CN108569336B - Steering control method based on vehicle kinematic model under dynamic constraint - Google Patents

Steering control method based on vehicle kinematic model under dynamic constraint Download PDF

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CN108569336B
CN108569336B CN201810386112.3A CN201810386112A CN108569336B CN 108569336 B CN108569336 B CN 108569336B CN 201810386112 A CN201810386112 A CN 201810386112A CN 108569336 B CN108569336 B CN 108569336B
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vehicle
control
slip angle
tire slip
model
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CN108569336A (en
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褚端峰
刘世东
高策
吴超仲
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Wuhan University of Technology WUT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D6/00—Arrangements for automatically controlling steering depending on driving conditions sensed and responded to, e.g. control circuits

Abstract

The invention discloses a vehicle kinematics model based steering control method under dynamic constraint, firstly, performing kinematics modeling on a vehicle model, and then performing linear discretization on a vehicle kinematics differential equation, because a model prediction control algorithm is generally a sampling control algorithm, and a computer is also discrete during optimization solution; and finally, designing an objective function and constraint, and converting the objective function into a standard quadratic form for solving. Compared with the prior art that the dynamic constraint model is used as a prediction model, the dynamic constraint parameter is converted into the control expression derived by using the kinematic model, and the design method of the controller considering the dynamic constraint avoids the problems of sideslip and rollover of the vehicle under the high-speed condition, so that the tracking accuracy and stability of the kinematic model can be ensured under the high-speed condition.

Description

Steering control method based on vehicle kinematic model under dynamic constraint
Technical Field
The invention belongs to the technical field of automobile safety, and particularly relates to a vehicle kinematics model-based steering control method under dynamic constraint.
Background
The models describing the vehicle operating state can be classified according to specific functions as follows: the vehicle dynamic characteristic is more prominent at low speed according to related researches on a kinematic model and a dynamic model; at high speeds, the dynamics of the vehicle are more prominent. In practical application, the increase of the complexity of the model cannot bring about the improvement of the accuracy generally, but leads to the reduction of the real-time performance of the algorithm, and the establishment of a reasonable vehicle system model is not only a premise of designing a model predictive controller, but also a basis for realizing a vehicle road tracking function. How to consider the dynamics constraint on the basis of using a simple kinematics model is significant, so that the kinematics model can still ensure the tracking accuracy at a higher speed.
Disclosure of Invention
The invention aims to solve the technical problem of providing a vehicle kinematics model based steering control method under dynamics constraint, reasonably establishing a vehicle kinematics model, taking the kinematics model as a prediction model, designing a controller based on a model prediction control algorithm, considering the dynamics constraint on the basis of constraining a control quantity and a control increment through linear discretization and designing an objective function, and finally solving the objective function to ensure that the vehicle can still realize accurate track tracking at high speed.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method comprises the following steps of firstly, obtaining vehicle structure parameter information and vehicle running state information, carrying out vehicle kinematics modeling,
Figure GDA0002223059210000011
wherein: (x, y) is the coordinate of the center of the rear axle of the vehicle, theta is the course angle of the vehicle, omega is the yaw velocity, v is the longitudinal velocity of the center of the rear axle of the vehicle, the vehicle kinematic model is used as a prediction model, and the state quantity is selected
Figure GDA0002223059210000021
Selecting a control quantity
Figure GDA0002223059210000022
The above-mentioned vehicle kinematic differential equation is expressed as:
Figure GDA0002223059210000023
step two, for a reference track planned by a planning layer, each point on the reference track needs to satisfy the vehicle kinematic differential equation, and a subscript r represents a point on the reference track, so that the reference track can be represented as follows:
Figure GDA0002223059210000024
wherein:
Figure GDA0002223059210000025
after a Taylor series formula is adopted to expand a vehicle kinematic differential equation to a first derivative term (neglecting the high-order term) at any reference track point, a linear discretization equation can be obtained:
Figure GDA0002223059210000026
wherein:
Figure GDA0002223059210000027
Figure GDA0002223059210000028
t is the sampling time, vrIs the longitudinal velocity at the reference trajectory point; thetarThe longitudinal speed and course angle at the reference track point, and t represents the current moment; k represents the kth step after the current time;
step three, designing a target function:
in order to ensure that the unmanned vehicle accurately and stably tracks the expected track, the state quantity, the control quantity and the control quantity increment of the system need to be optimized, the following objective functions are selected,
Figure GDA0002223059210000029
wherein:
Figure GDA00022230592100000210
n represents a control time domain (i.e., a prediction time domain); q represents the weight of the state quantity and control quantity set; r represents a controlled increase
A weight of the quantity; ρ represents a weight coefficient; represents a relaxation factor; i represents the ith step after the current time;
and step four, obtaining a tire slip angle expression of the vehicle, and representing the tire slip angle by using a control quantity, wherein the unknown number of the target function is a control increment, so that the tire slip angle is represented by using the control increment and then directly used for the target function.
The method comprises the steps of designing a MPC controller, wherein the MPC controller has the advantages of being capable of processing various constraints, considering dynamic constraints on the basis of control quantity limit value constraints and control increment limit value constraints in a control process, particularly tire slip angle constraints, representing a parameter in a control quantity form or directly in a control increment form, and verifying a controller, wherein the verification controller needs to carry out simulation verification on a designed steering controller through the steps and the derivation of a control algorithm, and is verified through building a Carsim/Simulink combined simulation platform, wherein Carsim is simulation software specially used for modeling a vehicle model and building a working condition, Simulink is simulation specially used for a submodule of MAT L AB, and the designed controller is analyzed and verified through using the simulation platform.
According to the technical scheme, in the fourth step, the expression of the tire slip angle specifically comprises the following steps:
Figure GDA0002223059210000031
wherein α represents a tire slip angle, a front wheel steering angle, and vyRepresents the lateral velocity; v. ofxRepresents the longitudinal speed; omega
Representing a yaw rate; a represents the distance of the front axle from the centroid.
According to the technical scheme, in the fourth step, the tire slip angle is represented by the control quantity, and the method specifically comprises the following steps:
Figure GDA0002223059210000032
in the formula, αmaxRepresenting the upper limit of the tire slip angle αminRepresents the lower limit of the tire slip angle.
According to the technical scheme, in the fourth step, the control quantity is converted into a control increment, and the tire slip angle constraint is calculated, wherein the method specifically comprises the following steps:
Umin≤AΔUt+Ut-1≤Umax
in the formula (I), the compound is shown in the specification,
Figure GDA0002223059210000033
Umin,Umaxrepresenting a set of controlled variables, Ut-1A set of control amount components at the last time is shown,
Figure GDA0002223059210000034
representing column vectors with the number of rows Nc, which is the control time domain; i ismRepresenting an identity matrix of dimension m.
According to the technical scheme, the objective function is simplified into a standard quadratic form, and an algorithm is used for solving to obtain the system output in the control domain:
Figure GDA0002223059210000035
in the formula (I), the compound is shown in the specification,
Figure GDA0002223059210000036
represents the set of optimal system outputs computed within the control domain,
Figure GDA0002223059210000037
indicating the optimal output of the first step in the control domain.
According to the technical scheme, in the first step, the vehicle structure parameter information comprises a vehicle wheel base, and the vehicle running state information comprises a vehicle speed and a course angle.
Considering the dynamic constraints on the basis of constraints on the control quantities and control increments should satisfy the following requirements in 3 respects:
(1) the ultimate goal of autonomous driving is to enable the vehicle to safely track the driver's desired trajectory, which requires that the vehicle still ensure accurate trajectory tracking at higher speeds.
(2) The model predictive control algorithm has the advantages that the constraint can be freely designed, but the constraint on which parameters needs to be considered whether the parameters can be converted into a control increment form or not.
(3) The limit value of the restraint is reasonably designed, and the restraint value is required to be ensured within the running limit value of the vehicle.
In conclusion, the invention designs the controller of the unmanned vehicle, considers the vehicle dynamics constraint when using a simple kinematics model, ensures that the unmanned vehicle can still ensure the tracking effect at higher speed, and designs the unmanned vehicle control system aiming at the expressway.
The invention has the following beneficial effects: the invention discloses a steering control method based on a vehicle kinematic model under dynamic constraint, which is based on a model predictive control algorithm and aims at solving the problem that the vehicle cannot ensure the tracking accuracy at a higher speed under the condition of using the kinematic model. The invention comprehensively considers the kinematic characteristics and the dynamic characteristics of the automobile and utilizes the kinetic theory of the automobile to analyze the tire slip angle of the automobile. Compared with the existing pure kinematics model trajectory tracking calculation method, the method has the advantages of high calculation speed and high reliability.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic diagram of a vehicle kinematics model-based steering control method under dynamic constraints in accordance with an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In the embodiment of the invention, as shown in fig. 1, a vehicle kinematics model based steering control method under dynamic constraint is provided, which comprises the following steps of firstly, obtaining vehicle structure parameter information and vehicle running state information, carrying out vehicle kinematics modeling,
Figure GDA0002223059210000041
wherein: (x, y) are coordinates of the center of the rear axle of the vehicle, theta is the heading angle of the vehicle, omega is the yaw rate, and v isSelecting the state quantity by using the vehicle kinematic model as a prediction model
Figure GDA0002223059210000051
Selecting a control quantity
Figure GDA0002223059210000052
The above-mentioned vehicle kinematic differential equation is expressed as:
Figure GDA0002223059210000053
step two, for a reference track planned by a planning layer, each point on the reference track needs to satisfy the vehicle kinematic differential equation, and a subscript r represents a point on the reference track, so that the reference track can be represented as follows:
Figure GDA0002223059210000054
wherein:
Figure GDA0002223059210000055
after a Taylor series formula is adopted to expand a vehicle kinematic differential equation to a first derivative term (neglecting the high-order term) at any reference track point, a linear discretization equation can be obtained:
Figure GDA0002223059210000056
wherein:
Figure GDA0002223059210000057
Figure GDA0002223059210000058
t is the sampling time, vrIs the longitudinal velocity at the reference trajectory point; thetarThe longitudinal speed and course angle at the reference track point, and t represents the current moment; k represents the current timeStep k after carving;
step three, designing a target function:
in order to ensure that the unmanned vehicle accurately and stably tracks the expected track, the state quantity, the control quantity and the control quantity increment of the system need to be optimized, the following objective functions are selected,
Figure GDA0002223059210000059
wherein:
Figure GDA00022230592100000510
n represents a control time domain (i.e., a prediction time domain); q represents the weight of the state quantity and control quantity set; r represents the weight of the control increment; ρ represents a weight coefficient; represents a relaxation factor; i represents the ith step after the current time;
and step four, obtaining a tire slip angle expression of the vehicle, and representing the tire slip angle by using a control quantity, wherein the unknown number of the target function is a control increment, so that the tire slip angle is represented by using the control increment and then directly used for the target function.
The method comprises the steps of designing a MPC controller, wherein the MPC controller has the advantages of being capable of processing various constraints, considering dynamic constraints on the basis of control quantity limit value constraints and control increment limit value constraints in a control process, particularly tire slip angle constraints, representing a parameter in a control quantity form or directly in a control increment form, and verifying a controller, wherein the verification controller needs to carry out simulation verification on a designed steering controller through the steps and the derivation of a control algorithm, and is verified through building a Carsim/Simulink combined simulation platform, wherein Carsim is simulation software specially used for modeling a vehicle model and building a working condition, Simulink is simulation specially used for a submodule of MAT L AB, and the designed controller is analyzed and verified through using the simulation platform.
Further, in the fourth step, the expression of the tire slip angle specifically includes:
Figure GDA0002223059210000061
wherein α represents a tire slip angle, a front wheel steering angle, and vyRepresents the lateral velocity; v. ofxRepresents the longitudinal speed; omega
Representing a yaw rate; a represents the distance of the front axle from the centroid.
Further, in the fourth step, the tire slip angle is expressed by a control quantity, specifically:
Figure GDA0002223059210000062
in the formula, αmaxRepresenting the upper limit of the tire slip angle αminRepresents the lower limit of the tire slip angle.
Further, in the fourth step, the control quantity is converted into a control increment, and the tire slip angle constraint is calculated, specifically:
Umin≤AΔUt+Ut-1≤Umax
in the formula (I), the compound is shown in the specification,
Figure GDA0002223059210000063
Umin,Umaxrepresenting a set of controlled variables, Ut-1A set of control amount components at the previous time is shown.
Further, the objective function is simplified into a standard quadratic form, and an algorithm is used for solving to obtain the system output in the control domain:
Figure GDA0002223059210000064
in the formula (I), the compound is shown in the specification,
Figure GDA0002223059210000065
representing the optimal system output calculated in the control domainIn the collection of the images, the image data is collected,
Figure GDA0002223059210000066
indicating the optimal output of the first step in the control domain.
Further, in the first step, the vehicle structure parameter information includes a vehicle wheel base, and the vehicle operation state information includes a vehicle speed and a heading angle.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (6)

1. A steering control method based on a vehicle kinematic model under dynamic constraint is characterized by comprising the following steps of obtaining vehicle structure parameter information and vehicle running state information, carrying out vehicle kinematic modeling,
Figure FDA0002478726460000011
wherein: (x, y) is the coordinate of the center of the rear axle of the vehicle, theta is the course angle of the vehicle, omega is the yaw velocity, v is the longitudinal velocity of the center of the rear axle of the vehicle, the vehicle kinematic model is used as a prediction model, and the state quantity is selected
Figure FDA0002478726460000012
Selecting a control quantity
Figure FDA0002478726460000013
The above-mentioned vehicle kinematic differential equation is expressed as:
Figure FDA0002478726460000014
step two, for a reference track planned by a planning layer, each point on the reference track needs to satisfy the vehicle kinematic differential equation, and a subscript r represents a point on the reference track, so that the reference track can be represented as follows:
Figure FDA0002478726460000015
wherein:
Figure FDA0002478726460000016
after the vehicle kinematic differential equation is expanded to a first derivative term at any reference track point by adopting a Taylor series formula, a linear discretization equation can be obtained:
Figure FDA0002478726460000017
wherein:
Figure FDA0002478726460000018
Figure FDA0002478726460000019
t is the sampling time, vrIs the longitudinal velocity at the reference trajectory point; thetarThe longitudinal speed and course angle at the reference track point, and t represents the current moment; k represents the kth step after the current time;
step three, designing a target function:
the following objective function is chosen and,
Figure FDA00024787264600000110
wherein:
Figure FDA0002478726460000021
n represents a control time domain; q represents the weight of the state quantity and control quantity set; r represents the weight of the control increment; ρ represents a weight coefficient; represents a relaxation factor; i represents the ith step after the current time;
and step four, obtaining a tire slip angle expression of the vehicle, expressing the tire slip angle by using a control quantity, expressing the tire slip angle by using a control increment, and directly using the tire slip angle in the objective function.
2. The vehicle kinematic model based steering control method under dynamic constraints according to claim 1, wherein in the fourth step, the expression of the tire slip angle is specifically as follows:
Figure FDA0002478726460000022
wherein α represents a tire slip angle, a front wheel steering angle, and vyRepresents the lateral velocity; v. ofxRepresents the longitudinal speed; ω represents yaw rate; a represents the distance of the front axle from the centroid.
3. The vehicle kinematic model based steering control method under dynamic constraints according to claim 2, wherein in the fourth step, the tire slip angle is expressed by a control quantity, specifically:
Figure FDA0002478726460000023
in the formula, αmaxRepresenting the upper limit of the tire slip angle αminRepresents the lower limit of the tire slip angle.
4. The vehicle kinematic model based steering control method under the dynamic constraint according to claim 3, wherein in the fourth step, the control quantity is converted into a control increment to calculate the tire slip angle constraint, specifically:
Umin≤AΔUt+Ut-1≤Umax
in the formula (I), the compound is shown in the specification,
Figure FDA0002478726460000024
Umin,Umaxrepresenting a set of controlled variables, Ut-1A set of control amount components at the last time is shown,
Figure FDA0002478726460000025
representing column vectors with the number of rows Nc, which is the control time domain; i ismAn identity matrix with dimension m, m being the dimension of the control quantity, in particular [ v, ω]2 dimensions of (a).
5. The vehicle kinematics model-based steering control method under dynamic constraints of claim 4, wherein the objective function is reduced to a standard quadratic form and solved using an algorithm to obtain the system output within the control domain:
Figure FDA0002478726460000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002478726460000032
represents the set of optimal system outputs computed within the control domain,
Figure FDA0002478726460000033
indicating the optimal output of the first step in the control domain.
6. The steering control method based on the vehicle kinematic model under the dynamic constraint according to claim 1 or 2, characterized in that in the first step, the vehicle structure parameter information comprises a vehicle wheel base, and the vehicle running state information comprises a vehicle speed and a heading angle.
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