CN111258218A - Intelligent vehicle path tracking method based on maximum correlation entropy criterion - Google Patents

Intelligent vehicle path tracking method based on maximum correlation entropy criterion Download PDF

Info

Publication number
CN111258218A
CN111258218A CN202010050982.0A CN202010050982A CN111258218A CN 111258218 A CN111258218 A CN 111258218A CN 202010050982 A CN202010050982 A CN 202010050982A CN 111258218 A CN111258218 A CN 111258218A
Authority
CN
China
Prior art keywords
time
model
prediction
path tracking
increment
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202010050982.0A
Other languages
Chinese (zh)
Other versions
CN111258218B (en
Inventor
周楠
杜元花
秦豪
郭超
蒋涛
李平
蒲红平
付克昌
刘甲甲
袁建英
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chengdu University of Information Technology
Original Assignee
Chengdu University of Information Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chengdu University of Information Technology filed Critical Chengdu University of Information Technology
Priority to CN202010050982.0A priority Critical patent/CN111258218B/en
Publication of CN111258218A publication Critical patent/CN111258218A/en
Application granted granted Critical
Publication of CN111258218B publication Critical patent/CN111258218B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Steering Control In Accordance With Driving Conditions (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses an intelligent vehicle path tracking method based on a maximum correlation entropy criterion, 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 methodkThe 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 wheelfControl increments of (c). The method adopts the measurement of the maximum correlation entropy criterion to establish the path tracking model, and the model can effectively inhibit or eliminate the influence from noise or local outliers to realize the stable path tracking of the vehicle.

