CN111258218B - Intelligent vehicle path tracking method based on maximum correlation entropy criterion - Google Patents
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Abstract
The invention disclosesAn intelligent vehicle path tracking method based on the maximum correlation entropy criterion is provided, which belongs to the field of trajectory tracking and comprises the steps of constructing a vehicle dynamics model; converting the vehicle dynamics model to a system state model; carrying out discrete linearization processing on the system state model, and constructing an output model for forming a prediction time domain; constructing a solving control increment delta u based on a maximum correlation entropy criterion and a half-square method k The path tracking model of (1); solving the path tracking model to obtain the speed v based on the mass center of the vehicle and the steering angle sigma of the front wheel f Control increments of (c). According to the scheme, the path tracking model is established by adopting the measurement of the maximum correlation entropy criterion, and the model can effectively inhibit or eliminate the influence from noise or local points to realize the stable path tracking of the vehicle.
Description
Technical Field
The invention relates to a vehicle path tracking control method, in particular to an intelligent vehicle path tracking method based on a maximum correlation entropy criterion.
Background
The main popular path tracking control algorithm at present is as follows: PID control, a linear quadratic regulator LQR tracking controller, pure tracking control and the like.
The PID control is a control algorithm which is widely applied in the field of industrial control, the method has the advantage that a model does not need to be built, but the control parameters of the method need to be continuously tested and found out once and again, and the method is tedious, tedious and time-consuming work. Therefore, although PID is simple, the adaptability to the vehicle speed is extremely poor, and other vehicle parameters or road environment parameters have a great influence on PID control.
The linear quadratic regulator LQR tracking controller has the principle that in the control time domain, a tracking error model in the whole system is subjected to linearization processing to obtain a linear quadratic model convenient to calculate. And setting an optimal linear quadratic function according to the requirements of the whole system, and carrying out optimal solution on the function in the whole situation to obtain the optimal track control input. LQR is essentially a linear optimization algorithm that does not take into account the effects of vehicle dynamics constraints and external factors of the vehicle environment. Vehicle lateral deflection instability may occur when driving in harsh operating conditions. And the LQR method has high requirement on the precision of the control model, and the parameters and the environment of the automobile in actual running have great uncertainty, so the optimal control cannot be always kept optimal.
The pure tracking control is essentially a proportional controller which converts the lateral deviation of the self position from the expected position at the preview into a lateral control quantity. The method has good robustness, and can achieve good tracking effect even under the conditions of large transverse deviation and discontinuous reference path curvature. The method has the defects that the pre-aiming distance is easily influenced by more parameters (reference path curvature, vehicle speed transverse deviation and the like), and the stability of the vehicle is difficult to guarantee under the condition of ensuring stronger tracking capability.
Disclosure of Invention
Aiming at the defects in the prior art, the intelligent vehicle path tracking method based on the maximum correlation entropy criterion solves the problems of GPS drift and sensor error disturbance in vehicle positioning.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
provided is an intelligent vehicle path tracking method based on a maximum correlation entropy criterion, which comprises the following steps:
s1, constructing a vehicle dynamic model:
wherein the content of the first and second substances,
is the speed in the x direction;
a speed in the y direction;
is the course angular velocity; psi is the heading angle; v is vehicle center of mass velocity; delta is a front wheel declination; l is the length of the wheel base of the vehicle;
s2, converting the vehicle dynamic model into a system state model:
wherein the content of the first and second substances,
derivation with respect to time for all state variables; χ is the system state; u is based on the vehicle mass center velocity v and the front wheel steering angle sigma f The control variable of (d); [.] T Is a transposed symbol;
s3, carrying out discrete linearization processing on the system state model, and constructing an output model forming a prediction time domain:
y＝ψ k ξ(k|k)+Θ k Δu
wherein y is the output of the prediction time domain; psi k A transformation matrix for state prediction and output prediction;
predicting a state quantity of the controller for the model; x (k | k) is the state at time k; u (k-1| k) is the input at time k-1; k is the kth moment of discrete time; theta k A transformation matrix for input and output prediction; Δ u is a predicted input variable at a plurality of times; η (k +1| k) is the prediction output from time k to time k + 1; η (k +2| k) is the prediction output from time k to time k + 2; eta (k + N) p I k) is the prediction time domain N p A corresponding predicted output quantity;
is the relation between input and state quantity recursion;
the state at the moment k is converted into the state at the moment k + 1; i is a unit array; a. the k Is a linear motion model state parameter; b is k Inputting parameters for the linear motion model;
is composed of
N of (A) p The power;
is composed of
N of (A) p -to the power of 1;
is composed of
Is/are as follows Np -N C -to the power of 1; Δ u (k +1| k) is the predicted output increment at time k to time k + 1; Δ u (k +2| k) is the predicted output increment at time k to time k + 2; Δ u (k + N) p | k) is a predicted output increment of k moment to k + Np moment; Δ u (k | k) is the predicted output increment at time k; Δ u (k + N) c -1| k) is the predicted output increment at time k to time k + Nc-1; xi (k + N) p | k) is the prediction time domain N p The corresponding predicted state quantity;
s4, constructing and solving control increment delta u based on maximum correlation entropy criterion and half-square method k The path tracking model of (2):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b
wherein, J HQ (Δu k P) is an objective function; Δ u k ＝[Δu(k|k) T ,Δu(k+1|k) T ,...,Δu(k+N C -1|k) T ] T The predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k) T Transpose of the predicted output increment for time k; Δ u (k +1| k) T Transpose of the predicted output increment for time k to time k + 1; Δ u (k + N) C -1|k) T Transpose of the prediction output increment for time k to time k + Nc-1;
is a dual variable;
a lower bound for all control increments;
controlling the transposition of the lower bound of the increment for each moment;
an upper bound for all control increments;
controlling the transposition of the upper bound of the increment for each moment; a ═ B T ,-B T ] T Is a coefficient matrix; b is 1 ═ 1,1] T A lower triangular matrix of elements;
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o is MCC (Δu k P) is a fitting term measured as MCC;
is a regularization term for all control increments; theta ki Is theta k The ith row of block; i is more than or equal to 1 and less than or equal to N p Is an index set;
the expected error for all predicted moments;
the expected error at the 1 st time;
the expected error at the 2 nd time;
the expected error at the Np th moment; q is a diagonal weighting matrix;
is p i A dual function of (d); p is a radical of i Is the ith dual variable; u. of b Is the upper bound of the linear inequality constraint;
s5, solving the path tracking model to obtain the speed v based on the mass center of the vehicle and the steering angle sigma of the front wheel f Control increment of Δ u k ＝[Δu(k|k) Τ ,...,Δu(k|k+N c -1) Τ ] Τ 。
The beneficial effects of the invention are as follows: according to the scheme, the path tracking control model is established by adopting the measurement of the maximum correlation entropy criterion, the influence from noise or local outliers can be effectively inhibited or eliminated in the path tracking process of the unmanned vehicle through the established path tracking control model, the robustness of the model to the serious deviation and the local outliers disturbance existing in the GPS signal is improved, and the unmanned vehicle is more effective in the path tracking process.
Drawings
FIG. 1 is a flow chart of an intelligent vehicle path tracking method based on maximum correlation entropy criteria.
Fig. 2 is a simplified schematic diagram of a front-wheel steering vehicle kinematics model according to the present solution.
Fig. 3 is a diagram of tracking effect in the simulation process.
FIG. 4 shows the x-direction error in the simulation process.
FIG. 5 shows the y-direction error during the simulation.
FIG. 6 shows the z-direction error during the simulation.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Referring to FIG. 1, FIG. 1 shows a flow chart of an intelligent vehicle path tracking method based on maximum correlation entropy criteria; as shown in fig. 1, the method S includes steps S1 to S5.
In step S1, a vehicle dynamics model is constructed:
wherein the content of the first and second substances,
is the speed in the x direction;
a speed in the y direction;
is the course angular velocity; psi is the heading angle; v is vehicle center of mass velocity; delta is a front wheel declination; l is the length of the wheel base of the vehicle;
the vehicle kinematics model can reflect the relation among the position, the speed and the acceleration of the vehicle, when the model is established, the model is as simple as possible while reflecting the motion characteristic of the vehicle, and the scheme assumes to adopt a bicycle model when establishing the vehicle dynamics model:
assume one: only the motion of the vehicle in the X-Y horizontal plane direction is considered and the motion in the Z-axis direction is ignored;
assume two: the left wheel and the right wheel have the same turning angle when turning, so that the left wheel and the right wheel can be combined into one wheel when modeling;
suppose three: the vehicle speed changes slowly, and the load transfer of the front axle and the rear axle can be ignored;
assume four: the vehicle body and suspension system are rigid.
A simplified front wheel steering vehicle kinematics model is shown in fig. 2, where in fig. 2, O is the instantaneous center of steering of the vehicle, OM and ON are the vertical lines of orientation of the two wheels, respectively, and the following table is a definition of some of the symbols in fig. 2 and in this application:
under the global coordinate system xoy, the vehicle kinematics model can be represented as:
sliding angle
When the vehicle model considers Ackermann steering to indicate that the vehicle is front wheel steering, the sigma is r It can be assumed that 0, the slip angle is also small, and the model can be further simplified:
in step S2, the vehicle dynamics model is converted into a system state model:
wherein the content of the first and second substances,
derivation with respect to time for all state variables;χ is the system state; u is based on the vehicle mass center velocity v and the front wheel steering angle sigma f The control variable of (d); [] T Is a transposed symbol;
in step S3, a discrete linearization process is performed on the system state model to construct an output model forming a prediction time domain:
y＝ψ k ξ(k|k)+Θ k Δu
wherein y is the output of the prediction time domain; psi k A transformation matrix for state prediction and output prediction;
predicting a state quantity of the controller for the model; x (k | k) is the state at time k; u (k-1| k) is the input at time k-1; k is the kth moment of discrete time; theta k A transformation matrix for input and output prediction; Δ u is a predicted input variable at a plurality of times; η (k +1| k) is the prediction output from time k to time k + 1; η (k +2| k) is the prediction output from time k to time k + 2; eta (k + N) p I k) is the prediction time domain N p A corresponding predicted output quantity;
is the relation between input and state quantity recursion;
the state at the moment k is converted into the state at the moment k + 1; i is a unit array; a. the k Is a linear motion model state parameter; b is k Is in linear motionInputting parameters by a model;
is composed of
N of (A) p The power of the wave;
is composed of
N of (2) p -to the power of 1;
is composed of
Is Np -N C -to the power of 1; Δ u (k +1| k) is the predicted output increment at time k to time k + 1; Δ u (k +2| k) is the predicted output increment at time k to time k + 2; Δ u (k + N) p | k) is a predicted output increment of k moment to k + Np moment; Δ u (k | k) is the predicted output increment at time k; Δ u (k + N) c -1| k) is the predicted output increment at time k to time k + Nc-1; xi (k + N) p I k) is the prediction time domain N p The corresponding predicted state quantity;
in one embodiment of the present invention, step S3 further includes:
taylor expansion is carried out on the state model and high-order terms are ignored to obtain:
wherein f is χ 、f u Jacobian matrices for f with respect to χ and u, respectively;
constructing a linear error model of the vehicle according to the Taylor expanded model:
wherein the content of the first and second substances,
a desired velocity in the x-direction;
a desired velocity in the x-direction;
a desired angular velocity; v. of ref A desired speed; delta fref A desired front wheel turning angle;
discretizing the system state model to obtain a linear model:
wherein the content of the first and second substances,
the state at time k is derived with respect to time;
the state at the time k + 1;
the state at the moment k; t is a discretization period;
predicting the state quantity of the controller according to the semantic model, and expressing the linear model as:
wherein eta is observation data;
let the prediction time domain and the control time domain be N respectively p And N c Obtaining a predicted time domain N from the linear model p Corresponding prediction state quantity and prediction time domain N p Corresponding toAnd (3) predicting output quantity:
from the prediction time domain N p Corresponding prediction state quantity and prediction time domain N p And (3) constructing an output model forming a prediction time domain according to the corresponding prediction output quantity:
y＝ψ k ξ(k|k)+Θ k Δu。
in step S4, a solution control increment Δ u is constructed based on the maximum correlation entropy criterion and the half-square method k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b
wherein, J HQ (Δu k P) is an objective function; Δ u k ＝[Δu(k|k) T ,Δu(k+1|k) T ,...,Δu(k+N C -1|k) T ] T The predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k) T Transpose of the predicted output increment for time k; Δ u (k +1| k) T Transpose of the predicted output increment for time k to time k + 1; Δ u (k + N) C -1|k) T Predicted output increment for time k to time k + Nc-1Transposing;
is a dual variable;
a lower bound for all control increments;
controlling the transposition of the lower bound of the increment for each moment;
an upper bound for all control increments;
controlling the transposition of the upper bound of the increment for each moment; a ═ B T ,-B T ] T Is a coefficient matrix; b is 1 ═ 1,1] T A lower triangular matrix of elements;
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o is MCC (Δu k P) is a fitting term measured as MCC;
is a regularization term for all control increments; theta ki Is theta k The ith row of block; i is more than or equal to 1 and less than or equal to N p Is an index set;
the expected error for all predicted moments;
the expected error at the 1 st time;
the expected error at the 2 nd time;
the expected error at the Np th moment; q is a diagonal weighting matrix;
is p i A dual function of (d); p is a radical of i Is the ith dual variable; u. of b Is the upper bound of the linear inequality constraint;
the first item of the path tracking model reflects the tracking capability, the second item reflects the requirement for stable change of the control quantity, and the third item ensures a feasible solution.
The maximum correlation entropy criterion is explained below:
the local similarity of two random variables can be expressed as: v σ (A,B)＝E[k σ (A-B)]Wherein k is σ (.) is a kernel function, E is a mathematical expectation; the scheme adopts a kernel function method to map an input space to a high-dimensional space, and selects a Gaussian kernel function k σ (.) is:
two finite set data
The correlation entropy of (d) can be determined by:
to estimate, for any two vectors of the same dimension, to simplify the calculation and without loss of generality
And
is obtained by making a difference
Wherein e j ＝a j -b j Then e j Has a maximum correlation entropy of
Within a small neighborhood determined by the kernel width σ, the correlation entropy can be regarded as a measure of the similarity of two random variables.
The larger the correlation entropy, the higher the similarity between two variables, when V σ When (a, B) takes the maximum value, the error E between a and B is the minimum, which is the maximum correlation entropy criterion (MCC).
In an embodiment of the present invention, the step S4 further includes:
s41, taking the maximum correlation entropy criterion as distance measurement, and constructing a solving control increment delta u k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b ；
s42, simplifying the path tracking model through a Half-square method (HQ) to obtain a final solving control increment delta u k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b 。
in step S5, the path tracking model is solved based on the vehicle center-of-mass velocity v and the front wheel steering angle σ f Control increment of (Δ u) k ＝[Δu(k|k) Τ ,...,Δu(k|k+N c -1) Τ ] Τ 。
In this embodiment, preferably, the step S5 further includes:
converting a solution path tracking model into an iterative update
And
wherein the content of the first and second substances,
predicting the variable number t +1 iteration for the control increment; p is a radical of t+1 For the t +1 th iteration of the dual variable;
when exp (-x) takes a maximum value at z-exp (-x) and
when determined, the update is iterated
It is solved into
Γ () is the mapping function;
is a dual function; solving an upper bound function; z is a dual variable;
solving by interior point method
According to obtaining
Calculating p t+1 Then iteratively updated
And p t+1 Obtain the control increment delta u k ＝[Δu(k|k) Τ ,...,Δu(k|k+N c -1) Τ ] Τ 。
The following adopts MATLAB simulation experiment to compare the effect of the tracking method of the scheme with the traditional MPC algorithm for explanation:
the simulation is to trace a given reference path, and for convenience, the reference path is taken as a sin curve, and the specific expression is as follows:
reference course angle
Vehicle parameters are shown in the following table:
in order to illustrate the tracking effect of the path tracking method provided by the scheme, the tracking effect of the scheme is compared with the traditional MPC algorithm, and the time domain N is predicted p Take 60 as the control time domain N c And taking the value as 30, setting the simulation time as 20s by adopting the vehicle kinematics model constructed by the scheme, adding a large-offset reference path point to the system in a 5s-7s time period to simulate the influence of the GPS field value of the system on the tracking effect, and showing the tracking result of the sin curve as 3.
In fig. 3, c represents a reference trajectory, b represents a tracking trajectory of the present solution, and a represents a tracking trajectory of the conventional MCC algorithm, it can be seen from fig. 3 that, before the system adds a large offset reference point, the tracking effect difference between the conventional MPC algorithm and the present solution for the sin curve is not obvious, and the tracking effects are both relatively ideal. When a large offset reference point is added into the system, the traditional MCC algorithm is greatly influenced, and has obvious offset on the tracking of the sin curve, and the tracking method of the scheme keeps an ideal tracking effect. Meanwhile, the Gaussian kernel function adopted by the scheme has strong anti-jamming capability.
In order to highlight the performance of the tracking method of the scheme, the tracking method of the scheme is compared with the position error and the heading error of the traditional MPC, wherein the position error comprises errors in the x direction and the y direction. The results are shown in FIGS. 4 to 6.
As can be seen from fig. 4 to 6, in the case of noise, the errors of the tracking method in the x direction, the y direction and the heading angle are significantly smaller than those of the conventional MPC algorithm. Therefore, the simulation result fully proves that the anti-interference capability of the tracking method is obviously superior to that of the traditional MPC algorithm while the tracking precision is ensured.
Claims (5)
1. The intelligent vehicle path tracking method based on the maximum correlation entropy criterion is characterized by comprising the following steps of:
s1, constructing a vehicle dynamic model:
wherein the content of the first and second substances,
is the speed in the x direction;
a speed in the y direction;
the course angular velocity; psi is the heading angle; v is vehicle center of mass velocity; delta is a front wheel declination; l is the length of the wheel base of the vehicle;
s2, converting the vehicle dynamic model into a system state model:
wherein, the first and the second end of the pipe are connected with each other,
derivation with respect to time for all state variables; χ is the system state; u is based on the vehicle mass center velocity v and the front wheel steering angle delta f The control variable of (d); [.] T Is a transposed symbol;
s3, carrying out discrete linearization processing on the system state model, and constructing an output model forming a prediction time domain:
y＝ψ k ξ(k|k)+Θ k Δu
wherein y is the output of the prediction time domain; psi k A transformation matrix for state prediction and output prediction;
u (k-1| k) is the input at time k-1; k isThe kth moment of discrete time; theta k A transformation matrix for input and output prediction; Δ u is a predicted input variable at a plurality of times; η (k +1| k) is the prediction output from time k to time k + 1; η (k +2| k) is the prediction output from time k to time k + 2; eta (k + N) p I k) is the prediction time domain N p A corresponding predicted output quantity;
is the relation between input and state quantity recursion;
Δu(k+N c -1| k) is the predicted output increment at time k to time k + Nc-1; xi (k + N) p I k) is the prediction time domain N p The corresponding predicted state quantity;
s4, constructing and solving control increment delta u based on maximum correlation entropy criterion and half-square method k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b
wherein, J HQ (Δu k P) is an objective function; Δ u k ＝[Δu(k|k) T ,Δu(k+1|k) T ,...,Δu(k+N C -1|k) T ] T The predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k) T Transpose of the predicted output increment for time k; Δ u (k +1| k) T Transpose of the predicted output increment for time k to time k + 1; Δ u (k + N) C -1|k) T Transpose of the predicted output increment for time k to time k + Nc-1;
is a dual variable;
lower bound for all control increments;
controlling the transposition of the lower bound of the increment for each moment;
an upper bound for all control increments;
controlling the transposition of the upper bound of the increment for each moment; a ═ B T ,-B T ] T Is a coefficient matrix; b is 1 ═ 1,1] T A lower triangular matrix of elements;
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o is MCC (Δu k P) is a fitting term measured as MCC;
is a regularization term for all control increments; theta ki Is theta k The ith row of block; i is more than or equal to 1 and less than or equal to N p Is an index set;
the expected error for all predicted moments;
the expected error at the 1 st time;
the expected error at the 2 nd time;
the expected error at the Np th moment; q is a diagonal weighting matrix;
is p i Is dual functionCounting; p is a radical of i Is the ith dual variable; u. of b Is the upper bound of the linear inequality constraint; σ is the kernel width;
s5, solving the path tracking model to obtain the speed v based on the mass center of the vehicle and the steering angle sigma of the front wheel f Control increment of Δ u k ＝[Δu(k|k) Τ ,...,Δu(k|k+N c -1) Τ ] Τ 。
2. The intelligent vehicle path tracking method based on maximum correlation entropy criterion as claimed in claim 1, wherein the step S5 further comprises:
converting a solution path tracking model into an iterative update
And p t+1 ：
Wherein the content of the first and second substances,
predicting the variable number t +1 iteration for the control increment; p is a radical of formula t+1 For the t +1 th iteration of the dual variable;
when exp (-x) gets the maximum value at z ═ exp (-x) and
when determined, the update is iterated
It is solved into
Γ () is the mapping function;
solving by interior point method
According to obtaining
Calculating p t+1 Then iteratively updated
And p t+1 Obtain the control increment delta u k ＝[Δu(k|k) Τ ,...,Δu(k|k+N c -1) Τ ] Τ 。
3. The intelligent vehicle path tracking method based on maximum correlation entropy criterion as claimed in claim 1, wherein the step S4 further comprises:
s41, taking the maximum correlation entropy criterion as distance measurement, and constructing a solving control increment delta u k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b ；
s42, simplifying the path tracking model through a half-square method to obtain a final solving control increment delta u k The path tracking model of (1):
s.t.Δu min ≤Δu k ≤Δu max
AΔu k ≤u b 。
4. the intelligent vehicle path tracking method based on the maximum correlation entropy criterion as claimed in claim 3, wherein the Gaussian kernel function g (x, σ) adopted in the process of constructing the path tracking model in the step S41 is as follows:
wherein exp (. lamda.) is a natural exponential function.
5. The intelligent vehicle path tracking method based on maximum correlation entropy criterion as claimed in claim 1, wherein the step S3 further comprises:
taylor expansion is carried out on the state model and high-order terms are ignored to obtain:
wherein f is χ 、f u Jacobian matrices for f with respect to χ and u, respectively;
according to the Taylor expanded model, constructing a linear error model of the vehicle:
wherein the content of the first and second substances,
a desired velocity in the x-direction;
a desired velocity in the x-direction;
a desired angular velocity; v. of ref A desired speed;
a desired front wheel turning angle;
discretizing the system state model to obtain a linear model:
wherein the content of the first and second substances,
deriving time for the state at time k;
the state at the time k + 1;
the state at the moment k; t is a discretization period;
from the state quantities of the model predictive controller, the linear model is represented as:
wherein eta is observation data;
let the prediction time domain and the control time domain be N respectively p And N c Obtaining a predicted time domain N from the linear model p Corresponding prediction state quantity and prediction time domain N p The corresponding predicted output:
from the prediction time domain N p Corresponding prediction state quantity and prediction time domain N p And (3) constructing an output model forming a prediction time domain according to the prediction output quantity:
y＝ψ k ξ(k|k)+Θ k Δu。
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