model prediction control algorithm, inputting the mass center speed, the course angle, the yaw angular velocity and the vehicle position in a vehicle coordinate system as the model prediction controller, outputting a front wheel steering angle as the controller, calculating a track point in a prediction time domain and a control sequence in a control time domain according to the current state and a target track, converting the problem into a quadratic programming problem to solve the optimal solution, and updating the vehicle state; and 6, sequentially controlling the steering of the target vehicle according to the control quantity obtained by the model prediction controller.
Description
Technical Field
The invention belongs to the technical field of intelligent automobile control, and particularly relates to a control method for transverse motion of an unmanned vehicle based on GK clustering algorithm model prediction.
Background
In the prior art, many assumptions are made in the study of the vehicle dynamic lateral control, especially in the aspect of tire characteristics, only a linear region with a slip angle smaller than 5 degrees is usually considered, so that the accuracy of a model is greatly simplified, and the control accuracy is reduced.
Disclosure of Invention
The method is based on an improved G-K clustering algorithm to linearize the nonlinear part of the relationship between the tire lateral force and the slip angle in a segmented manner, and then the transverse control of the vehicle is carried out through a linear time-varying model predictive control algorithm. The adopted specific technical scheme is as follows:
a control method of unmanned vehicle lateral motion based on GK clustering algorithm model prediction provides steering wheel turning angles for a control object vehicle in real time, thereby realizing the control of the lateral motion of a control target, and comprises the following steps:
And 2, acquiring surrounding environment information of the automobile by using an industrial camera and a millimeter wave radar, and determining a travelable area so as to plan the expected path in real time.
Step 3, establishing a monorail complete vehicle model: and (3) utilizing a GK clustering algorithm to carry out piecewise linearization on a nonlinear part in the relation between the tire cornering power and the tire cornering angle to obtain a piecewise function of the affine back relation between the tire cornering power and the tire cornering angle, and utilizing the piecewise function to be brought into a vehicle dynamic model to obtain a single-track whole vehicle model expression.
And 4, converting the nonlinear single-track whole vehicle model into a state space equation of a linear error model by using a Taylor formula, wherein the state quantity is used for measuring the mass center speed, the course angle, the yaw angular velocity and the vehicle position under a geodetic coordinate system, and the control quantity is used for measuring the front wheel turning angle and carrying out discretization treatment on the front wheel turning angle.
And 5, establishing a linear time-varying model prediction controller by using a linear time-varying model prediction control algorithm, taking the mass center speed, the course angle, the yaw angle speed and the vehicle position under a geodetic coordinate system as the input of the model prediction controller, taking the front wheel turning angle as the output of the controller, calculating track points in a prediction time domain and a control sequence in a control time domain according to the current state and a target track, establishing a target function for obtaining the control sequence, converting the problem into a quadratic programming problem to obtain an optimal solution, and taking the first element of the control sequence as the control quantity of an actual control target. And updating the state of the vehicle, and repeating the steps to realize the rolling optimization function of model prediction.
And 6, sequentially controlling the steering of the target vehicle according to the control quantity obtained by the model predictive controller.
Further, in step 1:
the real-time acquisition of the current state information of the vehicle is real-time acquisition by using inertial navigation, and the speed information is acquired by a wheel speed sensor in real time.
Further, in step 2:
the method for planning the expected path in real time is to utilize an industrial camera and a millimeter wave radar to acquire the surrounding environment information of the automobile and determine a drivable area so as to plan the expected path in real time.
Further, in step 3:
establishing a single-track whole vehicle model, which comprises the following specific processes:
and performing piecewise affine on a nonlinear part in the relation between the tire cornering power F and the tire cornering angle alpha by using a GK clustering method to form a plurality of linear models, wherein model parameter identification comprises data subspace segmentation, parameter estimation of each subspace linear model and equation coefficient estimation of a switching surface. The method is characterized in that a multi-dimensional force sensor is used for collecting test data of a tire side deflection angle alpha and a tire side deflection force F under various working conditions, a piecewise affine model of tire side deflection characteristics is subjected to parameter identification, and the technical scheme of the method is described by taking a front wheel as an example. Constructing a regression equation based on experimental data obtained by a sensor: y (k) = f (x (k)) + e (k), where x (k) is a regression vector constructed from the historical input and output vectors of the systemTo, x (k) = [ y (k-1) … y (k-n) a ),u(k-1)…u(k-n a )](ii) a e (k) is additive noise for a known probability density distribution, y (k) is the measured output signal, and u (k) is the measured input signal.