Description

Intelligent vehicle path tracking method based on maximum correlation entropy criterion
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:
Figure BDA0002371176800000021
wherein the content of the first and second substances,
Figure BDA0002371176800000022
is the speed in the x direction;
Figure BDA0002371176800000023
a speed in the y direction;
Figure BDA0002371176800000024
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:
Figure BDA0002371176800000025
wherein the content of the first and second substances,
Figure BDA0002371176800000026
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 sigmafThe control variable of (d); [.]TIs a transposed symbol;
s3, carrying out discrete linearization processing on the system state model, and constructing an output model forming a prediction time domain:
Figure BDA0002371176800000027
Figure BDA0002371176800000028
y＝ψkξ(k|k)+ΘkΔu
Figure BDA0002371176800000031
wherein y is the output of the prediction time domain; psikA transformation matrix for state prediction and output prediction;
Figure BDA0002371176800000032
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; thetakA transformation matrix for input and output prediction, Δ u is a prediction input variable at a plurality of time instants, η (k +1| k) is a prediction output from time k to time k +1, η (k +2| k) is a prediction output from time k to time k +2, η (k + N)pI k) is the prediction time domain NpA corresponding predicted output quantity;
Figure BDA0002371176800000033
is the relation between input and state quantity recursion;
Figure BDA0002371176800000034
is the state at time k andchanging the state at the moment k + 1; i is a unit array; a. thekIs a linear motion model state parameter; b iskInputting parameters for the linear motion model;
Figure BDA0002371176800000035
is composed of
Figure BDA0002371176800000036
N of (A)pThe power;
Figure BDA0002371176800000037
is composed of
Figure BDA0002371176800000038
N of (A)p-to the power of 1;
Figure BDA0002371176800000039
is composed of
Figure BDA00023711768000000310
Is/are as followsNp-NC-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 for time k to time k + Nc-1, ξ (k + N)pI k) is the prediction time domain NpThe corresponding predicted state quantity;
s4, constructing and solving control increment delta u based on maximum correlation entropy criterion and half-square methodkThe path tracking model of (1):
Figure BDA00023711768000000311
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub
Figure BDA0002371176800000041
Figure BDA0002371176800000042
wherein, JHQ(ΔukP) is an objective function; Δ uk＝[Δu(k|k)T,Δu(k+1|k)T,...,Δu(k+NC-1|k)T]TThe predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k)TTranspose of the predicted output increment for time k; Δ u (k +1| k)TTranspose of the predicted output increment for time k to time k + 1; Δ u (k + N)C-1|k)TTranspose of the prediction output increment for time k to time k + Nc-1;
Figure BDA0002371176800000043
is a dual variable;
Figure BDA0002371176800000044
a lower bound for all control increments;
Figure BDA0002371176800000045
controlling the transposition of the lower bound of the increment for each moment;
Figure BDA0002371176800000046
an upper bound for all control increments;
Figure BDA0002371176800000047
controlling the transposition of the upper bound of the increment for each moment; a ═ BT,-BT]TIs a coefficient matrix; b is 1 ═ 1,1]TA lower triangular matrix of elements;
Figure BDA0002371176800000048
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o isMCC(ΔukP) is a fitting term measured as MCC;
Figure BDA0002371176800000049
is a regularization term for all control increments；ΘkiIs thetakThe ith row of block; i is more than or equal to 1 and less than or equal to NpIs an index set;
Figure BDA00023711768000000410
the expected error for all predicted moments;
Figure BDA00023711768000000411
the expected error at the 1 st time;
Figure BDA00023711768000000412
the expected error at the 2 nd time;
Figure BDA00023711768000000413
the expected error at the Np th moment; q is a diagonal weighting matrix;
Figure BDA00023711768000000414
is piA dual function of (d); p is a radical ofiIs the ith dual variable; u. ofbIs 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 wheelfControl increment of Δ uk＝[Δu(k|k)Τ,...,Δu(k|k+Nc-1)Τ]Τ。
The invention has the beneficial effects that: 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:
Figure BDA0002371176800000051
wherein the content of the first and second substances,
Figure BDA0002371176800000052
is the speed in the x direction;
Figure BDA0002371176800000053
a speed in the y direction;
Figure BDA0002371176800000054
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:
Figure BDA0002371176800000061
under the global coordinate system xoy, the vehicle kinematics model can be represented as:
Figure BDA0002371176800000062
Figure BDA0002371176800000063
Figure BDA0002371176800000064
sliding angle
Figure BDA0002371176800000065
When the vehicle model considers Ackermann steering to indicate that the vehicle is front wheel steering, the sigma isrIt can be assumed that 0, the slip angle is also small, and the model can be further simplified:
Figure BDA0002371176800000071
in step S2, the vehicle dynamics model is converted into a system state model:
