CN111750866B - Intelligent automobile transverse and longitudinal coupling path planning method based on regional virtual force field - Google Patents

Intelligent automobile transverse and longitudinal coupling path planning method based on regional virtual force field Download PDF

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CN111750866B
CN111750866B CN202010647239.3A CN202010647239A CN111750866B CN 111750866 B CN111750866 B CN 111750866B CN 202010647239 A CN202010647239 A CN 202010647239A CN 111750866 B CN111750866 B CN 111750866B
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郭洪艳
刘畅
赵小明
薄悦
陈虹
高振海
高炳钊
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Jilin University
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Abstract

The invention provides an intelligent automobile transverse and longitudinal coupling path planning method based on a regional virtual force field, which models a road environment by the regional virtual force field, predicts the future state of a vehicle by using model prediction control, and completes the task of transverse and longitudinal coupling path planning based on the model prediction control, and specifically comprises the following steps: step one, establishing a dynamics and kinematics model of a main vehicle; step two, dividing a vehicle driving lane region; step three, establishing a road environment model based on the regional virtual force field, and step four, designing a model prediction controller by using the model established in the step three; the method considers the transverse and longitudinal running of the vehicle and the dynamic running of the multi-obstacle vehicle at the same time, can ensure the safety and avoid collision.

Description

Intelligent automobile transverse and longitudinal coupling path planning method based on regional virtual force field
Technical Field
The invention relates to an intelligent automobile transverse and longitudinal coupling path planning method based on a regional virtual force field.
Background
With the development and progress of social economy and manufacturing industry, the automobile industry is rapidly growing, and the problem of driving safety is more serious.
The intelligent vehicle as an important component of the intelligent traffic system can finish autonomous obstacle avoidance and improve driving safety. The path planning is one of key technologies, and means that a sequence point or a curve meeting a driving target is formed according to surrounding environment information and a driving state of a vehicle, and currently, most of the path planning neglects the longitudinal direction and only plans transverse motion, but a vehicle system is an extremely complex nonlinear system, and the motion planning is difficult on the premise of meeting dynamic constraints, so that how to perform the path planning of transverse and longitudinal coupling is a key problem of path planning research.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an intelligent automobile transverse and longitudinal coupling path planning method based on a regional virtual force field.
The purpose of the invention is realized by the following technical scheme:
the intelligent automobile transverse and longitudinal coupling path planning method based on the regional virtual force field is characterized by comprising the following specific steps of:
step one, establishing a dynamics and kinematics model of the main vehicle:
(1) main vehicle dynamics model establishment
Considering the lateral motion dynamics, the yaw kinematics and the longitudinal dynamics of the vehicle, establishing a vehicle body coordinate system, wherein the vehicle mass center o is a coordinate origin, the vehicle body advancing direction is the positive direction of an x-axis, the direction vertical to the x-axis is the positive direction of a z-axis, and a two-degree-of-freedom dynamic equation can be obtained according to the dynamics knowledge as shown in the following formula (1):
Figure GDA0003274115550000011
wherein m is the mass of the vehicle in kg; a isyThe inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；IzIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; fxfLongitudinal force for the front wheels of the vehicle, unit: n; fyfLateral force for the front wheels of the vehicle, unit: n; fyrFor the rear wheels of vehiclesLateral force of (d), unit: n; deltafIs the steering angle of the front wheels of the vehicle, and the unit is: rad; r is the yaw rate of the vehicle, unit: rad/s;
under small angle assumptions and using a linear tire model:
Figure GDA0003274115550000021
in the formula, CfTire cornering stiffness for a front wheel of a vehicle, unit: n · rad; crTire cornering stiffness for a rear wheel of a vehicle, unit: n · rad; alpha is alphafIs the tire slip angle of the front wheel of the vehicle, unit: rad; alpha is alpharIs the tire slip angle of the rear wheel of the vehicle, unit: rad;