1) Piecewise affine data subspace partitioning
For an input-output signal sequence Z = (x (k), y (k)), k =1, … T, T > 0, a mode function is defined: μ (k) {1, … T } → {1, … s }, μ (k): = i, where × (k) ∈ χ i And the improved G-K clustering method is adopted to realize the solution of the mode function mu, so that the clustering result meets the following objective function:
wherein m belongs to [1, ∞) represents an adjustable parameter of the clustering fuzzy degree, represents the overlapping degree between each category, and takes m =2.d (z) j ,v i ) Representing a sample z j And the clustering center v i The distance between them determines the shape of the cluster, and the algorithm is defined here as an adaptive distance measurement method:
d 2 (z j -v i )＝(z j -v i ) T M i (z j -v i ) (2)
wherein M is i Is a positive definite matrix and the matrix is a negative definite matrix,
wherein, F i Is a clustering covariance matrix that is,
given a data set Z, the clustering algorithm main steps are as shown in figure 2,
the method comprises the following steps: calculating a covariance matrix of the experimental data set Z, selecting the two farthest samples from the Z as initial clustering centers, and calculating a membership matrix
Let l =1
Step two: computing a clustering covariance matrix F i Extracting characteristic value and characteristic vector to adjust covariance
Step three: calculating M i Distance d from square 2
Step four: recalculating membership matrix
Step five: judge U l -U l-1 If the result is | is more than epsilon, returning to the step two if the result is yes, and continuing to the step six if the result is not so
Step six: keep this time clustering center
And membership matrix>
Performing clustering validity verification, namely judging that c is less than or equal to c max If the step is directly jumped to the step nine, if not, the step seven is continued
Step seven: c = c +1, according to membership matrix
Finding a sample z that is dissimilar to each subset k
Step eight: according to the new cluster initial center, calculating corresponding new initial membership matrix
Step nine: and determining the optimal clustering number, and dividing a data set according to the membership degree of the subset to which each group of samples belongs.
2) Piecewise affine sub-model parameter identification
After the data subspace division is obtained based on the clustering method, the problem of sub-model parameter identification is simplified into a linear optimization problem, and the method adopts a weighted least square method for calculation. According to the sub-data set Z i The input/output data of (2) is formed by the sum of squares of output deviations between the actual system and the submodelFunction of criterion whose minimum value corresponds to sub-model parameter vector theta i An estimate of (d).
Wherein, y i (j) To output a signal, x i (j) Is the input signal.
3) Estimation of equation coefficients for a plane of handover
Due to each scope
The convex polyhedron of (1) has no overlapping part except the common boundary, and the identification of the equation coefficient of the switching surface can be converted into the linear segmentation problem of the clustering data. The invention adopts a method based on a support vector machine to solve the hyperplane equation coefficient, and for the convex polyhedron interval of the sub-model action domain: />
The equation for the switching surface can be described as: h is ji ＝{w i x(k)+b i ＝0}，w i 、b i And respectively obtaining coefficient vectors, compromising the maximum classification interval and the minimum misclassification samples, establishing a generalized optimal classification surface, and selecting a linear kernel function meeting the Mercer condition to form a support vector so as to obtain the system hyperplane equation coefficient h.
Because the subspace number c of the piecewise affine system is determined by the extreme value of the optimization index, an overestimation situation may occur, the similarity of each submodel is judged by adopting a post-verification method, and the combination of the similar submodels and the re-identification of the model parameters are realized.
Clustering affine relationship obtained by clustering the affine tire cornering force F and the cornering angle alpha through a GK clustering algorithm is as follows:
wherein the content of the first and second substances,
parameter vector for affine submodel->
For affine submodels, and assuming that the convexities have no overlapping regions except for a common boundary, i.e.
