CN110262229B - Vehicle self-adaptive path tracking method based on MPC - Google Patents

Vehicle self-adaptive path tracking method based on MPC Download PDF

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CN110262229B
CN110262229B CN201910445420.3A CN201910445420A CN110262229B CN 110262229 B CN110262229 B CN 110262229B CN 201910445420 A CN201910445420 A CN 201910445420A CN 110262229 B CN110262229 B CN 110262229B
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王立辉
石佳晨
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Southeast University
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Abstract

The invention discloses a vehicle self-adaptive path tracking method based on MPC, comprising the following steps: 1. establishing a kinematic model of the vehicle, and predicting an equivalent sideslip angle; 2. designing a vehicle model predictive controller based on the established vehicle kinematics model; 3. and acquiring the state of the vehicle at the current moment, and correcting the parameters of the vehicle model predictive controller at the current moment through fuzzy control. 4. Solving an objective function of the vehicle model predictive controller to obtain a first variable of an optimal solution as an increment of a control quantity at the current moment; 5. and controlling the steering angle of the tire according to the increment of the control quantity and the equivalent sideslip angle, controlling the vehicle to run, and calculating the increment of the control quantity in the next control period in the steering step 2. The method improves the stability and accuracy of path tracking when the vehicle generates slip.

Description

Vehicle self-adaptive path tracking method based on MPC
Technical Field
The invention belongs to the field of automatic driving control of vehicles, and particularly relates to a vehicle path tracking method.
Background
At present, two types of methods are mainly adopted for tracking the automatic driving path of the vehicle: a method based on geometric tracking and a method based on MPC (Model Predictive Control). Geometric tracking based methods, such as pure tracking algorithms, require the creation of accurate kinematic models, which are very limited in application. The MPC path tracking method based on kinematics does not depend on an extremely accurate model, and adopts a rolling optimization method to obtain more and more favor of more and more applications in a mode of replacing a global optimal solution with a local optimal solution.
In the MPC path tracking method based on the kinematic model, when the vehicle generates slip, no parameter in the kinematic model generates corresponding anti-interference measures to the vehicle, thereby reducing the stability and precision of path tracking.
Disclosure of Invention
The purpose of the invention is as follows: in view of the problems in the prior art, the invention provides an MPC-based vehicle adaptive path tracking method, which improves the stability and accuracy of path tracking when a vehicle generates slip.
The technical scheme is as follows: the invention adopts the following technical scheme:
the vehicle self-adaptive path tracking method based on the MPC comprises the following steps:
step 1, establishing a kinematic model of a vehicle, and predicting an equivalent sideslip angle, comprising the following steps:
(11) the coordinates of the vehicle have the following relationship with the heading angle and the tire steering angle:
Figure GDA0003512298840000011
wherein X and Y are the coordinates of the vehicle in the X and Y axes, θhIs the vehicle heading angle, /)wbIs the wheelbase of the front and rear axles of the vehicle, v is the running speed of the vehicle, thetawsIs the tire steering angle;
Figure GDA0003512298840000012
the speed of the vehicle in the X-axis and Y-axis respectively,
Figure GDA0003512298840000013
is the steering angular velocity of the vehicle;
(12) by X ═ X y thetah]TIs a vehicle state quantity, u ═ θws]TFor the control quantities, a general kinematic model of the vehicle is constructed:
Figure GDA0003512298840000014
wherein the content of the first and second substances,
Figure GDA0003512298840000021
the general form of the kinematic model at the current reference point r on the reference trajectory is:
Figure GDA0003512298840000022
(13) linearizing and discretizing a general vehicle kinematic model:
expanding (2) at the reference point by using Taylor series, and neglecting high-order terms, then:
Figure GDA0003512298840000023
subtracting equation (3) from equation (4) yields:
Figure GDA0003512298840000024
xr、yr、θhrthe coordinates, the course angle theta and the X axis and the Y axis of the vehicle at the current reference point r are respectivelywsrIs the tire steering angle at the current reference point r;
discretizing the formula (5), wherein the discretized general form is as follows:
Figure GDA0003512298840000025
wherein the content of the first and second substances,
Figure GDA0003512298840000026
t is the sampling period, Ak,tAnd Bk,tRespectively predicting a state coefficient matrix and a control coefficient matrix of the state at the moment k according to the current moment t;