the slip angle of the tire is calculated using the longitudinal speed and the lateral speed as:
Figure GDA0003274115550000022
the dynamic model of the vehicle can be obtained through arrangement:
Figure GDA0003274115550000023
(2) modeling the main vehicle kinematics:
the motion of the vehicle is described mathematically, taking into account only the geometric relationships of the vehicle systems:
Figure GDA0003274115550000024
in the formula, xoIs the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y isoIs the lateral position of the vehicle mass center o under the inertial system, the unit: m; r is the yaw rate of the vehicle, unit: rad/s;
Figure GDA0003274115550000025
as vehiclesYaw angle, unit: rad;
the analysis of the vehicle steering motion can obtain the component of the motion acceleration of the vehicle mass center in the vehicle body coordinate system:
Figure GDA0003274115550000031
and (3) arranging to obtain a kinematic model of the vehicle:
Figure GDA0003274115550000032
(3) establishing a model of the dynamics and kinematics of the main vehicle
And (3) arranging the main vehicle dynamics model and the kinematics model to obtain the main vehicle dynamics and kinematics model:
Figure GDA0003274115550000033
vxis the longitudinal speed under the coordinate system of the vehicle body, and the unit is as follows: m/s; v. ofyLateral speed in the coordinate system of the vehicle body is shown as the following unit: m/s;
Figure GDA0003274115550000034
yaw angle of the vehicle, unit: rad; r is the yaw rate of the vehicle, unit: rad/s; deltafIs the front wheel angle of the vehicle, unit: rad; a isxIs the inertial acceleration of the vehicle's center of mass in the x-axis direction, called longitudinal acceleration, in units: m/s2；ayIs the inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；x0Is the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y is0Is the lateral position of the vehicle mass center o under the inertial system, the unit: m; i iszIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; m is the mass of the vehicle,unit: kg;
selecting
Figure GDA0003274115550000041
Selecting front wheel steering angle delta as system state variablefAnd longitudinal acceleration axAs a system control input, equation (8) is expressed as:
Figure GDA0003274115550000042
at an arbitrary point (x)r，ur) Performing Taylor expansion nearby, keeping a first-order term, and performing linearization to obtain:
Figure GDA0003274115550000043
wherein Jf(x) And Jf(u) Jacobian matrices of f versus x and u, respectively, for the linearized time-varying system described above, written as:
Figure GDA0003274115550000044
wherein Δ x ═ x-xr，Δu＝u-ur，Ac(t) and Bc(t) is a Jacobian matrix, which is expressed as follows
Figure GDA0003274115550000045
Step two, dividing the driving lane area of the vehicle
Taking two lanes as an example, the sensing module scans the road environment to obtain a road boundary line f1(x)、f2(x) And f3(x) Dividing the road into lane areas, L1Is 1 lane, i.e. f1(x) And f2(x) Road area within range, L2Is 2 lanes, i.e. f2(x) And f3(x) Road area within range, L12' is an inter-lane region, L1′、L2' is the area in the lane, d is the vehicle width, and the mathematical description is:
Figure GDA0003274115550000051
step three, establishing a road environment model based on the regional virtual force field:
considering the area division in the step two and establishing an area virtual force field by the obstacle vehicles, wherein the area virtual force field comprises a virtual rectangular repulsion field and a lane keeping area virtual gravitational field which are arranged around the obstacle vehicles along the road direction;
1) lane area keeping virtual gravitational field:
the lane area-keeping virtual gravitational field comprises two parts, one part is the gravitational force F for driving the vehicle in the road area1The other part is the gravity F for making the vehicle to run in the lane as much as possible2Gravitational force F1And gravitational force F2The force of (d) is defined as:
Figure GDA0003274115550000052
in the formula (d)roadIs the width of the area in the lane, unit: m; ddeIs the distance of the host vehicle from the lane area, unit: m; v is the host vehicle speed, unit: m/s; lambda [ alpha ]i,κiTo adjust the factor, λiDetermining the magnitude of the applied force, κiDetermining the change speed of the acting force;
virtual gravitational field f of lane keeping areahIs defined as:
Figure GDA0003274115550000053
2) virtual rectangular repulsive field of barrier vehicle:
in order to avoid collision between the main vehicle and the obstacle vehicle, a virtual rectangular repulsive field of the obstacle vehicle is establishedArea of influence D from Ds1、Ds2And Ds3Three parameters were determined, defined as:
