CN110262229B - Vehicle self-adaptive path tracking method based on MPC - Google Patents
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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
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:
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;the speed of the vehicle in the X-axis and Y-axis respectively,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:
the general form of the kinematic model at the current reference point r on the reference trajectory is:
(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:
subtracting equation (3) from equation (4) yields:
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:
wherein,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-1And (6) calculating the theoretical value of the state quantity at the time kLet k be the actual state quantity at timeThe threshold value isIf it isJudging 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;
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:
wherein,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:
wherein,Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
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)
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:
wherein,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,
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:
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;
(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:
(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:
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:
if the quality is M, the value rule of the weight matrix Q is shown as the following table:
if the quality is L, the value rule of the weight matrix Q is shown as the following table:
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:
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;the speed of the vehicle in the X-axis and Y-axis respectively,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:
the general form of the kinematic model at the current reference point r on the reference trajectory is:
(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:
subtracting equation (3) from equation (4) yields:
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:
wherein,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-1And (6) calculating the theoretical value of the state quantity at the time kLet k be the actual state quantity at timeThe threshold value isIf it isJudging 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 valueGenerally, 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 angleThe angle between the actual speed direction and the direction in which sideslip occurs is the sideslip angle of the rear wheelIs the angle between the actual speed direction and the theoretical speed direction.
Tire steering angle thetawsSteering radius R and equivalent sideslip angle of vehicleThe relationship of (1) is:
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:
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:
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:
wherein,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:
wherein,Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
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,ξ (t | t) is the state quantity at the current time t,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
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,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:
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,
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:
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.
(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:
(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:
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
TABLE 3 second fuzzy controller fuzzyQRule at quality M
TABLE 4 second fuzzy controller fuzzyQRule of quality L
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:
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;the speed of the vehicle in the X-axis and Y-axis respectively,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:
the general form of the kinematic model at the current reference point r on the reference trajectory is:
(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:
subtracting equation (3) from equation (4) yields:
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:
wherein,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-1And (6) calculating the theoretical value of the state quantity at the time kLet k be the actual state quantity at timeThe threshold value isIf it isJudging 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;
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:
wherein,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:
wherein,Δ U (k | t) is a matrix of the amount of change in the control amount at time k from the current time t,
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)
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:
wherein,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,
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:
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;
(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:
3. The vehicle adaptive path tracking method according to claim 2, wherein the first fuzzy controllerIs 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:
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:
if the quality is M, the value rule of the weight matrix Q is shown as the following table:
if the quality is L, the value rule of the weight matrix Q is shown as the following table:
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