(14) judging whether slippage occurs;
according to the actual state quantity at the moment of k-1
Figure GDA0003512298840000027
And (6) calculating the theoretical value of the state quantity at the time k
Figure GDA0003512298840000028
Let k be the actual state quantity at time
Figure GDA0003512298840000029
The threshold value is
Figure GDA00035122988400000210
If it is
Figure GDA00035122988400000211
Judging that slippage occurs, and entering the step (15) to calculate an equivalent sideslip angle; otherwise, skipping the step (15), and enabling the equivalent sideslip angle to be 0;
(15) if slip occurs, calculating the equivalent sideslip angle
Figure GDA00035122988400000212
Figure GDA0003512298840000031
Wherein
Figure GDA0003512298840000032
Is the side slip angle of the front wheel,
Figure GDA0003512298840000039
is a rear wheel side slip angle;
step 2: designing a vehicle model predictive controller based on the established vehicle kinematics model, comprising the steps of:
(21) state quantity ξ (k | t) for predicting k time from current time t is defined:
Figure GDA0003512298840000033
wherein the content of the first and second substances,
Figure GDA0003512298840000034
x (k | t) is a vehicle state quantity at the moment k according to the current moment t, and u (k-1| t) is a control quantity at the moment k-1 according to the current moment t;
the state space expression for the vehicle is then:
Figure GDA0003512298840000035
wherein the content of the first and second substances,
Figure GDA0003512298840000036
Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
Figure GDA0003512298840000037
suppose that:
Figure GDA0003512298840000038
wherein A ist,tAnd Bt,tRespectively a state coefficient matrix and a control coefficient matrix of the current moment t;
(22) calculating a predicted output expression of the system, the predicted output expression of the system being:
Y(t)＝Ψtξ(t|t)+ΘtΔU(t) (13)
wherein the content of the first and second substances,
Figure GDA0003512298840000041
ξ (t | t) is the state quantity at the current time t,
Figure GDA0003512298840000042
Ncfor controlling the time-domain range parameter, NpIs a predicted time domain range parameter;
(23) the objective function of the system is:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t)T,ε]THt[ΔU(t)T,ε]+Gt[ΔU(t)T,ε] (15)
the constraint conditions are as follows:
Figure GDA0003512298840000043
wherein the content of the first and second substances,
Figure GDA0003512298840000044
et＝X(t)-Xru (t-1) is the control quantity at the moment t-1, and delta U (t) is a matrix formed by the variation quantity of the control quantity at the moment t; r, Q is a weight matrix, rho is a weight coefficient, and epsilon is a relaxation factor; u shapemin、UmaxRespectively, a set of minimum and maximum values of the control quantity in the control time domain, Delta Umin、ΔUmaxRespectively a set of the minimum value and the maximum value of the control quantity variation in the control time domain; u (t) is a matrix composed of control quantities at time t, A is Nc×NcThe lower triangular array of the three-dimensional array,
Figure GDA0003512298840000045
and 3, modifying parameters of the model predictive controller according to the running condition of the vehicle, wherein the method comprises the following steps:
(31) according to the deviation e of the current time of the vehicletAnd the radius of curvature C at the current reference point r on the reference trackrCorrecting the control time domain range parameter N of the model predictive controller of the vehicle at the current timecPredicting a time domain range parameter Np；
(32) Acquiring the current mass m and the running speed v of the vehicle and a sequence of the control quantity variation of the last control period, and correcting a weight matrix Q of a model predictive controller of the vehicle at the current moment;
step 4, solving an objective function of the vehicle model predictive controller to obtain a control quantity at the current moment;
(41) solving equation (15), i.e., solving equation J (ξ (t), u (t-1), Δ u (t)) equal to 0, and adding constraint conditions of the solution according to equation (16), obtains a controlled variable sequence of the optimal solution:
Figure GDA0003512298840000051
the desired increment of the control amount at the present time is
Figure GDA0003512298840000052
Step 5, controlling the steering angle of the tire according to the increment of the control quantity and the equivalent sideslip angle, controlling the vehicle to run, judging whether the reference point r needs to be updated, and then entering the step 2 to continue the control of the next period;
(51) inputting the control quantity to a steering wheel to control the vehicle to run;
calculated according to the step (15)
Figure GDA0003512298840000053
The control quantity at the current moment is as follows:
Figure GDA0003512298840000054
(52) judging whether the current reference point r on the reference track is reached or exceeded, and if the current reference point r on the reference track is reached or exceeded, taking the next point on the reference track as the reference point r; and jumping to the step 2 to continue the loop of the next control period.