The switching occurs when the state of the system reaches the border area. The slip angle α during control can be calculated according to the following relationship:
wherein
And &>
The longitudinal speed, the lateral speed and the vehicle yaw velocity under a vehicle coordinate system are respectively obtained by calculating the state quantity of a vehicle model in real time in the control process, delta f The front wheel steering angle of the vehicle is the control quantity of a vehicle model, the control quantity is obtained through real-time calculation in the control process, and a and b are the distances from the center of mass of the vehicle to the front axle and the rear axle respectively. And (3) bringing the lateral force into a monorail vehicle model to obtain a mathematical model:
wherein, F cf ,F cr Lateral forces respectively applied to front and rear tires of a vehicleWhich has been represented by the clustering algorithm segments; f lf ，F lr The longitudinal forces borne by the front tire and the rear tire of the vehicle are related to the longitudinal rigidity and the slip ratio of the tires respectively; delta. For the preparation of a coating f Turning a front wheel of the vehicle;
is the vehicle yaw angle; a is the distance from the front axle to the center of mass, b is the distance from the rear axle to the center of mass, I Z Is the moment of inertia of the vehicle about the z-axis.
Further, in the step 4:
the obtained single-track vehicle dynamic model is a nonlinear model, so that the model can be expressed by a state space equation only through linearization, wherein the state quantity is the mass center speed, the course angle, the yaw angular velocity and the vehicle position in a geodetic coordinate system, and the front wheel turning angle is controlled and measured. The specific method comprises the following steps:
the single rail vehicle dynamics model is written as:
where ξ is the state quantity and μ is the control quantity, it is set at an arbitrary point ([ ξ ]) r ,u r ) And (3) processing Taylor expansion, only keeping a first-order term, and neglecting a high-order term to obtain:
in addition, at this arbitrary point:
subtracting the equations (9) and (10) yields:
in the formula (I), the compound is shown in the specification,
/>
discretizing the state space equation by a first-order difference quotient method to obtain a discretized linear model expression:
where a (k) = I + TA (T), B (k) = TB (T), and T is a sampling time.
Further, in step 5:
according to the characteristics of model predictive control, a vehicle model is converted into a linear error model to be brought into a model predictive controller, a group of control sequences are obtained through calculation by an optimized solving function in the model predictive controller, a first quantity of the control sequences acts on a controlled object, and then the steps are repeated, wherein the steps are specifically divided into description, optimized solving and feedback calculation of state variables and output variables. The specific process is as follows:
1) Description of state variables and output variables
For ease of solution, the above equation (15) is written merged as:
obtaining a new state space expression:
wherein the content of the first and second substances,
Selecting a prediction time domain as 10, controlling the time domain as 3, and expressing the output quantity in the system prediction time domain as follows in a matrix form:
the output in the control time domain is->
The future output of the system can be written as: y (k +10 purple) = S x x(k)+S u Δ U (k), wherein
2) And (3) optimizing and solving:
the cost function is set as:
the first term reflects the tracking capability of the reference track, the second term reflects the stable change of the control process, Q, R are the weight matrixes of the two terms respectively, and rho epsilon 2 Is to avoid the relaxation factor increased by the absence of solution during the optimization. Conversion to the standard quadratic programming problem:
3) And (3) feedback updating:
the solution of the quadratic programming problem is completed, and the control quantity in the control time domain can be obtained:
further, in step 6:
the first element of the control sequence obtained from the linear time-varying Model Predictive Controller (MPC) acts on the vehicle, and since the model is established based on the linear error, the obtained control quantity needs to be added with the control quantity at the previous moment to obtain the actual control quantity at the next moment. Namely:
the invention has the beneficial effects that:
1. compared with the traditional method that the slip angle is less than 5 degrees, the method only considers the hypothesis in the linear range, can improve the application range of the controller, thereby improving the control precision, and has positive promotion effect on the high speed and intellectualization of the increasingly developed intelligent vehicle.
2. Compared with the traditional PID control, the method has better control precision by adopting the model predictive control algorithm, and can improve the stability of the vehicle when the vehicle runs at high speed.
3. The invention adopts model predictive control based on linear time variation, has higher real-time performance compared with nonlinear model predictive control, and particularly improves the performance of computer hardware at present, so that the speed of calculation and solution is faster.
Drawings
FIG. 1 is a schematic view of a monorail model of a vehicle;
FIG. 2 is a schematic diagram of subspace partitioning based on an improved G-K clustering algorithm;
fig. 3 is a control flow chart.