Figure BDA0002371176800000072
wherein the content of the first and second substances,
Figure BDA0002371176800000073
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 sigmafThe control variable of (d); []TIs a transposed symbol;
in step S3, the system state model is subjected to discrete linearization processing to construct an output model forming a prediction time domain:
Figure BDA0002371176800000074
Figure BDA0002371176800000075
y＝ψkξ(k|k)+ΘkΔu
Figure BDA0002371176800000076
wherein y is the output of the prediction time domain; psikA transformation matrix for state prediction and output prediction;
Figure BDA0002371176800000077
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; thetakA transformation matrix for input and output prediction, Δ u is a prediction input variable at a plurality of time instants, η (k +1| k) is a prediction output from time k to time k +1, η (k +2| k) is a prediction output from time k to time k +2, η (k + N)pI k) is the prediction time domain NpA corresponding predicted output quantity;
Figure BDA0002371176800000078
is the relation between input and state quantity recursion;
Figure BDA0002371176800000079
the state at the moment k is converted into the state at the moment k + 1; i is a unit array; a. thekIs a linear motion model state parameter; b iskInputting parameters for the linear motion model;
Figure BDA0002371176800000081
is composed of
Figure BDA0002371176800000082
N of (A)pThe power;
Figure BDA0002371176800000083
is composed of
Figure BDA0002371176800000084
N of (A)p-to the power of 1;
Figure BDA0002371176800000085
is composed of
Figure BDA0002371176800000086
Is/are as followsNp-NC-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 for time k to time k + Nc-1, ξ (k + N)pI k) is the prediction time domain NpThe 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:
Figure BDA0002371176800000087
wherein f isχ、fuJacobian matrices for f with respect to χ and u, respectively;
according to the Taylor expanded model, constructing a linear error model of the vehicle:
Figure BDA0002371176800000088
wherein the content of the first and second substances,
Figure BDA0002371176800000089
a desired velocity in the x-direction;
Figure BDA00023711768000000810
a desired velocity in the x-direction;
Figure BDA00023711768000000811
a desired angular velocity; v. ofrefA desired speed; deltafrefA desired front wheel turning angle;
discretizing the system state model to obtain a linear model:
Figure BDA00023711768000000812
wherein the content of the first and second substances,
Figure BDA00023711768000000813
deriving time for the state at time k;
Figure BDA00023711768000000814
the state at the time k + 1;
Figure BDA00023711768000000815
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:
Figure BDA0002371176800000091
wherein η is observed data;
let the prediction time domain and the control time domain be N respectivelypAnd NcObtaining a predicted time domain N from the linear modelpCorresponding prediction state quantity and prediction time domain NpThe corresponding predicted output:
Figure BDA0002371176800000092
Figure BDA0002371176800000093
from the prediction time domain NpCorresponding prediction state quantity and prediction time domain NpAnd (3) constructing an output model forming a prediction time domain according to the corresponding prediction output quantity:
y＝ψkξ(k|k)+ΘkΔu。
in step S4, a solution control increment Δ u is constructed based on the maximum correlation entropy criterion and the half-square methodkThe path tracking model of (1):
Figure BDA0002371176800000094
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub
Figure BDA0002371176800000095
Figure BDA0002371176800000096
wherein, JHQ(ΔukP) is an objective function; Δ uk＝[Δu(k|k)T,Δu(k+1|k)T,...,Δu(k+NC-1|k)T]TThe predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k)TOutputting increments for prediction of time kTransposing; Δ u (k +1| k)TTranspose of the predicted output increment for time k to time k + 1; Δ u (k + N)C-1|k)TTranspose of the prediction output increment for time k to time k + Nc-1;
Figure BDA0002371176800000097
is a dual variable;
Figure BDA0002371176800000098
a lower bound for all control increments;
Figure BDA0002371176800000099
controlling the transposition of the lower bound of the increment for each moment;
Figure BDA0002371176800000101
an upper bound for all control increments;
Figure BDA0002371176800000102
controlling the transposition of the upper bound of the increment for each moment; a ═ BT,-BT]TIs a coefficient matrix; b is 1 ═ 1,1]TA lower triangular matrix of elements;
Figure BDA0002371176800000103
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o isMCC(ΔukP) is a fitting term measured as MCC;
Figure BDA0002371176800000104
is a regularization term for all control increments; thetakiIs thetakThe ith row of block; i is more than or equal to 1 and less than or equal to NpIs an index set;
Figure BDA0002371176800000105
the expected error for all predicted moments;
Figure BDA0002371176800000106
the expected error at the 1 st time;
Figure BDA0002371176800000107
the expected error at the 2 nd time;
Figure BDA0002371176800000108
the expected error at the Np th moment; q is a diagonal weighting matrix;
Figure BDA0002371176800000109