In the step 3, the fuzzy controller is adopted to correct the control time domain range parameter N of the vehicle model predictive controllercAnd a predicted temporal range parameter NpModified control time domain range parameter N of vehicle model predictive controllercAnd a predicted temporal range parameter NpComprises the following steps:
Figure GDA0003512298840000055
wherein
Figure GDA0003512298840000056
Is a first fuzzy controller.
The first fuzzy controller
Figure GDA0003512298840000057
Is set as follows:
(311) will deviate from etDividing the data into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; by the size of the value of the radius of curvatureDividing the system into five domains, namely { S, XS, M, XL, L }; will NpAnd NcDividing the system into five domains, namely { S, XS, M, XL, L };
(312)Ncand NpThe value rules are as follows:
Figure GDA0003512298840000061
in the step (32), the fuzzy controller is adopted to correct the weight matrix Q of the vehicle model predictive controller, and the corrected weight matrix Q of the vehicle model predictive controller is as follows:
Q＝fuzzyQ(m,v,ΔU(t-1))
wherein fuzzyQ(. cndot.) is a second fuzzy controller.
Second fuzzy controller fuzzyQThe settings of (c) are as follows:
(321) dividing the mass M into three domains according to the value, wherein the domains are { S, M and L }; dividing the running speed v of the vehicle into five domains according to the value, wherein the domains are { S, XS, M, XL and L }; dividing the variable quantity delta U (t-1) of the control quantity into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; dividing values on the diagonal line of the weight matrix Q into five domains, namely { S, XS, M, XL, L };
(322) if the quality is S, the value rule of the weight matrix Q is shown as the following table:
Figure GDA0003512298840000071
if the quality is M, the value rule of the weight matrix Q is shown as the following table:
Figure GDA0003512298840000072
if the quality is L, the value rule of the weight matrix Q is shown as the following table:
Figure GDA0003512298840000073
has the advantages that: compared with the prior art, the MPC-based vehicle adaptive path tracking method disclosed by the invention has the following advantages: 1. the established vehicle kinematic model is provided with a slip parameter, when the vehicle slips, the control quantity can generate anti-interference measures, and the stability and the accuracy of path tracking are improved; 2. the parameters of the vehicle model prediction controller are adjusted in real time by combining the parameters of the vehicle position and the reference path parameters, so that the stability and the accuracy of path tracking are further improved.
Drawings
FIG. 1 is a flow chart of a vehicle adaptive path tracking method according to the present disclosure;
Detailed Description
As shown in fig. 1, the present invention discloses an MPC-based adaptive vehicle path tracking method, which comprises the following steps:
step 1, establishing a kinematic model of a vehicle, and predicting an equivalent sideslip angle, comprising the following steps:
(11) the coordinates of the vehicle have the following relationship with the heading angle and the tire steering angle:
Figure GDA0003512298840000081
wherein X and Y are the coordinates of the vehicle in the X and Y axes, θhIs the vehicle heading angle, /)wbIs the wheelbase of the front and rear axles of the vehicle, v is the running speed of the vehicle, thetawsIs the tire steering angle;
Figure GDA0003512298840000082
the speed of the vehicle in the X-axis and Y-axis respectively,
Figure GDA0003512298840000083
is the steering angular velocity of the vehicle.
(12) By X ═ X y thetah]TIs a vehicle state quantity, u ═ θws]TFor the control quantities, a general kinematic model of the vehicle is constructed:
Figure GDA0003512298840000084
wherein the content of the first and second substances,
Figure GDA0003512298840000085
the general form of the kinematic model at the current reference point r on the reference trajectory is:
Figure GDA0003512298840000086
(13) for subsequent prediction control needs, a general vehicle kinematic model is linearized and discretized:
expanding (2) at the reference point by using Taylor series, and neglecting high-order terms, then:
Figure GDA0003512298840000087
subtracting equation (3) from equation (4) yields:
Figure GDA0003512298840000091
xr、yr、θhrthe coordinates, the course angle theta and the X axis and the Y axis of the vehicle at the current reference point r are respectivelywsrIs the tire steering angle at the current reference point r;
discretizing the formula (5), wherein the discretized general form is as follows:
Figure GDA0003512298840000092
wherein the content of the first and second substances,
Figure GDA0003512298840000093
t is the sampling period, Ak,tAnd Bk,tRespectively predicting a state coefficient matrix and a control coefficient matrix of the state at the moment k according to the current moment t;
(14) judging whether slippage occurs;
according to the actual state quantity at the moment of k-1
Figure GDA0003512298840000094
And (6) calculating the theoretical value of the state quantity at the time k
Figure GDA0003512298840000095
Let k be the actual state quantity at time
Figure GDA0003512298840000096
The threshold value is
Figure GDA0003512298840000097
If it is
Figure GDA0003512298840000098
Judging that slippage occurs, entering the step (15) to calculate an equivalent sideslip angle, and if not, skipping the step (15) to enable the equivalent sideslip angle to be 0;
wherein the threshold value
Figure GDA0003512298840000099
Generally, the vehicle running speed and the ground environment are set according to actual conditions.
(15) If the slippage is generated, calculating an equivalent sideslip angle;
defining front wheel slip angle
Figure GDA00035122988400000910
The angle between the actual speed direction and the direction in which sideslip occurs is the sideslip angle of the rear wheel
Figure GDA00035122988400000911
Is the angle between the actual speed direction and the theoretical speed direction.
Tire steering angle thetawsSteering radius R and equivalent sideslip angle of vehicle
Figure GDA00035122988400000912
The relationship of (1) is:
Figure GDA00035122988400000913
vehicle steering radius r without side slip0Steering radius r due to rear wheel slip anglerSteering radius r due to front wheel slip anglefSatisfies the following relation with the steering radius R:
Figure GDA0003512298840000101
by linearizing equation (8), i.e. neglecting the high-order terms after taylor expansion, the relationship between the equivalent slip angle and the front and rear wheel slip angles can be estimated as:
Figure GDA0003512298840000102
step 2: designing a vehicle model predictive controller based on the established vehicle kinematics model, comprising the steps of:
(21) state quantity ξ (k | t) for predicting k time from current time t is defined:
Figure GDA0003512298840000103
wherein the content of the first and second substances,
Figure GDA0003512298840000104
x (k | t) is a vehicle state quantity predicted at the time k from the current time t, and u (k-1| t) is a control quantity predicted at the time k-1 from the current time t.
The state space expression for the vehicle is then:
Figure GDA0003512298840000105
wherein the content of the first and second substances,
Figure GDA0003512298840000106
Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
Figure GDA0003512298840000107
to simplify the calculation, assume:
Figure GDA0003512298840000108
wherein A ist,tAnd Bt,tRespectively a state coefficient matrix and a control coefficient matrix of the current moment t;
(22) predictive output expression for computing systems
From equation (11), a predicted output expression of the system can be derived:
Y(t)＝Ψtξ(t|t)+ΘtΔU(t) (13)
wherein the content of the first and second substances,
Figure GDA0003512298840000111
ξ (t | t) is the state quantity at the current time t,
Figure GDA0003512298840000112
Ncfor controlling the time-domain range parameter, NpIs a predicted time domain range parameter;
(23) according to equation (13), the objective function may take the form
Figure GDA0003512298840000113
Wherein R, Q is a weight matrix, ρ is a weight coefficient, and ε is a relaxation factor.