Detailed Description
The method is based on an improved G-K clustering algorithm, the nonlinear part of the relation between the tire lateral force and the slip angle is linearized in a segmented mode, and then the transverse control of the vehicle is carried out through a linear time-varying model predictive control algorithm. The control flow is shown in fig. 3, and the adopted specific technical scheme is as follows:
a control method of unmanned vehicle lateral motion based on GK clustering algorithm model prediction provides steering wheel turning angles for a control object vehicle in real time, thereby realizing the control of the lateral motion of a control target, and comprises the following steps:
And 2, acquiring the surrounding environment information of the automobile by using an industrial camera and a millimeter wave radar, and determining a drivable area so as to plan the expected path in real time.
Step 3, establishing a monorail complete vehicle model: and (3) carrying out piecewise linearization on a nonlinear part in the relation between the tire cornering power and the tire cornering angle by utilizing a GK clustering algorithm to obtain a piecewise function of the affine-back relation between the tire cornering power and the tire cornering angle, and substituting the piecewise function into a vehicle dynamics model to obtain a single-track whole vehicle model expression.
And 4, converting the nonlinear monorail vehicle model into a state space equation of a linear error model by using a Taylor formula, wherein the state quantity is used for measuring the mass center speed, the course angle, the yaw angular velocity and the vehicle position under a geodetic coordinate system, the front wheel turning angle is controlled and measured, and the front wheel turning angle is subjected to discretization treatment.
And 5, establishing a linear time-varying model prediction controller by using a linear time-varying model prediction control algorithm, taking the mass center speed, the course angle, the yaw angular velocity and the vehicle position under the geodetic coordinate system under a vehicle coordinate system as the input of the model prediction controller, taking the front wheel steering angle as the output of the controller, calculating track points in a prediction time domain and a control sequence in a control time domain according to the current state and a target track, establishing a target function for obtaining the control sequence, converting the problem into a quadratic programming problem to obtain an optimal solution, and taking the first element of the control sequence as the control quantity of an actual control target. And updating the state of the vehicle, and repeating the steps to realize the rolling optimization function of model prediction.
And 6, sequentially controlling the steering of the target vehicle according to the control quantity obtained by the model predictive controller.
Further, in step 1:
the real-time acquisition of the current state information of the vehicle is real-time acquisition by using inertial navigation, and the speed information is acquired by a wheel speed sensor in real time.
Further, in step 2:
the method for planning the expected path in real time is to utilize an industrial camera and a millimeter wave radar to acquire the surrounding environment information of the automobile and determine a drivable area so as to plan the expected path in real time.
Further, in step 3:
a single-track vehicle dynamic model is established, and the specific process is as follows:
and (3) utilizing a GK clustering method to perform piecewise affine on a nonlinear part in the relation between the tire cornering force F and the tire cornering angle alpha to form several linear models, wherein the model parameter identification comprises data subspace segmentation, linear model parameter estimation of each subspace and switching surface equation coefficient estimation. The method is characterized in that a multi-dimensional force sensor is used for collecting test data of a tire side deflection angle alpha and a tire side deflection force F under various working conditions, a piecewise affine model of tire side deflection characteristics is subjected to parameter identification, and the technical scheme of the method is described by taking a front wheel as an example. Based on experimental data obtained by the sensor, a regression equation is constructed: y (k) = f (x (k)) + e (k), wherein x (k) is a regression vector and is composed of historical input and output vectors of the system, and x (k) = [ y (k-1) … y (k-n) a ),u(k-1)…u(k-n a )](ii) a e (k) is additive noise for a known probability density distribution, y (k) is the measured output signal, and u (k) is the measured input signal.