is piA dual function of (d); p is a radical ofiIs the ith dual variable; u. ofbIs 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: vσ(A,B)＝E[kσ(A-B)]Wherein k isσ(.) 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 kσ(.) is:
Figure BDA00023711768000001010
two finite set data
Figure BDA00023711768000001011
The correlation entropy of (d) can be determined by:
Figure BDA00023711768000001012
to estimate, for any two vectors of the same dimension, to simplify the calculation and without loss of generality
Figure BDA00023711768000001013
And
Figure BDA00023711768000001014
is obtained by making a difference
Figure BDA00023711768000001015
Wherein ej＝aj-bjThen ejHas a maximum correlation entropy of
Figure BDA00023711768000001016
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 the two variables, when VσWhen (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 ukThe path tracking model of (1):
Figure BDA0002371176800000111
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub；
s42, simplifying the path tracking model through a Half-square method (HQ) to obtain a final solving control increment delta ukThe path tracking model of (1):
Figure BDA0002371176800000112
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub。
in step S5, the path tracking model is solved based on the vehicle center-of-mass velocity v and the front wheel steering angle σfControl increment of Δ uk＝[Δu(k|k)Τ,...,Δu(k|k+Nc-1)Τ]Τ。
In this embodiment, preferably, the step S5 further includes:
converting a solution path tracking model into an iterative update
Figure BDA0002371176800000113
And
Figure BDA0002371176800000114
Figure BDA0002371176800000115
Figure BDA0002371176800000116
wherein the content of the first and second substances,
Figure BDA0002371176800000117
predicting the variable number t +1 iteration for the control increment; p is a radical oft+1For the t +1 th iteration of the dual variable;
when exp (-x) takes a maximum value at z-exp (-x) and
Figure BDA0002371176800000121
when determined, the update is iterated
Figure BDA0002371176800000122
It is solved into
Figure BDA0002371176800000123
Γ () is the mapping function;
Figure BDA0002371176800000124
is a dual function; solving an upper bound function; z is a dual variable;
solving by interior point method
Figure BDA0002371176800000125
According to obtaining
Figure BDA0002371176800000126
Calculating pt+1Then iteratively updated
Figure BDA0002371176800000127
And pt+1Obtain the control increment delta uk＝[Δu(k|k)Τ,...,Δu(k|k+Nc-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:
Figure BDA0002371176800000128
reference course angle
Figure BDA0002371176800000129
Vehicle parameters are shown in the following table:
Figure BDA00023711768000001210
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 predictedpTake 60 as the control time domain NcAnd 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:
Figure FDA0002371176790000011
wherein the content of the first and second substances,
Figure FDA0002371176790000012
is the speed in the x direction;
Figure FDA0002371176790000013
a speed in the y direction;
Figure FDA0002371176790000014
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:
Figure FDA0002371176790000015
χ＝[x y ψ]T，u＝[v σf]T
wherein the content of the first and second substances,
Figure FDA0002371176790000016
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 sigmafThe control variable of (d); [.]TIs a transposed symbol;
s3, carrying out discrete linearization processing on the system state model, and constructing an output model forming a prediction time domain:
Figure FDA0002371176790000017
Figure FDA0002371176790000018
y＝ψkξ(k|k)+ΘkΔu
Figure FDA0002371176790000019
wherein y is the output of the prediction time domain; psikA transformation matrix for state prediction and output prediction;
Figure FDA00023711767900000110
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; thetakA transformation matrix for input and output prediction, Δ u is a prediction input variable at a plurality of time instants, η (k +1| k) is a prediction output from time k to time k +1, η (k +2| k) is a prediction output from time k to time k +2, η (k + N)pI k) is the prediction time domain NpA corresponding predicted output quantity;
Figure FDA0002371176790000021
is the relation between input and state quantity recursion;
Figure FDA0002371176790000022
the state at the moment k is converted into the state at the moment k + 1; i is a unit array; a. thekIs a linear motion model state parameter; b iskInputting parameters for the linear motion model;
Figure FDA0002371176790000023
is composed of
Figure FDA0002371176790000024
N of (A)pThe power;
Figure FDA0002371176790000025
is composed of
Figure FDA0002371176790000026
N of (A)p-to the power of 1;
Figure FDA0002371176790000027
is composed of
Figure FDA0002371176790000028
N of (A)p-NC-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 for time k to time k + Nc-1, ξ (k + N)pI k) is the prediction time domain NpThe corresponding predicted state quantity;
s4, constructing and solving control increment delta u based on maximum correlation entropy criterion and half-square methodkThe path tracking model of (1):
Figure FDA0002371176790000029
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub
Figure FDA00023711767900000210