Converting equation (14) to a standard quadratic form and combining constraints, the finally designed vehicle model predictive controller takes the following equation as an objective function:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t)T,ε]THt[ΔU(t)T,ε]+Gt[ΔU(t)T,ε] (15)
wherein the content of the first and second substances,
Figure GDA0003512298840000114
et＝X(t)-Xru (t-1) is the control quantity at the moment t-1, and delta U (t) is a matrix formed by the variation quantity of the control quantity at the moment t;
the constraint of equation (15) is:
Figure GDA0003512298840000121
wherein, Umin、UmaxRespectively, a set of minimum and maximum values of the control quantity in the control time domain, Delta Umin、ΔUmaxAre respectively a set of the minimum value and the maximum value of the control quantity change quantity in the control time domain, Umin、Umax、ΔUmin、ΔUmaxIs determined by the actual physical conditions of the vehicle; u (t) is a matrix composed of control quantities at time t, A is Nc×NcThe lower triangular array of the three-dimensional array,
Figure GDA0003512298840000122
and 3, modifying parameters of the model predictive controller according to the running condition of the vehicle, wherein the method comprises the following steps:
(31) according to the deviation e of the current time of the vehicletAnd the radius of curvature C at the current reference point r on the reference trackrCorrecting the control time domain range parameter N of the model predictive controller of the vehicle at the current timecPredicting a time domain range parameter Np；
(32) And acquiring the current mass m and the running speed v of the vehicle and the sequence of the control quantity variation of the last control period, and correcting the weight matrix Q of the model predictive controller of the vehicle at the current moment.
And 4, solving an objective function of the vehicle model predictive controller to obtain the control quantity at the current moment.
(41) Solving equation (15), i.e., solving equation J (ξ (t), u (t-1), Δ u (t)) equal to 0, and adding constraint conditions of the solution according to equation (16), obtains a controlled variable sequence of the optimal solution:
Figure GDA0003512298840000123
the desired increment of the control amount at the present time is
Figure GDA0003512298840000124
And 5, obtaining the control quantity at the current moment according to the increment of the control quantity and the equivalent sideslip angle, controlling the vehicle to run, judging whether the current reference point r needs to be updated or not, and skipping to the step 2 to continue the control of the next period.
(51) And inputting the control quantity to the steering wheel to control the vehicle to run.
Calculated according to the step (15)
Figure GDA0003512298840000125
The control quantity at the current moment is as follows:
Figure GDA0003512298840000126
(52) judging whether the current reference point r on the reference track is reached or exceeded, and if the current reference point r on the reference track is reached or exceeded, taking the next point on the reference track as the reference point r; and jumping to the step 2 to continue the next control period loop.
In the step (31), the fuzzy controller is adopted to correct the parameters of the vehicle model predictive controller, and the corrected control time domain range parameter N of the vehicle model predictive controllercAnd a predicted temporal range parameter NpComprises the following steps:
Figure GDA0003512298840000131
first fuzzy controller
Figure GDA0003512298840000132
Is set as follows:
(311) will deviate from etDividing the data into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; dividing the curvature radius into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; will NpAnd NcDividing the data into five domains according to the value, wherein the domains are { S, XS, M, XL, L };
(312)Ncand NpThe value rule of (a) is shown in table 1:
TABLE 1 first fuzzy controller
Figure GDA0003512298840000133
Rule of
Figure GDA0003512298840000134
And (4) correcting the weight matrix Q of the vehicle model prediction controller by adopting a fuzzy controller in the step (32), wherein the corrected weight matrix Q of the vehicle model prediction controller is as follows:
Q＝fuzzyQ(m,v,ΔU(t-1))
second fuzzy controller fuzzyQThe settings of (c) are as follows:
(321) dividing the mass M into three domains according to the value, wherein the domains are { S, M and L }; dividing the running speed v of the vehicle into five domains according to the value, wherein the domains are { S, XS, M, XL and L }; dividing the variable quantity delta U (t-1) of the control quantity into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; according to the equation (15), the weight matrix Q is a diagonal matrix, and the diagonal value is within the interval (0, 1). Dividing values on the diagonal line of the weight matrix Q into five domains, namely { S, XS, M, XL, L };
(322) the value rule of the weight matrix Q is shown in tables 2, 3 and 4:
TABLE 2 second fuzzy controller fuzzyQRule in quality S
Figure GDA0003512298840000141
TABLE 3 second fuzzy controller fuzzyQRule at quality M
Figure GDA0003512298840000142
TABLE 4 second fuzzy controller fuzzyQRule of quality L
Figure GDA0003512298840000151

Claims (5)

1. The vehicle adaptive path tracking method based on the MPC is characterized by comprising the following steps:
step 1, establishing a kinematic model of a vehicle, and predicting an equivalent sideslip angle, comprising the following steps:
(11) the coordinates of the vehicle have the following relationship with the heading angle and the tire steering angle:
Figure FDA0003512298830000011
wherein X and Y are the coordinates of the vehicle in the X and Y axes, θhIs the vehicle heading angle, /)wbIs the wheelbase of the front and rear axles of the vehicle, v is the running speed of the vehicle, thetawsIs the tire steering angle;
Figure FDA0003512298830000012
the speed of the vehicle in the X-axis and Y-axis respectively,
Figure FDA0003512298830000013
for turning of vehiclesA heading angular velocity;
(12) by X ═ X y thetah]TIs a vehicle state quantity, u ═ θws]TFor the control quantities, a general kinematic model of the vehicle is constructed:
Figure FDA0003512298830000014
wherein the content of the first and second substances,
Figure FDA0003512298830000015
the general form of the kinematic model at the current reference point r on the reference trajectory is:
Figure FDA0003512298830000016
(13) linearizing and discretizing a general vehicle kinematic model:
expanding (2) at the reference point by using Taylor series, and neglecting high-order terms, then:
Figure FDA0003512298830000017
subtracting equation (3) from equation (4) yields:
Figure FDA0003512298830000018
xr、yr、θhrthe coordinates, the course angle theta and the X axis and the Y axis of the vehicle at the current reference point r are respectivelywsrIs the tire steering angle at the current reference point r;
discretizing the formula (5), wherein the discretized general form is as follows:
Figure FDA0003512298830000019
wherein the content of the first and second substances,
Figure FDA0003512298830000021
t is the sampling period, Ak,tAnd Bk,tRespectively predicting a state coefficient matrix and a control coefficient matrix of the state at the moment k according to the current moment t;
(14) judging whether slippage occurs;
according to the actual state quantity at the moment of k-1
Figure FDA0003512298830000022
And (6) calculating the theoretical value of the state quantity at the time k
Figure FDA0003512298830000023
Let k be the actual state quantity at time
Figure FDA0003512298830000024
The threshold value is
Figure FDA0003512298830000025
If it is
Figure FDA0003512298830000026
Judging that slippage occurs, and entering the step (15) to calculate an equivalent sideslip angle; otherwise, skipping the step (15), and enabling the equivalent sideslip angle to be 0;
(15) if slip occurs, calculating the equivalent sideslip angle
Figure FDA0003512298830000027
Figure FDA0003512298830000028
Wherein
Figure FDA0003512298830000029
Is the side slip angle of the front wheel,
Figure FDA00035122988300000210
is a rear wheel side slip angle;
step 2: designing a vehicle model predictive controller based on the established vehicle kinematics model, comprising the steps of:
(21) state quantity ξ (k | t) for predicting k time from current time t is defined:
Figure FDA00035122988300000211
wherein the content of the first and second substances,
Figure FDA00035122988300000212
x (k | t) is a vehicle state quantity at the moment k according to the current moment t, and u (k-1| t) is a control quantity at the moment k-1 according to the current moment t;
the state space expression for the vehicle is then:
Figure FDA00035122988300000213
wherein the content of the first and second substances,
Figure FDA0003512298830000031
Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
Figure FDA0003512298830000032
suppose that:
Figure FDA0003512298830000033
wherein A ist,tAnd Bt,tRespectively a state coefficient matrix and a control coefficient matrix of the current moment t;
(22) predictive output expression for computing systems
The predicted output expression of the system is:
Y(t)＝Ψtξ(t|t)+ΘtΔU(t) (13)
wherein the content of the first and second substances,
Figure FDA0003512298830000034
ξ (t | t) is the state quantity at the current time t,
Figure FDA0003512298830000035
Ncfor controlling the time-domain range parameter, NpIs a predicted time domain range parameter;
(23) the objective function of the system is:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t)T,ε]THt[ΔU(t)T,ε]+Gt[ΔU(t)T,ε] (15)
the constraint conditions are as follows:
Figure FDA0003512298830000036
wherein the content of the first and second substances,
Figure FDA0003512298830000041