1) Piecewise affine data subspace partitioning
For an input-output signal sequence Z = (x (k), y (k)), k =1, … T, T > 0, a mode function is defined: μ (k) {1, … T } → {1, … s }, μ (k): = i, where × (k) ∈ χ i And the improved G-K clustering method is adopted to realize the solution of the mode function mu, so that the clustering result meets the following objective function:
wherein, m belongs to [1, ∞ ] represents adjustable parameters of clustering fuzzy degree, represents the overlapping degree between each category, and takesm＝2。d(z j ,v i ) Representing a sample z j And the clustering center v i The distance between them determines the shape of the cluster, and the algorithm is defined here as an adaptive distance measurement method:
d 2 (z j -v i )＝(z j -v i ) T M i (z j -v i ) (2)
wherein M is i Is a positive definite matrix, formed by clustering covariance matrices F i Determining
Given a data set Z, the clustering algorithm has the main steps as shown in figure 2,
the method comprises the following steps: calculating a covariance matrix of the experimental data set Z, selecting the two farthest samples from the Z as initial clustering centers, and calculating a membership matrix
Let l =1
Step two: computing a clustering covariance matrix F i Extracting characteristic value and characteristic vector to adjust covariance
Step three: calculating M i Distance d from square 2
Step four: recalculating membership matrix
Step five: judge | | | U l -U l-1 If | > epsilon, returning to the step two if yes, and if not, continuing to the step six
Step six: keeping the clustering center of this time
And membership degree matrix->
Carrying out clustering validity verification, namely judging that c is less than or equal to c max If the step is directly jumped to the step nine, if not, the step seven is continued
Step seven: c = c +1, according to membership matrix
Finding a sample z that is dissimilar to each subset k
Step eight: according to the new clustering initial center, calculating corresponding new initial membership degree matrix
Step nine: and determining the optimal clustering number, and dividing the data set according to the membership degree of the subset to which each group of samples belongs.
2) Piecewise affine sub-model parameter identification
After the data subspace division is obtained based on the clustering method, the problem of sub-model parameter identification is simplified into a linear optimization problem, and the method adopts a weighted least square method for calculation. According to the sub-data set Z i The input and output data of (2) form a criterion function as shown below by the sum of squares of the output deviations between the actual system and the submodel, and the minimum value of the criterion corresponds to the parameter vector theta of the submodel i An estimate of (d).
3) Estimation of equation coefficients for a plane of handover
Due to each scope
The convex polyhedron of (1) has no overlapping part except the common boundary, and the identification of the equation coefficient of the switching surface can be converted into the linear segmentation problem of the clustering data. The invention adopts a method based on a support vector machine to solve the hyperplane equation coefficient, and for the convex polyhedron interval of the sub-model action domain: />
The equation of the switching surface can be describedComprises the following steps: h is a total of ji ＝{w i x(k)+b i And =0, the maximum classification interval and the least misclassification samples are considered in a compromise manner, a generalized optimal classification surface is established, and a linear kernel function meeting the Mercer condition is selected to form a support vector, so that a system hyperplane equation coefficient h is obtained.
Because the subspace number c of the piecewise affine system is determined by the extreme value of the optimization index, an overestimation situation may occur, the similarity of each submodel is judged by adopting a post-verification method, and the combination of the similar submodels and the re-identification of the model parameters are realized.
Clustering affine tire cornering power and cornering angle through a GK clustering algorithm to obtain a clustering affine relation as follows:
wherein the content of the first and second substances,
parameter vector for affine submodel->
Acting on convex body intervals for affine submodels, and assuming that each convex body has no overlapping interval except for a common boundary, i.e. < >>
The switching occurs when the state of the system reaches the border area. The slip angle α during control can be calculated according to the following relationship:
wherein
And &>
The longitudinal speed, the lateral speed and the vehicle yaw velocity under a vehicle coordinate system are respectively obtained by calculating the state quantity of a vehicle model in real time in the control process, delta f The front wheel steering angle of the vehicle is the control quantity of a vehicle model, the control quantity is obtained through real-time calculation in the control process, and a and b are the distances from the center of mass of the vehicle to the front axle and the rear axle respectively. Introducing the lateral force into the monorail vehicle model (as in FIG. 1) results in a mathematical model:
wherein, F cf ,F cr The lateral forces respectively applied to the front tire and the rear tire of the vehicle are represented by the clustering algorithm in a segmented manner; f lf ，F lr The longitudinal forces borne by the front tire and the rear tire of the vehicle are related to the longitudinal rigidity and the slip ratio of the tires respectively; delta f Is the vehicle front wheel corner;
is the vehicle yaw angle; a is the distance from the front axle to the center of mass, b is the distance from the rear axle to the center of mass, I Z Is the moment of inertia of the vehicle about the z-axis.