Figure FDA00023711767900000211
wherein, JHQ(ΔukP) is an objective function; Δ uk＝[Δu(k|k)T,Δu(k+1|k)T,...,Δu(k+NC-1|k)T]TThe predicted output increment for k pairs subsequent up to time Nc-1; delta u (k | k)TTranspose of the predicted output increment for time k; Δ u (k +1| k)TTranspose of the predicted output increment for time k to time k + 1; Δ u (k + N)C-1|k)TTranspose of the prediction output increment for time k to time k + Nc-1;
Figure FDA0002371176790000031
is a dual variable;
Figure FDA0002371176790000032
a lower bound for all control increments;
Figure FDA0002371176790000033
controlling the transposition of the lower bound of the increment for each moment;
Figure FDA0002371176790000034
an upper bound for all control increments;
Figure FDA0002371176790000035
controlling the transposition of the upper bound of the increment for each moment; a ═ BT,-BT]TIs a coefficient matrix; b is 1 ═ 1,1]TA lower triangular matrix of elements;
Figure FDA0002371176790000036
a block diagonal matrix of diagonal elements in R; r is a weighted diagonal matrix; o isMCC(ΔukP) is a fitting term measured as MCC;
Figure FDA0002371176790000037
is a regularization term for all control increments; thetakiIs thetakThe ith row of block; i is more than or equal to 1 and less than or equal to NpIs an index set;
Figure FDA0002371176790000038
the expected error for all predicted moments;
Figure FDA0002371176790000039
the expected error at the 1 st time;
Figure FDA00023711767900000310
the expected error at the 2 nd time;
Figure FDA00023711767900000311
the expected error at the Np th moment; q is a diagonal weighting matrix;
Figure FDA00023711767900000312
is piA dual function of (d); p is a radical ofiIs the ith dual variable; u. ofbIs 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 wheelfControl increment of Δ uk＝[Δu(k|k)T，...，Δu(k|k+Nc-1)T]T。
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
Figure FDA00023711767900000314
And pk+1：
Figure FDA00023711767900000315
Figure FDA00023711767900000316
Wherein the content of the first and second substances,
Figure FDA00023711767900000317
predicting the variable number t +1 iteration for the control increment; p is a radical oft+1For the t +1 th iteration of the dual variable;
when exp (-x) takes a maximum value at z-exp (-x) and
Figure FDA00023711767900000318
when determined, the update is iterated
Figure FDA00023711767900000319
It is solved into
Figure FDA00023711767900000320
Γ () is the mapping function;
Figure FDA00023711767900000321
is a dual function; solving an upper bound function; z is a dual variable;
solving by interior point method
Figure FDA0002371176790000041
According to obtaining
Figure FDA0002371176790000042
Calculating pt+1Then iteratively updated
Figure FDA0002371176790000043
And pt+1Obtain the control increment delta uk＝[Δu(k|k)Τ,...,Δu(k|k+Nc-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 ukThe path tracking model of (1):
Figure FDA0002371176790000044
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub；
s42, simplifying the path tracking model through a half-square method to obtain a final solving control increment delta ukThe path tracking model of (1):
Figure FDA0002371176790000045
s.t.Δumin≤Δuk≤Δumax
AΔuk≤ub。
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:
Figure FDA0002371176790000046
wherein σ is the kernel width; exp (.) 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:
Figure FDA0002371176790000051
wherein f isχ、fuJacobian matrices for f with respect to χ and u, respectively;
according to the Taylor expanded model, constructing a linear error model of the vehicle:
Figure FDA0002371176790000052
wherein the content of the first and second substances,
Figure FDA0002371176790000053
a desired velocity in the x-direction;
Figure FDA0002371176790000054
a desired velocity in the x-direction;
Figure FDA0002371176790000055
a desired angular velocity; v. ofrefA desired speed;
Figure FDA0002371176790000056
a desired front wheel turning angle;
discretizing the system state model to obtain a linear model:
Figure FDA0002371176790000057
wherein the content of the first and second substances,
Figure FDA0002371176790000058
deriving time for the state at time k;
Figure FDA0002371176790000059
the state at the time k + 1;
Figure FDA00023711767900000510
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:
Figure FDA00023711767900000511
wherein η is observed data;
let the prediction time domain and the control time domain be N respectivelypAnd NcObtaining a predicted time domain N from the linear modelpCorresponding prediction state quantity and prediction time domain NpThe corresponding predicted output:
Figure FDA00023711767900000512
Figure FDA0002371176790000061
from the prediction time domain NpCorresponding prediction state quantity and prediction time domain NpAnd (3) constructing an output model forming a prediction time domain according to the corresponding prediction output quantity:
y＝ψkξ(k|k)+ΘkΔu。
CN202010050982.0A 2020-01-17 2020-01-17 Intelligent vehicle path tracking method based on maximum correlation entropy criterion Active CN111258218B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010050982.0A CN111258218B (en) 2020-01-17 2020-01-17 Intelligent vehicle path tracking method based on maximum correlation entropy criterion