et＝X(t)-Xru (t-1) is the control quantity at the moment t-1, and delta U (t) is a matrix formed by the variation quantity of the control quantity at the moment t; r, Q is a weight matrix, rho is a weight coefficient, and epsilon is a relaxation factor; u shapemin、UmaxRespectively, a set of minimum and maximum values of the control quantity in the control time domain, Delta Umin、ΔUmaxRespectively a set of the minimum value and the maximum value of the control quantity variation in the control time domain; u (t) is a matrix composed of control quantities at time t, A is Nc×NcThe lower triangular array of the three-dimensional array,
Figure FDA0003512298830000042
and 3, modifying parameters of the model predictive controller according to the running condition of the vehicle, wherein the method comprises the following steps:
(31) according to the deviation e of the current time of the vehicletAnd the radius of curvature C at the current reference point r on the reference trackrCorrecting the control time domain range parameter N of the model predictive controller of the vehicle at the current timecPredicting a time domain range parameter Np；
(32) Acquiring the current mass m and the running speed v of the vehicle and a sequence of the control quantity variation of the last control period, and correcting a weight matrix Q of a model predictive controller of the vehicle at the current moment;
step 4, solving an objective function of the vehicle model predictive controller to obtain a control quantity at the current moment;
(41) solving equation (15), i.e., solving equation J (ξ (t), u (t-1), Δ u (t)) equal to 0, and adding constraint conditions of the solution according to equation (16), obtains a controlled variable sequence of the optimal solution:
Figure FDA0003512298830000043
the desired increment of the control amount at the present time is
Figure FDA0003512298830000044
Step 5, controlling the steering angle of the tire according to the increment of the control quantity and the equivalent sideslip angle, controlling the vehicle to run, judging whether the reference point r needs to be updated, and then entering the step 2 to continue the control of the next period;
(51) inputting the control quantity to a steering wheel to control the vehicle to run;
calculated according to the step (15)
Figure FDA0003512298830000045
The control quantity at the current moment is as follows:
Figure FDA0003512298830000046
(52) judging whether the current reference point r on the reference track is reached or exceeded, and if the current reference point r on the reference track is reached or exceeded, taking the next point on the reference track as the reference point r; and jumping to the step 2 to continue the loop of the next control period.
2. The vehicle adaptive path tracking method according to claim 1, wherein the fuzzy controller is adopted to modify the control time domain range parameter N of the vehicle model predictive controller in the step 3cAnd a predicted temporal range parameter NpModified control time domain range parameter N of vehicle model predictive controllercAnd a predicted temporal range parameter NpComprises the following steps:
Figure FDA0003512298830000051
wherein
Figure FDA0003512298830000052
Is a first fuzzy controller.
3. The vehicle adaptive path tracking method according to claim 2, wherein the first fuzzy controller
Figure FDA0003512298830000053
Is set as follows:
(311) will deviate from etDividing the data into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; dividing the curvature radius into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; will NpAnd NcDividing the system into five domains, namely { S, XS, M, XL, L };
(312)Ncand NpThe value rules are as follows:
Figure FDA0003512298830000054
4. the vehicle adaptive path tracking method according to claim 1, wherein the fuzzy controller is adopted to modify the weight matrix Q of the vehicle model predictive controller in the step (32), and the modified weight matrix Q of the vehicle model predictive controller is:
Q＝fuzzyQ(m,v,ΔU(t-1))
wherein fuzzyQ(. cndot.) is a second fuzzy controller.
5. The vehicle adaptive path tracking method according to claim 4, wherein the second fuzzy controller fuzzyQThe settings of (c) are as follows:
(321) dividing the mass M into three domains according to the value, wherein the domains are { S, M and L }; dividing the running speed v of the vehicle into five domains according to the value, wherein the domains are { S, XS, M, XL and L }; dividing the variable quantity delta U (t-1) of the control quantity into five domains according to the value, wherein the domains are { S, XS, M, XL, L }; dividing values on the diagonal line of the weight matrix Q into five domains, namely { S, XS, M, XL, L };
(322) if the quality is S, the value rule of the weight matrix Q is shown as the following table:
Figure FDA0003512298830000061
if the quality is M, the value rule of the weight matrix Q is shown as the following table:
Figure FDA0003512298830000071
if the quality is L, the value rule of the weight matrix Q is shown as the following table:
Figure FDA0003512298830000072
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