Figure GDA0003274115550000061
in the formula (d)0For a safe distance, aObsIs the average braking acceleration of the obstacle vehicle, ahostAverage braking acceleration of the main vehicle, Ts1、Ts2And Ts3Is a weight coefficient;
the obstacle vehicle virtual rectangular repulsive force is defined as:
Figure GDA0003274115550000062
in the formula, vObs(j) Representing the speed, x, of the jth obstacle vehicleObs(j) Represents the longitudinal position of the jth obstacle vehicle, yObs(j) Representing the lateral position of the jth obstacle vehicle, D is the influence area of the virtual rectangular repulsive force field of the obstacle vehicle, eta1、η2And η3To regulate the factor, η1Determining the emergency degree and eta of the potential energy change of the dynamic rectangular virtual repulsive force field of the obstacle vehicle2Representing the degree of correlation, eta, of potential energy change with relative velocity3Representing the degree of correlation of potential energy change with relative position;
step four, designing a model predictive controller by using the road environment model based on the regional virtual force field established in the step three:
discretizing the linear system obtained in the step one to obtain an incremental state space model:
Figure GDA0003274115550000063
wherein the content of the first and second substances,
Figure GDA0003274115550000064
Figure GDA0003274115550000071
t is the discrete system sampling time, Δ x (k) ═ x (k) — x (k-1), Δ u (k) ═ u (k) — u (k-1);
supposing that the prediction time domain is P, the control time domain is M and M is less than or equal to P, supposing that the control quantity outside the control time domain is kept unchanged, and deducing the output Y at the moment k based on the measurement information of the current moment and the historical information of the process according to the basic principle of model prediction controlPThe prediction equation for (k +1) and state X (k +1) is:
Figure GDA0003274115550000072
wherein the content of the first and second substances,
Figure GDA0003274115550000073
Figure GDA0003274115550000074
in summary, the optimization problem is as follows:
Figure GDA0003274115550000075
satisfies the following conditions:
Figure GDA0003274115550000081
wherein J is an objective function of the optimization function; v (i) represents the predicted velocity of the host vehicle at step i, in units: m/s; f. ofx(i) Is the longitudinal gravity of the predicted position of the ith step of the host vehicle, fy(i) Is the lateral gravity of the predicted position of the ith step of the main vehicle; lambda1,Λ2,Λ3,Λ4Weighting factors added for balancing each target respectively; deltafmaxThe maximum value of the turning angle of the front wheels,
Figure GDA0003274115550000083
maximum value of front wheel steering angle change rate, unit: rad; a isxmaxIs the maximum value of the longitudinal acceleration and,
Figure GDA0003274115550000082
maximum longitudinal acceleration rate, unit: m/s2(ii) a T is discrete system sampling time;
according to the principle of model predictive control, a first group of control quantities (delta) of a control sequence U obtained by solving an optimization problem is selectedf,ax) And the control input is used as the control input of the tracking controller, the control input is acted on the controlled vehicle, and the optimization problem is solved again according to the vehicle state information at the current moment at the next moment to obtain a new optimal control sequence, so that the rolling optimization control of the vehicle is realized.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, a vehicle nonlinear system model is established in the first step, and the transverse and longitudinal running is considered, so that the actual running condition of the vehicle can be better reflected;
2. in the second step of the method, when the road area is divided, the lane width and the vehicle body width are considered, so that the driving safety of the vehicle is ensured to the maximum extent;
3. the method adopts the model predictive control algorithm in the fourth step, can predict the state of the vehicle at the future moment, and further improves the driving safety.
Drawings
Fig. 1 is a flow chart of an intelligent automobile transverse and longitudinal coupling path planning method based on a regional virtual force field provided by the invention.
Fig. 2 is a schematic diagram of the road area division according to the present invention.
FIG. 3 is a schematic view of a regional virtual force field scope.
FIG. 4 is a schematic view of a main vehicle dynamics model.
FIG. 5 is a schematic view of a kinematic model of a host vehicle.