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010050982.0A CN111258218B (en) 2020-01-17 2020-01-17 Intelligent vehicle path tracking method based on maximum correlation entropy criterion

Publications (2)

Publication Number Publication Date
CN111258218A true CN111258218A (en) 2020-06-09
CN111258218B CN111258218B (en) 2022-08-12

Family

ID=70945246

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010050982.0A Active CN111258218B (en) 2020-01-17 2020-01-17 Intelligent vehicle path tracking method based on maximum correlation entropy criterion

Country Status (1)

Country Link
CN (1) CN111258218B (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112764347A (en) * 2021-01-07 2021-05-07 成都信息工程大学 Intelligent vehicle path tracking method based on maximum correlation entropy criterion
CN112949230A (en) * 2021-02-26 2021-06-11 山东英信计算机技术有限公司 Nonlinear circuit macro model extraction method, system and medium
CN113110500A (en) * 2021-05-10 2021-07-13 的卢技术有限公司 Transverse control method for low-speed automatic parking of automatic-driving automobile
CN113985868A (en) * 2021-10-09 2022-01-28 北京科技大学 Method for realizing hierarchical path tracking control of wheeled mobile robot
CN115087092A (en) * 2022-05-25 2022-09-20 电子科技大学 Multi-sensor maximum correlation entropy expansion information filtering layered fusion method

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109764886A (en) * 2019-01-15 2019-05-17 成都信息工程大学 A kind of paths planning method
CN109884900A (en) * 2019-04-03 2019-06-14 东南大学 The design method of cropper path following control device based on adaptive model PREDICTIVE CONTROL
CN110209177A (en) * 2019-07-02 2019-09-06 天津大学 Pilotless automobile control system and method based on model prediction and active disturbance rejection
CN110262229A (en) * 2019-05-27 2019-09-20 东南大学 Vehicle Adaptive Path method for tracing based on MPC
CN110619340A (en) * 2018-06-19 2019-12-27 广州汽车集团股份有限公司 Method for generating lane change rule of automatic driving automobile

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105737828B (en) * 2016-05-09 2018-07-31 郑州航空工业管理学院 A kind of Combinated navigation method of the joint entropy Extended Kalman filter based on strong tracking
CN109001789B (en) * 2018-06-05 2020-05-22 西安交通大学 Unmanned vehicle positioning fusion method based on cross-correlation entropy registration
CN108562290B (en) * 2018-07-13 2020-10-27 深圳市戴升智能科技有限公司 Navigation data filtering method and device, computer equipment and storage medium

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110619340A (en) * 2018-06-19 2019-12-27 广州汽车集团股份有限公司 Method for generating lane change rule of automatic driving automobile
CN109764886A (en) * 2019-01-15 2019-05-17 成都信息工程大学 A kind of paths planning method
CN109884900A (en) * 2019-04-03 2019-06-14 东南大学 The design method of cropper path following control device based on adaptive model PREDICTIVE CONTROL
CN110262229A (en) * 2019-05-27 2019-09-20 东南大学 Vehicle Adaptive Path method for tracing based on MPC
CN110209177A (en) * 2019-07-02 2019-09-06 天津大学 Pilotless automobile control system and method based on model prediction and active disturbance rejection