Further, in step 4:
the obtained single-track vehicle dynamic model is a nonlinear model, so that the model can be expressed by a state space equation only through linearization, wherein the state quantity is the mass center speed, the course angle, the yaw angular velocity and the vehicle position in a geodetic coordinate system, and the front wheel turning angle is controlled and measured. The specific method comprises the following steps:
the single rail vehicle dynamics model is written as:
wherein xi is a state quantity, mu is a control quantity, taylor expansion is carried out on the state quantity and mu at any point, only a first-order term is reserved, and a high-order term is ignored to obtain:
in addition, at this arbitrary point:
subtracting the equations (9) and (10) yields:
in the formula (I), the compound is shown in the specification,
discretizing the state space equation by a first-order difference quotient method to obtain a discretized linear model expression:
where a (k) = I + TA (t), B (k) = TB (t).
Further, in step 5:
according to the characteristics of model predictive control, a vehicle model is converted into a linear error model to be brought into a model predictive controller, a group of control sequences are obtained through calculation through an optimization solving function in the model predictive controller, a first quantity of the control sequences acts on a controlled object, and then the steps are repeated, and the method is specifically divided into description, optimization solving and feedback calculation of state variables and output variables. The specific process is as follows:
1) Description of state variables and output variables
For ease of solution, equation (15) above is written merged as:
obtaining a new state space expression:
wherein the content of the first and second substances,
Selecting a prediction time domain as 10, controlling the time domain as 3, and expressing the output quantity in the system prediction time domain as follows in a matrix form:
the output in the control time domain is->
The future output of the system can be written as: y (k +10 purple) = S x x(k)+S u Δ U (k), wherein
2) And (3) optimizing and solving:
the cost function is set as:
wherein the first term is inverseMapping the tracking ability of the reference track, reflecting the stable change of the control process by the second term, Q, R being the weight matrix of the two terms respectively, rho epsilon 2 Is an increased relaxation factor in order to avoid a solution-free situation during the optimization. Conversion to the standard quadratic programming problem:
3) And (3) feedback updating:
the solution of the quadratic programming problem is completed, and the control quantity in the control time domain can be obtained:
further, in step 6:
the first element of the control sequence obtained from the linear time-varying Model Predictive Controller (MPC) acts on the vehicle, and since the model is built based on the linear error, the obtained control quantity needs to be added with the control quantity at the previous moment to obtain the actual control quantity at the next moment. Namely:
the above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
Claims (5)
1. A control method for unmanned vehicle transverse motion based on GK clustering algorithm model prediction is characterized by comprising the following steps:
step 1, obtaining the current state of a vehicle in real time by using a vehicle sensor, wherein the current state comprises mass center speed, course angle, yaw angular velocity, current coordinates of the vehicle, tire slip angle and vehicle speed information;
step 2, collecting surrounding environment information of the automobile by using an industrial camera and a millimeter wave radar, determining a travelable area, and planning an expected path in real time;
step 3, establishing a monorail complete vehicle model: the method comprises the steps that a nonlinear part in the relation between the tire cornering power and the tire cornering angle is subjected to piecewise linearization by using a GK clustering algorithm to obtain a piecewise function of an affine back relation between the tire cornering power and the tire cornering angle, and the piecewise function is brought into a vehicle dynamic model to obtain a single-track whole vehicle model;
the single-track whole vehicle model expression in the step 3 is as follows:
wherein, F cf ,F cr The lateral forces respectively applied to the front tire and the rear tire of the vehicle are represented by the clustering algorithm in a segmented manner; f lf ，F lr The longitudinal forces borne by the front tire and the rear tire of the vehicle are related to the longitudinal rigidity and the slip ratio of the tires respectively; delta. For the preparation of a coating f Turning a front wheel of the vehicle;
is the vehicle yaw angle; a is the distance from the front axle to the center of mass, b is the distance from the rear axle to the center of mass, I Z Is the moment of inertia of the vehicle about the z-axis;
the method for establishing the monorail complete vehicle model comprises the following steps:
utilizing a GK clustering method to affine non-linear parts in the relation between the tire cornering power F and the tire cornering angle alpha into several linear models in a piecewise manner, wherein model parameter identification comprises data subspace segmentation, parameter estimation of each subspace linear model and equation coefficient estimation of a switching surface; acquiring test data of a tire cornering angle alpha and a tire cornering force F under various working conditions, performing parameter identification on a piecewise affine model of tire cornering characteristics, and constructing a regression equation based on the test data obtained by a sensor: y (k) = f (x (k)) + e (k), where x (k) is a regression vector, consisting of the historical input and output vectors of the system,x(k)＝[y(k-1)…y(k-n a ),u(k-1)…u(k-n a )](ii) a e (k) is additive noise for a known probability density distribution, y (k) is the measured output signal, and u (k) is the measured input signal;
1) Piecewise affine data subspace partitioning
For an input-output signal sequence Z = (x (k), y (k)), k =1, … T, T > 0, a mode function is defined: μ (k) {1, … T } → {1, … s }, μ (k): = i, where × (k) ∈ χ i And the improved G-K clustering method is adopted to realize the solution of the mode function mu, so that the clustering result meets the following objective function:
wherein m belongs to [1, ∞) represents an adjustable parameter of the clustering fuzzy degree, represents the overlapping degree of each category, and takes m =2; d (z) j ,v i ) Represents a sample z j And the clustering center v i The distance between them determines the shape of the cluster, and adopts the self-adaptive distance measurement method:
d 2 (z j -v i )＝(z j -v i ) T M i (z j -v i )
wherein M is i Is a positive definite matrix, formed by clustering covariance matrices F i Determining
2) Piecewise affine sub-model parameter identification
After data subspace division is obtained based on a clustering method, simplifying the sub-model parameter identification problem into a linear optimization problem, and calculating by adopting a weighted least square method; according to subclass data set Z i The input and output data of (2) form a criterion function as shown below by the sum of squares of the output deviations between the actual system and the submodel, and the minimum value of the criterion corresponds to the parameter vector theta of the submodel i An estimated value of (d);
3) Estimation of coefficients of a switching surface equation
Due to each scope
The convex polyhedron of (1) has no overlapping part except the public boundary, and the switching surface equation coefficient identification can be converted into the linear segmentation problem of the clustering data; solving the hyperplane equation coefficient by adopting a method based on a support vector machine, and for the convex polyhedron interval of the sub-model action domain: />
The equation for the switching surface can be described as: h is ji ＝{w i x(k)+b i =0}, the maximum classification interval and the minimum misclassification samples are considered in a compromise mode, a generalized optimal classification surface is established, a linear kernel function meeting the Mercer condition is selected to form a support vector, and therefore the system hyperplane equation coefficient h is obtained;
judging the similarity of each submodel by adopting a post-verification method, and realizing the combination of similar submodels and the re-identification of model parameters;
clustering affine relations obtained by clustering the cornering power and the cornering angle of the affine tire through a GK clustering algorithm are as follows:
wherein the content of the first and second substances,
parameter vector for affine submodel->
Acting on convex body intervals for affine submodels, and assuming that each convex body has no overlapping interval except for a common boundary, i.e. < >>
When the state of the system reaches the boundary area, switching occurs, and the slip angle alpha is calculated according to the following relational expression in the control process:
wherein
And &>
The longitudinal speed, the lateral speed and the vehicle yaw velocity are respectively under a vehicle coordinate system, the quantities are obtained by real-time calculation of state quantities of a vehicle model in a control process, and delta f Is the front wheel steering angle of the vehicle, is the control quantity of the vehicle model, is calculated in real time in the control process, a and b are the distances from the center of mass of the vehicle to the front and rear axes respectively, and the side of the vehicle is connected with the front wheel steering angleAnd (3) carrying a single-rail whole vehicle model into the force to obtain a mathematical model:
wherein, F cf ,F cr The lateral forces respectively applied to the front tire and the rear tire of the vehicle are represented by the clustering algorithm in a segmented manner; f lf ，F lr The longitudinal forces borne by the front tire and the rear tire of the vehicle are related to the longitudinal rigidity and the slip ratio of the tires respectively; delta f Is the vehicle front wheel corner;
is the vehicle yaw angle; a is the distance from the front axle to the center of mass, b is the distance from the rear axle to the center of mass, I Z Is the moment of inertia of the vehicle about the z-axis;
the steps of the clustering algorithm are as follows:
the method comprises the following steps: calculating a covariance matrix of the experimental data set Z, selecting the two farthest samples from the Z as initial clustering centers, and calculating a membership matrix
Let l =1;
step two: computing a clustering covariance matrix F i Extracting a characteristic value and a characteristic vector, and adjusting covariance;
step three: calculating M i Distance d from square 2 ；
Step four: recalculating membership matrix
Step five: judge U l -U l-1 If the result is more than epsilon, returning to the step two if the result is yes, and continuing to the step six if the result is not so;
step six: keeping the clustering center of this time
And membership degree matrix->
Carrying out clustering validity verification, namely judging that c is less than or equal to c max If the step is directly skipped to the step nine, if not, the step seven is continued;
step seven: calculating variable c = c +1 according to membership matrix
Finding a sample z that is dissimilar to each subset k ；
Step eight: calculating a corresponding new initial membership matrix according to the new clustering initial center;
step nine: determining the optimal clustering number, and dividing a data set according to the membership degree of the subset to which each group of samples belongs;
step 4, converting the nonlinear three-degree-of-freedom single-track whole vehicle model obtained in the step 3 into a state space equation of a linear error model by using a Taylor formula, wherein the state quantity is used for measuring the mass center speed, the course angle, the yaw angular velocity and the vehicle position in a geodetic coordinate system, the control quantity is used for measuring the front wheel turning angle, and the front wheel turning angle is subjected to discretization processing;
step 5, establishing a linear time-varying model prediction controller by using a linear time-varying model prediction control algorithm, taking the centroid speed, the course angle, the yaw rate and the vehicle position under a geodetic coordinate system under a vehicle coordinate system as the input of the model prediction controller, taking the front wheel turning angle as the output of the controller, calculating track points in a prediction time domain and a control sequence in a control time domain according to the current state and a target track, establishing a target function for obtaining the control sequence, converting the problem into a quadratic programming problem to obtain an optimal solution, taking the first element of the control sequence as the control quantity of an actual control target, updating the state of the vehicle, and repeating the steps to realize the rolling optimization function of model prediction;
and 6, sequentially controlling the steering of the target vehicle according to the control quantity obtained by the model prediction controller.
2. The method as claimed in claim 1, wherein in the step 1, the real-time acquisition of the current state information of the vehicle is acquired in real time by inertial navigation, and the real-time acquisition of the vehicle speed information is acquired by a wheel speed sensor.
3. The method for controlling the lateral motion of the unmanned aerial vehicle based on GK clustering algorithm model prediction as claimed in claim 1, wherein the specific implementation of the step 4 comprises the following steps:
writing a single-rail whole vehicle model into:
wherein xi is a state quantity, mu is a control quantity, taylor expansion is carried out on the state quantity and mu at any point, only a first-order term is reserved, and a high-order term is ignored to obtain:
in addition, at this arbitrary point:
general formula
And &>
The subtraction yields:
in the formula (I), the compound is shown in the specification,
discretizing the state space equation by a first-order difference quotient method to obtain a discretized linearized model expression:
where a (k) = I + TA (t), B (k) = TB (t).
4. The method for controlling the lateral motion of the unmanned aerial vehicle based on GK clustering algorithm model prediction as claimed in claim 3, wherein the concrete implementation of the step 5 comprises the following steps:
1) Description of state variables and output variables
For the convenience of solution, will
The merge write:
obtaining a new state space expression:
wherein the content of the first and second substances,
selecting a prediction time domain as 10, controlling the time domain as 3, and expressing the output quantity in the system prediction time domain as follows in a matrix form:
the output in the control time domain is->
The future output of the system is written as: y (k +10 purple) = S x x(k)+S u Δ U (k), wherein
2) And (3) optimizing and solving:
the cost function is set as:
wherein the first term on the right of the equation reflects the tracking capability of the reference track, the second term reflects the stable change of the control process, Q, R are the weight matrixes of the two terms respectively, and rho epsilon 2 The relaxation factor is increased to avoid the situation of no solution in the optimization process;
conversion to the standard quadratic programming problem:
3) And (3) feedback updating:
and (3) completing the solution of the quadratic programming problem to obtain the control quantity in the control time domain:
5. the method for controlling the lateral motion of the unmanned aerial vehicle based on GK clustering algorithm model prediction as claimed in claim 4, wherein in the step 6, the actual control quantity for controlling the steering of the target vehicle is as follows: the control quantity obtained by adding the control quantity at the previous moment to the control quantity obtained by the model predictive controller is as follows:
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