Detailed Description
The invention is described in detail below with reference to the accompanying drawings:
the invention provides an intelligent automobile transverse and longitudinal coupling path planning method based on a regional virtual force field, which comprises the following specific implementation steps of:
step one, establishing a dynamics and kinematics model of the main vehicle:
(1) main vehicle dynamics model establishment
Considering the lateral motion dynamics, the yaw kinematics and the longitudinal dynamics of the vehicle, establishing a vehicle body coordinate system, wherein the vehicle mass center o is a coordinate origin, the vehicle body advancing direction is the positive direction of an x-axis, the direction vertical to the x-axis is the positive direction of a z-axis, and a two-degree-of-freedom dynamic equation can be obtained according to the dynamics knowledge as shown in the following formula (1):
Figure GDA0003274115550000091
wherein m is the mass of the vehicle in kg; a isyThe inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；IzIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; fxfLongitudinal force for the front wheels of the vehicle, unit: n; fyfLateral force for the front wheels of the vehicle, unit: n; fyrLateral force for the rear wheel of the vehicle, unit: n; deltafIs the steering angle of the front wheels of the vehicle, and the unit is: rad; r is the yaw rate of the vehicle, unit: rad/s;
under small angle assumptions and using a linear tire model:
Figure GDA0003274115550000092
in the formula, CfTire cornering stiffness for a front wheel of a vehicle, unit: n · rad; crTire cornering stiffness for a rear wheel of a vehicle, unit: n · rad; alpha is alphafIs the tire slip angle of the front wheel of the vehicle,unit: rad; alpha is alpharIs the tire slip angle of the rear wheel of the vehicle, unit: rad;
the slip angle of the tire is calculated using the longitudinal speed and the lateral speed as:
Figure GDA0003274115550000093
the dynamic model of the vehicle can be obtained through arrangement:
Figure GDA0003274115550000101
(2) modeling the main vehicle kinematics:
the motion of the vehicle is described mathematically, taking into account only the geometric relationships of the vehicle systems:
Figure GDA0003274115550000102
in the formula, xoIs the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y isoIs the lateral position of the vehicle mass center o under the inertial system, the unit: m; r is the yaw rate of the vehicle, unit: rad/s;
Figure GDA0003274115550000103
vehicle yaw angle, unit: rad;
the analysis of the vehicle steering motion can obtain the component of the motion acceleration of the vehicle mass center in the vehicle body coordinate system:
Figure GDA0003274115550000104
and (3) arranging to obtain a kinematic model of the vehicle:
Figure GDA0003274115550000105
(3) establishing a model of the dynamics and kinematics of the main vehicle
And (3) arranging the main vehicle dynamics model and the kinematics model to obtain the main vehicle dynamics and kinematics model:
Figure GDA0003274115550000111
vxis the longitudinal speed under the coordinate system of the vehicle body, and the unit is as follows: m/s; v. ofyLateral speed in the coordinate system of the vehicle body is shown as the following unit: m/s;
Figure GDA0003274115550000112
yaw angle of the vehicle, unit: rad; r is the yaw rate of the vehicle, unit: rad/s; deltafIs the front wheel angle of the vehicle, unit: rad; a isxIs the inertial acceleration of the vehicle's center of mass in the x-axis direction, called longitudinal acceleration, in units: m/s2；ayIs the inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；x0Is the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y is0Is the lateral position of the vehicle mass center o under the inertial system, the unit: m; i iszIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; m is the mass of the vehicle, in units: kg;
selecting
Figure GDA0003274115550000113
Selecting front wheel steering angle delta as system state variablefAnd longitudinal acceleration axAs a system control input, equation (8) is expressed as:
Figure GDA0003274115550000114
at an arbitrary point (x)r，ur) Performing Taylor expansion nearby, and retaining the first-order termLine linearization yields:
Figure GDA0003274115550000115
wherein Jf(x) And Jf(u) Jacobian matrices of f versus x and u, respectively, for the linearized time-varying system described above, written as:
Figure GDA0003274115550000121
wherein Δ x ═ x-xr，Δu＝u-ur，Ac(t) and Bc(t) is a Jacobian matrix, which is expressed as follows
Figure GDA0003274115550000122
Step two, dividing the driving lane area of the vehicle
Taking two lanes as an example, the sensing module scans the road environment to obtain a road boundary line f1(x)、f2(x) And f3(x) Dividing the road into lane areas, L1Is 1 lane, i.e. f1(x) And f2(x) Road area within range, L2Is 2 lanes, i.e. f2(x) And f3(x) Road area within range, L12' is an inter-lane region, L1′、L2' is the area in the lane, d is the vehicle width, and the mathematical description is:
Figure GDA0003274115550000123
step three, establishing a road environment model based on the regional virtual force field:
considering the area division in the step two and establishing an area virtual force field by the obstacle vehicles, wherein the area virtual force field comprises a virtual rectangular repulsion field and a lane keeping area virtual gravitational field which are arranged around the obstacle vehicles along the road direction;
1) lane area keeping virtual gravitational field:
the lane area-keeping virtual gravitational field comprises two parts, one part is the gravitational force F for driving the vehicle in the road area1The other part is the gravity F for making the vehicle to run in the lane as much as possible2Gravitational force F1And gravitational force F2The force of (d) is defined as:
Figure GDA0003274115550000131
in the formula (d)roadIs the width of the area in the lane, unit: m; ddeIs the distance of the host vehicle from the lane area, unit: m; v is the host vehicle speed, unit: m/s; lambda [ alpha ]i,κiTo adjust the factor, λiDetermining the magnitude of the applied force, κiDetermining the change speed of the acting force;
virtual gravitational field f of lane keeping areahIs defined as:
Figure GDA0003274115550000132
2) virtual rectangular repulsive field of barrier vehicle:
in order to avoid collision between the main vehicle and the obstacle vehicle, a virtual rectangular repulsive field of the obstacle vehicle is established, and an influence area D of the virtual rectangular repulsive field of the obstacle vehicle is defined by Ds1、Ds2And Ds3Three parameters were determined, defined as:
Figure GDA0003274115550000133
in the formula (d)0For a safe distance, aObsIs the average braking acceleration of the obstacle vehicle, ahostAverage braking acceleration of the main vehicle, Ts1、Ts2And Ts3Is a weight coefficient;
the obstacle vehicle virtual rectangular repulsive force is defined as:
Figure GDA0003274115550000141
in the formula, vObs(j) Representing the speed, x, of the jth obstacle vehicleObs(j) Represents the longitudinal position of the jth obstacle vehicle, yObs(j) Representing the lateral position of the jth obstacle vehicle, D is the influence area of the virtual rectangular repulsive force field of the obstacle vehicle, eta1、η2And η3To regulate the factor, η1Determining the emergency degree and eta of the potential energy change of the dynamic rectangular virtual repulsive force field of the obstacle vehicle2Representing the degree of correlation, eta, of potential energy change with relative velocity3Representing the degree of correlation of potential energy change with relative position;
step four, designing a model predictive controller by using the road environment model based on the regional virtual force field established in the step three:
discretizing the linear system obtained in the step one to obtain an incremental state space model:
Figure GDA0003274115550000142
wherein the content of the first and second substances,
Figure GDA0003274115550000143
Figure GDA0003274115550000144
t is the discrete system sampling time, Δ x (k) ═ x (k) — x (k-1), Δ u (k) ═ u (k) — u (k-1);
supposing that the prediction time domain is P, the control time domain is M and M is less than or equal to P, supposing that the control quantity outside the control time domain is kept unchanged, and deducing the output Y at the moment k based on the measurement information of the current moment and the historical information of the process according to the basic principle of model prediction controlPThe prediction equation for (k +1) and state X (k +1) is:
Figure GDA0003274115550000145
wherein the content of the first and second substances,
Figure GDA0003274115550000151
Figure GDA0003274115550000152
in order to ensure that the vehicle can successfully avoid obstacles and avoid collision. According to the established virtual rectangular repulsion field of the obstacle vehicle, when the vehicle drives into the repulsion field influence area, the larger the relative speed and the smaller the relative position of the main vehicle and the obstacle vehicle are, the larger the repulsion force borne by the main vehicle is, and when the vehicle drives out of the repulsion field influence area, the main vehicle is not influenced by the repulsion field and the repulsion force borne is zero. The target that the main vehicle and the obstacle vehicle do not collide is achieved by minimizing the potential energy borne in the virtual rectangular repulsive field of the obstacle vehicle. The objective function is as follows:
Figure GDA0003274115550000153
in order to ensure that the vehicle runs in the road area, the vehicle runs in the lane area as much as possible on the basis of the road area, and the lane changing frequency is reduced, so that the vehicle runs in the lane as much as possible. The virtual gravitational field is maintained according to the established lane area and can be understood by being divided into two parts, on one hand, the road boundary is taken as a line, the potential energy of the gravitational field outside the boundary is large, and the potential energy inside the boundary is small; on the other hand, according to the road area divided by the previous section, in the area between lanes, the potential energy is decreased from the lane line to the direction of the central line of the road, and in the area in the lane, the potential energy is zero. The method can be realized by keeping the potential energy minimization objective function of the virtual gravitational field in the lane area to ensure that the vehicle runs in the road area and runs in the lane as much as possible:
Figure GDA0003274115550000154
the objective of the desired longitudinal speed on vehicle tracking is achieved by minimizing the speed deviation, the objective function is as follows:
Figure GDA0003274115550000161
the smoothness of the vehicle is ensured, the optimized control quantity is as stable as possible, and the small amplitude change of the control action can be realized by a minimized objective function:
Figure GDA0003274115550000162
the four performance indexes J1, J2, J3 and J4 are mutually influenced and even contradicted, in order to obtain the best control effect, a weight coefficient is introduced to adjust the requirement conflict among the performance indexes, so that the performance index of the path planning controller based on model predictive control designed in this chapter is
J＝Λ1J1+Λ2J2+Λ3J3+Λ4J4 (23)
In order to solve the problem of actuator saturation, the front wheel steering angle, the acceleration and the change rate thereof are within the saturation threshold of the actuator, and therefore, the following constraints need to be satisfied
Figure GDA0003274115550000163
In summary, the optimization problem is as follows:
Figure GDA0003274115550000164
satisfies the following conditions:
Figure GDA0003274115550000165
wherein J is an optimization functionAn objective function; v (i) represents the predicted velocity of the host vehicle at step i, in units: m/s; f. ofx(i) Is the longitudinal gravity of the predicted position of the ith step of the host vehicle, fy(i) Is the lateral gravity of the predicted position of the ith step of the main vehicle; lambda1,Λ2,Λ3,Λ4Weighting factors added for balancing each target respectively; deltafmaxThe maximum value of the turning angle of the front wheels,
Figure GDA0003274115550000171
maximum value of front wheel steering angle change rate, unit: rad; a isxmaxIs the maximum value of the longitudinal acceleration and,
Figure GDA0003274115550000172
maximum longitudinal acceleration rate, unit: m/s2(ii) a T is discrete system sampling time; according to the principle of model predictive control, a first group of control quantities (delta) of a control sequence U obtained by solving an optimization problem is selectedf,ax) And the control input is used as the control input of the tracking controller, the control input is acted on the controlled vehicle, and the optimization problem is solved again according to the vehicle state information at the current moment at the next moment to obtain a new optimal control sequence, so that the rolling optimization control of the vehicle is realized.

Claims (1)

1. The intelligent automobile transverse and longitudinal coupling path planning method based on the regional virtual force field is characterized by comprising the following specific steps of:
step one, establishing a dynamics and kinematics model of the main vehicle:
(1) main vehicle dynamics model establishment
Considering the lateral motion dynamics, the yaw kinematics and the longitudinal dynamics of the vehicle, establishing a vehicle body coordinate system, wherein the vehicle mass center o is a coordinate origin, the vehicle body advancing direction is the positive direction of an x-axis, the direction vertical to the x-axis is the positive direction of a z-axis, and a two-degree-of-freedom dynamic equation can be obtained according to the dynamics knowledge as shown in the following formula (1):
Figure FDA0003274115540000011
wherein m is the mass of the vehicle in kg; a isyThe inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；IzIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; fxfLongitudinal force for the front wheels of the vehicle, unit: n; fyfLateral force for the front wheels of the vehicle, unit: n; fyrLateral force for the rear wheel of the vehicle, unit: n; deltafIs the steering angle of the front wheels of the vehicle, and the unit is: rad; r is the yaw rate of the vehicle, unit: rad/s;
under small angle assumptions and using a linear tire model:
Figure FDA0003274115540000012
in the formula, CfTire cornering stiffness for a front wheel of a vehicle, unit: n · rad; crTire cornering stiffness for a rear wheel of a vehicle, unit: n · rad; alpha is alphafIs the tire slip angle of the front wheel of the vehicle, unit: rad; alpha is alpharIs the tire slip angle of the rear wheel of the vehicle, unit: rad;
the slip angle of the tire is calculated using the longitudinal speed and the lateral speed as:
Figure FDA0003274115540000013
the dynamic model of the vehicle can be obtained through arrangement:
Figure FDA0003274115540000021
(2) modeling the main vehicle kinematics:
the motion of the vehicle is described mathematically, taking into account only the geometric relationships of the vehicle systems:
Figure FDA0003274115540000022
in the formula, xoIs the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y isoIs the lateral position of the vehicle mass center o under the inertial system, the unit: m; r is the yaw rate of the vehicle, unit: rad/s;
Figure FDA0003274115540000023
vehicle yaw angle, unit: rad;
the analysis of the vehicle steering motion can obtain the component of the motion acceleration of the vehicle mass center in the vehicle body coordinate system:
Figure FDA0003274115540000024
and (3) arranging to obtain a kinematic model of the vehicle:
Figure FDA0003274115540000025
(3) establishing a model of the dynamics and kinematics of the main vehicle
And (3) arranging the main vehicle dynamics model and the kinematics model to obtain the main vehicle dynamics and kinematics model:
Figure FDA0003274115540000031
vxis the longitudinal speed under the coordinate system of the vehicle body, and the unit is as follows: m/s; v. ofyLateral speed in the coordinate system of the vehicle body is shown as the following unit: m/s;
Figure FDA0003274115540000032
yaw angle of the vehicle, unit: rad; r isYaw rate of the vehicle, unit: rad/s; deltafIs the front wheel angle of the vehicle, unit: rad; a isxIs the inertial acceleration of the vehicle's center of mass in the x-axis direction, called longitudinal acceleration, in units: m/s2；ayIs the inertial acceleration of the vehicle's center of mass in the y-axis direction, called lateral acceleration, in units: m/s2；x0Is the longitudinal position of the vehicle mass center o in the inertial system, the unit: m; y is0Is the lateral position of the vehicle mass center o under the inertial system, the unit: m; i iszIs the moment of inertia of the vehicle about the z-axis, in units: kg m2(ii) a a is the distance from the vehicle centroid o to the vehicle front axle, in units: m; b is the distance from the vehicle centroid o to the vehicle rear axle, in units: m; m is the mass of the vehicle, in units: kg;
selecting
Figure FDA0003274115540000033
Selecting front wheel steering angle delta as system state variablefAnd longitudinal acceleration axAs a system control input, equation (8) is expressed as:
Figure FDA0003274115540000034
at an arbitrary point (x)r，ur) Performing Taylor expansion nearby, keeping a first-order term, and performing linearization to obtain:
Figure FDA0003274115540000035
wherein Jf(x) And Jf(u) Jacobian matrices of f versus x and u, respectively, for the linearized time-varying system described above, written as:
Figure FDA0003274115540000041
wherein Δ x ═ x-xr，Δu＝u-ur，Ac(t) and Bc(t) is a Jacobian matrix, which is expressed as follows
Figure FDA0003274115540000042
Figure FDA0003274115540000043
Step two, dividing the driving lane area of the vehicle
Taking two lanes as an example, the sensing module scans the road environment to obtain a road boundary line f1(x)、f2(x) And f3(x) Dividing the road into lane areas, L1Is 1 lane, i.e. f1(x) And f2(x) Road area within range, L2Is 2 lanes, i.e. f2(x) And f3(x) Road area within range, L12' is an inter-lane region, L1′、L2' is the area in the lane, d is the vehicle width, and the mathematical description is:
Figure FDA0003274115540000044
step three, establishing a road environment model based on the regional virtual force field:
considering the area division in the step two and establishing an area virtual force field by the obstacle vehicles, wherein the area virtual force field comprises a virtual rectangular repulsion field and a lane keeping area virtual gravitational field which are arranged around the obstacle vehicles along the road direction;
1) lane area keeping virtual gravitational field:
the lane area-keeping virtual gravitational field comprises two parts, one part is the gravitational force F for driving the vehicle in the road area1The other part is the gravity F for making the vehicle to run in the lane as much as possible2Gravitational force F1And gravitational force F2The force of (d) is defined as:
Figure FDA0003274115540000051
in the formula (d)roadIs the width of the area in the lane, unit: m; ddeIs the distance of the host vehicle from the lane area, unit: m; v is the host vehicle speed, unit: m/s; lambda [ alpha ]i,κiTo adjust the factor, λiDetermining the magnitude of the applied force, κiDetermining the change speed of the acting force;
virtual gravitational field f of lane keeping areahIs defined as:
Figure FDA0003274115540000052
2) virtual rectangular repulsive field of barrier vehicle:
in order to avoid collision between the main vehicle and the obstacle vehicle, a virtual rectangular repulsive field of the obstacle vehicle is established, and an influence area D of the virtual rectangular repulsive field of the obstacle vehicle is defined by Ds1、Ds2And Ds3Three parameters were determined, defined as:
Figure FDA0003274115540000053
in the formula (d)0For a safe distance, aObsIs the average braking acceleration of the obstacle vehicle, ahostAverage braking acceleration of the main vehicle, Ts1、Ts2And Ts3Is a weight coefficient;
the obstacle vehicle virtual rectangular repulsive force is defined as:
Figure FDA0003274115540000061
in the formula, vObs(j) Representing the speed, x, of the jth obstacle vehicleObs(j) Represents the longitudinal position of the jth obstacle vehicle, yObs(j) Representing the lateral position of the jth obstacle vehicle, D being obstacle vehicleRegion of influence, η, of a virtual rectangular repulsive field1、η2And η3To regulate the factor, η1Determining the emergency degree and eta of the potential energy change of the dynamic rectangular virtual repulsive force field of the obstacle vehicle2Representing the degree of correlation, eta, of potential energy change with relative velocity3Representing the degree of correlation of potential energy change with relative position;
step four, designing a model predictive controller by using the road environment model based on the regional virtual force field established in the step three:
discretizing the linear system obtained in the step one to obtain an incremental state space model:
Figure FDA0003274115540000062
wherein the content of the first and second substances,
Figure FDA0003274115540000063
Figure FDA0003274115540000064
t is the discrete system sampling time, Δ x (k) ═ x (k) — x (k-1), Δ u (k) ═ u (k) — u (k-1);
supposing that the prediction time domain is P, the control time domain is M and M is less than or equal to P, supposing that the control quantity outside the control time domain is kept unchanged, and deducing the output Y at the moment k based on the measurement information of the current moment and the historical information of the process according to the basic principle of model prediction controlPThe prediction equation for (k +1) and state X (k +1) is:
Figure FDA0003274115540000065
wherein the content of the first and second substances,
Figure FDA0003274115540000071
Figure FDA0003274115540000072
in summary, the optimization problem is as follows:
Figure FDA0003274115540000073
satisfies the following conditions:
Figure FDA0003274115540000074
wherein J is an objective function of the optimization function; v (i) represents the predicted velocity of the host vehicle at step i, in units: m/s; f. ofx(i) Is the longitudinal gravity of the predicted position of the ith step of the host vehicle, fy(i) Is the lateral gravity of the predicted position of the ith step of the main vehicle; lambda1,Λ2,Λ3,Λ4Weighting factors added for balancing each target respectively; deltafmaxThe maximum value of the turning angle of the front wheels,
Figure FDA0003274115540000075
maximum value of front wheel steering angle change rate, unit: rad; a isxmaxIs the maximum value of the longitudinal acceleration and,
Figure FDA0003274115540000076
maximum longitudinal acceleration rate, unit: m/s2(ii) a T is discrete system sampling time;
according to the principle of model predictive control, a first group of control quantities (delta) of a control sequence U obtained by solving an optimization problem is selectedf,ax) And the control input is used as the control input of the tracking controller, the control input is acted on the controlled vehicle, and the optimization problem is solved again according to the vehicle state information at the current moment at the next moment to obtain a new optimal control sequence, so that the rolling optimization control of the vehicle is realized.
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