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
周楠: "基于稀疏和信息论的无监督特征学习算法研究", 《中国优秀博硕士学位论文全文数据库(博士) 信息科技辑》 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112764347A (en) * 2021-01-07 2021-05-07 成都信息工程大学 Intelligent vehicle path tracking method based on maximum correlation entropy criterion
CN112764347B (en) * 2021-01-07 2023-08-22 成都信息工程大学 Intelligent vehicle path tracking method based on maximum correlation entropy criterion
CN112949230A (en) * 2021-02-26 2021-06-11 山东英信计算机技术有限公司 Nonlinear circuit macro model extraction method, system and medium
CN112949230B (en) * 2021-02-26 2023-05-23 山东英信计算机技术有限公司 Nonlinear circuit macro model extraction method, system and medium
CN113110500A (en) * 2021-05-10 2021-07-13 的卢技术有限公司 Transverse control method for low-speed automatic parking of automatic-driving automobile
CN113985868A (en) * 2021-10-09 2022-01-28 北京科技大学 Method for realizing hierarchical path tracking control of wheeled mobile robot
CN113985868B (en) * 2021-10-09 2023-08-08 北京科技大学 Layered path tracking control implementation method for wheeled mobile robot
CN115087092A (en) * 2022-05-25 2022-09-20 电子科技大学 Multi-sensor maximum correlation entropy expansion information filtering layered fusion method
CN115087092B (en) * 2022-05-25 2024-02-27 电子科技大学 Multi-sensor maximum relevant entropy expansion information filtering hierarchical fusion method

Also Published As

Publication number Publication date
CN111258218B (en) 2022-08-12

Similar Documents

Publication Publication Date Title
CN111258218B (en) Intelligent vehicle path tracking method based on maximum correlation entropy criterion
Tang et al. An improved kinematic model predictive control for high-speed path tracking of autonomous vehicles
CN109885883B (en) Unmanned vehicle transverse motion control method based on GK clustering algorithm model prediction
CN107415939B (en) Steering stability control method for distributed driving electric automobile
CN113110511B (en) Intelligent ship course control method based on generalized fuzzy hyperbolic model
Jiang et al. Model free predictive path tracking control of variable-configuration unmanned ground vehicle
CN113183957A (en) Vehicle control method, device and equipment and automatic driving vehicle
CN111813110A (en) Method for controlling snake-shaped robot to follow path to active disturbance rejection
CN111679575A (en) Intelligent automobile trajectory tracking controller based on robust model predictive control and construction method thereof
Chu et al. Observer-based gain scheduling path following control for autonomous electric vehicles subject to time delay
Zhang et al. Variable gain based composite trajectory tracking control for 4-wheel skid-steering mobile robots with unknown disturbances
Herlambang et al. Design of Navigation and Guidance Control System of Mobile Robot with Position Estimation Using Ensemble Kalman Filter (EnKF) and Square Root Ensemble Kalman Filter (SR-EnKF)
Mi et al. Integration of Motion Planning and Control for High-Performance Automated Vehicles Using Tube-based Nonlinear MPC
Yuan et al. Differential flatness-based adaptive robust tracking control for wheeled mobile robots with slippage disturbances
Weber et al. Modeling and Control for Dynamic Drifting Trajectories
CN112363538B (en) AUV (autonomous underwater vehicle) area tracking control method under incomplete speed information
CN115373287A (en) Adaptive parameter model prediction path tracking control method for articulated tractor
Chen et al. Path tracking controller design of automated parking systems via NMPC with an instructible solution
Wang et al. Path Tracking Method Based on Model Predictive Control and Genetic Algorithm for Autonomous Vehicle
Ran et al. Trajectory Tracking of Swing‐Arm Type Omnidirectional Mobile Robot
Yu et al. DGPR‐MPC: Learning‐based model predictive controller for autonomous vehicle path following
Ji et al. Optimal Path Tracking Control Based on Online Modeling for Autonomous Vehicle With Completely Unknown Parameters
Jiang et al. Approximated Long Horizon MPC with Hindsight for Autonomous Vehicles Path Tracking
Shen et al. Stability Analysis and Control Validation of DDEV in Handling Limit via SOSP: A Strategy Based on Stability Region
CN112764347B (en) Intelligent vehicle path tracking method based on maximum correlation entropy criterion

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant