CN113276813B - Method and device for correcting wheel slip ratio, electronic device, and medium - Google Patents
Method and device for correcting wheel slip ratio, electronic device, and medium Download PDFInfo
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- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
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Abstract
The present invention relates to the field of vehicle control, and in particular, to a method and an apparatus for correcting a wheel slip ratio, an electronic device, and a medium. The wheel slip ratio correction method comprises the following steps: building a 4+2 n-degree-of-freedom complete vehicle dynamics model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the side tilting direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom; determining vertical motion displacement and reference vehicle speed of each wheel based on a state observer and the whole vehicle dynamics model; and based on the principle of sliding mode control, taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip rate as input, and outputting the corrected braking torque of each wheel. The method can effectively correct and control the wheel slip rate under the bumpy road surface, improve the emergency braking strength and improve the driving safety.
Description
Technical Field
The present invention relates to the field of vehicle control, and in particular, to a method and an apparatus for correcting a wheel slip ratio, an electronic device, and a medium.
Background
Wheel slip rate control is a guarantee of automobile braking safety, common wheel slip rate control methods include a threshold method, a PID (proportional, Integral, Differential) method, a sliding mode control method and the like, and good control effects are achieved. However, when an automobile is emergently braked on a bumpy road surface, due to the fact that wheels jump up and down, in order to ensure that the wheel slip ratio is in an ideal range, a traditional wheel slip ratio control method can frequently apply pressurization and depressurization commands to a brake system, so that the brake force is insufficient, and even dangerous accidents are induced. Therefore, it is very important to design a wheel slip ratio correction control method under a bumpy road surface to improve the emergency braking strength.
In view of the above, the present invention is particularly proposed.
Disclosure of Invention
The invention aims to provide a method, a device, electronic equipment and a medium for correcting the wheel slip rate, wherein the method can effectively correct and control the wheel slip rate under a bumpy road surface, improve the emergency braking strength and improve the driving safety.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, the present invention provides a method for correcting a wheel slip ratio, comprising the steps of:
building a 4+2 n-degree-of-freedom complete vehicle dynamics model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the side tilting direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom;
determining vertical motion displacement and reference vehicle speed of each wheel based on a state observer and the whole vehicle dynamics model;
and based on the principle of sliding mode control, taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip rate as input, and outputting the corrected braking torque of each wheel.
As a further preferable technical solution, the building of the 4+2 n-degree-of-freedom complete vehicle dynamics model includes:
determining a whole vehicle dynamic model with 1+ n degrees of freedom of a vehicle body vertical direction and n wheel vertical directions according to the sprung mass, the wheel mass, the vehicle mass center vertical displacement, the wheel vertical motion displacement, the vertical unevenness of the ground and the suspension force;
determining a whole vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body rolling according to the rotational inertia of the vehicle body around the y axis, the rotational inertia of the vehicle body around the x axis, the vehicle body pitch angle acceleration, the vehicle body roll angle acceleration, the vehicle body longitudinal acceleration, the vehicle body lateral acceleration, the vertical distance from the vehicle mass center to the pitching center and the vertical distance from the vehicle mass center to the rolling center;
determining a whole vehicle dynamic model with one degree of freedom in the longitudinal direction of the vehicle body according to the mass of the whole vehicle, the longitudinal acceleration of the vehicle body and the longitudinal reaction force of the ground on each wheel;
determining a whole vehicle dynamic model with n degrees of freedom of rotation of n wheels according to the moment of inertia of the wheels, the rotating angular speed of the wheels, the longitudinal reaction force of the ground to the wheels, the braking moment of the wheels and the rolling radius of the wheels;
and determining the 4+2 n-degree-of-freedom complete vehicle dynamic model according to the complete vehicle dynamic model with 1+ n degrees of freedom of the vertical vehicle body and the vertical n wheels, the complete vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body side tilting, the complete vehicle dynamic model with one degree of freedom of the longitudinal vehicle body and the complete vehicle dynamic model with n degrees of freedom of the rotation of the n wheels.
As a further preferred technical solution, the determining the vertical movement displacement of each wheel and the reference vehicle speed based on the state observer and the entire vehicle dynamics model includes:
based on a state observer, carrying out state observation on the vertical displacement of the mass center of the vehicle, the pitch angle of the vehicle body and the roll angle of the vehicle body to obtain an observed value;
determining vertical movement displacement of each wheel according to the whole vehicle dynamic model, the observed value and the dynamic stroke of each suspension;
and determining the reference vehicle speed according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body, the angular acceleration of each wheel and the vertical motion displacement of each wheel on the basis of the state observer.
As a further preferable technical solution, the outputting the braking torque of each wheel by using the vertical movement displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel, and the target slip ratio as inputs based on the principle of sliding mode control includes:
determining a braking moment expression of each wheel according to the vertical movement displacement of each wheel;
and determining the corrected braking torque of each wheel according to the braking torque expression of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio based on the principle of sliding mode control.
As a further preferable technical solution, the determining the braking torque expression of each wheel according to the vertical movement displacement of each wheel includes:
determining the relationship between the vertical motion displacement of each wheel and a correction threshold according to the vertical motion displacement of each wheel, and whether each wheel jumps off the ground;
and determining the braking torque expression of each wheel according to the relationship and whether each wheel jumps away from the ground.
As a further preferable technical solution, determining each wheel braking torque expression according to the relationship and whether each wheel jumps off the ground includes:
if the vertical movement displacement of the wheel is lower than the correction threshold, determining that the wheel braking torque expression is a basic braking torque; the basic braking torque is based on a sliding mode control principle, and the basic braking torque is output by taking the reference vehicle speed, the wheel speed of a wheel and the target slip ratio as input;
if the vertical movement displacement of the wheel is larger than the correction threshold and the wheel does not jump off the ground, determining a wheel braking torque expression according to the basic braking torque, the maximum braking torque allowed by the vehicle, the vertical movement displacement of the wheel and the correction coefficient;
and if the wheel jumps away from the ground, determining a wheel braking torque expression according to the basic braking torque, the maximum allowable braking torque of the vehicle, the static radius of the wheel, the rolling radius of the wheel and the correction coefficient.
As a further preferable technical solution, the braking torque of each wheel is:
if the vertical movement displacement of the wheel is less than or equal to the correction threshold, the braking torque of the wheel is the basic braking torque;
if the vertical movement displacement of the wheel is larger than the correction threshold and the wheel does not jump off the ground, the braking torque of the wheel is the sum of the basic braking torque and a first correction torque, and the first correction torque is the product of the vertical movement displacement of the wheel, a correction coefficient and the maximum allowable braking torque of the vehicle;
if the wheel jumps off the ground, the wheel braking torque is the sum of the basic braking torque and a second correction torque, which is the product of the value of the wheel resting radius minus the wheel rolling radius, the correction factor and the maximum braking torque allowed by the vehicle.
In a second aspect, the present invention provides a wheel slip ratio correction apparatus comprising:
the dynamic model building module is used for building a 4+2 n-degree-of-freedom vehicle dynamic model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the heeling direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom;
the wheel vertical motion displacement and reference vehicle speed determining module is used for determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamic model;
and the braking torque output module is used for outputting the corrected braking torque of each wheel by taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip rate as input on the basis of the principle of sliding mode control.
In a third aspect, the present invention provides an electronic device, comprising:
at least one processor, and a memory communicatively coupled to at least one of the processors;
wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method described above.
In a fourth aspect, the present invention provides a medium having stored thereon computer instructions for causing the computer to perform the method described above.
Compared with the prior art, the invention has the beneficial effects that:
according to the method for correcting the wheel slip rate, a 4+2 n-degree-of-freedom complete vehicle dynamic model is built, only the four degrees of freedom of the vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the rolling direction and n degrees of freedom of rotation of n wheels are considered in a general dynamic model, so that the method is only suitable for the situation of running on a flat road surface, and the n degrees of freedom of the vertical direction of the n wheels are also considered in the complete vehicle dynamic model, so that the method is not only suitable for the situation of running on the flat road surface, but also is particularly suitable for the situation of running on a bumpy road surface. And secondly, determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamics model, so that the obtained vertical motion displacement and the reference vehicle speed of each wheel are more accurate and reliable, and the vertical motion displacement and the reference vehicle speed of each wheel are used as reference quantities for wheel slip rate correction control. And finally, outputting the corrected braking torque based on the principle of sliding mode control, thereby realizing the reliable control of the slip rate of the vehicle in the emergency braking process under the road surface (particularly the bumpy road surface), controlling the actual slip rate near the target slip rate, improving the emergency braking strength, avoiding the occurrence of dangerous accidents caused by insufficient braking force and ensuring the braking safety.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a flowchart of a wheel slip ratio correction method provided in embodiment 1;
FIG. 2 is a schematic diagram of a vehicle dynamics model provided in embodiment 1;
FIG. 3 is a flowchart of a wheel slip ratio correction method provided in embodiment 2;
FIG. 4 is a schematic illustration of a brake dynamics model provided in embodiment 2;
FIG. 5 is a schematic configuration diagram of a wheel slip ratio correction apparatus provided in embodiment 3;
fig. 6 is a schematic structural diagram of an electronic device provided in embodiment 4.
Detailed Description
The following description of the exemplary embodiments of the present application, taken in conjunction with the accompanying drawings, includes various details of the embodiments of the application for the understanding of the same, which are to be considered exemplary only. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present application. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
It should be noted that the "wheel" in the present invention refers to a tire, a rim, and a spoke combined together. "vertical" refers to a direction perpendicular to the direction of travel of the vehicle. "longitudinal" means in the direction of vehicle travel.
Example 1
Fig. 1 is a flowchart of a wheel slip ratio correction method according to an embodiment, which is suitable for correcting a wheel slip ratio during a vehicle running process. The method may be performed by a wheel slip ratio correction device, which may be constituted by software and/or hardware, and is generally integrated in an electronic device.
Referring to fig. 1, the method for correcting the wheel slip ratio includes the following steps:
s110, a 4+2 n-degree-of-freedom vehicle dynamics model is built, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the heeling direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom.
It is to be understood that n is a natural number greater than or equal to 4, preferably an even number, e.g. 4, 6, 8, etc. The "whole vehicle dynamics model" is also referred to as a whole vehicle dynamics equation, and is used for calculating parameters of unknown values in the equation according to the parameters of the known values in the equation. Illustratively, if the equation is F = ma, the value of F can be calculated from the equation if the values of m and a are known, and similarly, the value of a can be calculated from the equation if F and m are known.
Preferably, the building of the 4+2 n-degree-of-freedom whole vehicle dynamic model comprises:
determining a whole vehicle dynamic model with 1+ n degrees of freedom of a vehicle body vertical direction and n wheel vertical directions according to the sprung mass, the wheel mass, the vehicle mass center vertical displacement, the wheel vertical motion displacement, the vertical unevenness of the ground and the suspension force;
determining a whole vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body rolling according to the rotational inertia of the vehicle body around the y axis, the rotational inertia of the vehicle body around the x axis, the vehicle body pitch angle acceleration, the vehicle body roll angle acceleration, the vehicle body longitudinal acceleration, the vehicle body lateral acceleration, the vertical distance from the vehicle mass center to the pitching center and the vertical distance from the vehicle mass center to the rolling center;
determining a whole vehicle dynamic model with one degree of freedom in the longitudinal direction of the vehicle body according to the mass of the whole vehicle, the longitudinal acceleration of the vehicle body and the longitudinal reaction force of the ground on each wheel;
determining a whole vehicle dynamic model with n degrees of freedom of rotation of n wheels according to the moment of inertia of the wheels, the rotating angular speed of the wheels, the longitudinal reaction force of the ground to the wheels, the braking moment of the wheels and the rolling radius of the wheels;
and determining the 4+2 n-degree-of-freedom complete vehicle dynamic model according to the complete vehicle dynamic model with 1+ n degrees of freedom of the vertical vehicle body and the vertical n wheels, the complete vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body side tilting, the complete vehicle dynamic model with one degree of freedom of the longitudinal vehicle body and the complete vehicle dynamic model with n degrees of freedom of the rotation of the n wheels. Where "sprung mass" refers to the mass in the vehicle that is supported by the resilient element in the suspension system. "vertical displacement of the vehicle center of mass" refers to the displacement of the vehicle center of mass in a vertical motion. The "wheel vertical motion displacement" refers to the displacement of the wheel performing vertical motion. "vertical unevenness of the ground" means unevenness of a road surface in a direction perpendicular to the traveling direction of the vehicle. "suspension force" refers to the force provided to the vehicle body by the suspension system. "moment of inertia of the body about the y-axis" refers to a measure of inertia of the sprung mass of the vehicle as it rotates about a first horizontal axis directed to the left of the driver, the first horizontal axis being parallel to the horizontal plane and directed to the left of the driver, the y-axis being the first horizontal axis directed to the left of the driver, if the driver is facing north, the y-axis being the first horizontal axis directed to west. "moment of inertia of the body about the x-axis" refers to a measure of inertia of the sprung mass of the vehicle when it is rotated about a second horizontal axis pointing in the direction of forward movement of the vehicle, the second horizontal axis being an axis parallel to the horizontal plane, the second horizontal axis pointing in the direction of forward movement of the vehicle, and the x-axis being the second horizontal axis pointing in the direction of forward movement of the vehicle. "vehicle body pitch acceleration" refers to the second order differential of the angle of rotation of the vehicle body about the first horizontal axis on the left of the driver, which is the axis parallel to the horizontal plane, with the first horizontal axis pointing to the left of the driver. The "vehicle body roll angle acceleration" refers to a second order differential value of the rotation angle of the vehicle body about a second horizontal axis in the vehicle advancing direction, the second horizontal axis being an axis parallel to the horizontal plane, the second horizontal axis being directed in the vehicle advancing direction. The "longitudinal acceleration of the vehicle body" refers to a first order differential value of the traveling speed of the vehicle in the forward direction. The "vehicle body lateral acceleration" refers to a first order differential value of the traveling speed of the vehicle along the left side of the driver. "ground-to-wheel longitudinal reaction force" refers to the component of the ground-to-wheel reaction force at the intersection of the wheel plane and the ground plane, which may be expressed as a non-linear function of slip rate.
Fig. 2 is a schematic diagram of a complete vehicle dynamics model built according to the embodiment.
The following describes a preferred 4+2n degree of freedom vehicle dynamics model using 4 wheels as an example:
preferably, the complete vehicle dynamics model of 1+ n degrees of freedom of the vehicle body vertical direction and the n wheel vertical directions is as follows:
wherein m issIs sprung mass, muiFor each wheel mass, z is the vertical displacement of the vehicle's centroid, zuiFor vertical movement displacement of each wheel, zriVertical unevenness of the respective ground, FiFor each wheel suspension force, F1Left front wheel suspension force, F2Left rear wheel suspension force, F3Is the right front wheel suspension force, F4Is the right rear wheel suspension force, g is the gravitational acceleration,k tithe vertical stiffness of each wheel.
The calculation of the suspension forces of the individual wheels is as follows:
wherein, FiFor each wheel suspension force, ksiIs the suspension stiffness coefficient, ciTo the damping coefficient of the suspension, FaiActive power for each air suspension, zsiFor vertical displacement of each suspension and body mounting point, zuiAnd vertically moving and displacing each wheel.
Preferably, the full vehicle dynamics model of the two degrees of freedom of body pitch and body roll is as follows:
wherein, IyIs the moment of inertia of the vehicle body about the y-axis, IxIs the moment of inertia of the vehicle body about the x-axis,
in order to accelerate the pitch angle of the vehicle body,
for vehicle body roll angular acceleration, axFor longitudinal acceleration of the vehicle body, ayAs lateral acceleration of the vehicle body, hpIs the vertical distance h from the center of mass of the vehicle to the center of pitchrIs the vertical distance from the center of mass of the vehicle to the center of roll, F1、F2、F3、F4The suspension forces of four wheels are respectively, g is the gravity acceleration, b is the distance from the center of mass of the whole vehicle to the rear axle, a is the distance from the center of mass of the whole vehicle to the front axle, and m issIs sprung mass, and B is the track width of the left and right front wheels of the vehicle.
Preferably, the complete vehicle dynamics model of n degrees of freedom for n wheel rotations is as follows:
wherein, IwiAs for the moment of inertia of each wheel,
for each wheel rotational angular velocity, FxwiFor the ground braking force to which each wheel is subjected, MbiR is the rolling radius of the wheel, which is the braking torque of each wheel.
Wherein the ground braking force F experienced by each wheelxwiThe calculation method of (c) is as follows:
Preferably, the whole vehicle dynamic model of one degree of freedom in the longitudinal direction of the vehicle body is as follows:
And S120, determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamic model.
Where "reference vehicle speed" refers to an estimate of the true longitudinal speed of the vehicle.
Preferably, the state observer is a kalman filter.
Preferably, the determining the vertical movement displacement of each wheel and the reference vehicle speed based on the state observer and the whole vehicle dynamics model comprises:
based on a state observer, carrying out state observation on the vertical displacement of the mass center of the vehicle, the pitch angle of the vehicle body and the roll angle of the vehicle body to obtain an observed value;
determining vertical movement displacement of each wheel according to the whole vehicle dynamic model, the observed value and the dynamic stroke of each suspension;
and determining the reference vehicle speed according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body, the angular acceleration of each wheel and the vertical motion displacement of each wheel on the basis of the state observer.
The optimal mode is based on the state observer, the observed value is obtained firstly, then the vertical motion displacement of each wheel is determined by combining the whole vehicle dynamic model and the dynamic stroke of each suspension, and the reference vehicle speed is determined based on the state observer. The vertical movement displacement and the reference vehicle speed of each wheel obtained by the method are accurate and reliable.
Where "suspension travel" refers to the relative displacement of the center of the sprung mass and the center of the unsprung mass, where the unsprung mass refers to the mass that is not supported by the spring elements in the suspension.
Specifically, based on the state observer, the state observation is carried out on the vertical displacement of the mass center of the vehicle, the pitch angle of the vehicle body and the roll angle of the vehicle body, and the acquisition of an observed value comprises the following steps:
the vehicle mass center vertical displacement observer is designed by adopting the following formula:
in the formula, xv,kRepresenting the state vector, x, of the observer of the centroid vertical displacement at the current momentv,k+1Representing the state vector, y, of the observer of the vertical displacement of the centroid at the next momentv,k+1Represents the observation vector u of the centroid vertical displacement observer at the next momentv,kAs an input vector, Av、Bv、CvRespectively representing the system matrix, the input matrix and the observation matrix of the centroid vertical displacement observer, qv,kIs process noise, rv,kTo observe noise, msIs sprung mass, F1、F2、F3、F4Four wheel suspension forces, g is gravitational acceleration, AVIn (1)TIn order to be the time of sampling,y km the measured value of the vertical displacement of the mass center of the whole vehicle at the current moment is obtained.
The pitch angle of the vehicle body is designed by adopting the following formula:
in the formula, xpIs a state vector, ypTo observe the vector, upAs an input vector, ApIs a system matrix, BpAs an input matrix, CpTo observe the matrix, qpIs process noise with variance Qp，rpTo observe noise, its variance is Rp，axmAnd
respectively the longitudinal acceleration and pitch angle speed m of the vehicle body measured by the sensorsIs sprung mass, hpIs the vertical distance from the center of mass of the vehicle to the center of pitch, IyIs the moment of inertia of the vehicle body about the y-axis, F1、F2、F3、F4Respectively four wheel suspension forces, phi is the pitch angle of the vehicle body, aymThe measured value of the transverse acceleration of the vehicle body is b, the distance from the center of mass of the whole vehicle to the rear axle is b, and the distance from the center of mass of the whole vehicle to the front axle is a.
The kalman filtering process is as follows:
(1) discretizing a state equation:
(8) in the formula (I), wherein,
where T is the sampling time, xp,kIs the state vector at the current time, xp,k+1Is the state vector, u, at the next time instantp,kAs input vector at the current time, qp,kAs a result of the process noise at the current time,Iis an identity matrix, APIs a system matrix, BPIs an input matrix.
(2) Initialization: setting an initial state
(9) (ii) a Initial covariance
（10）。
(3) And (3) time updating: further state prediction
(11) (ii) a Further prediction of covariance
(12). Wherein x isp,k|k-1Updating the vector for the prediction state, Ap,k-1For the system matrix at the last moment, Bp,k-1For the input matrix at the last moment, xp,k-1Is the state vector, u, at the previous momentp,k-1Is the input vector at the previous moment, Pk|k-1Is covariance, qp,k-1The process noise at the previous time.
(4) And (3) updating the state: filter gain
(13) In which C isp,kIs an observation matrix at the current time, rp,kThe observed noise at the current moment; covariance matrix update
(14) (ii) a Status update
(15) Wherein, yp,kIs the observation vector of the current moment.
The observation method of the roll angle of the vehicle body is consistent with the pitch angle of the vehicle body, and the detailed description is omitted here.
Specifically, according to the vehicle dynamics model, the observed value, and the dynamic travel of each suspension, determining the vertical movement displacement of each wheel includes:
and calculating the vertical motion displacement of each wheel by adopting the following formula:
Specifically, based on the state observer, determining the reference vehicle speed according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body, the angular acceleration of each wheel, and the vertical motion displacement of each wheel includes:
the reference vehicle speed is calculated according to the wheel speed of each wheel and the longitudinal acceleration of the vehicle body, and meanwhile, the confidence coefficient (which can also be understood as a weight, and the reference vehicle speed can be calculated according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body and the weight) of the longitudinal acceleration of the vehicle body is determined according to the angular acceleration of the wheel and the vertical motion state. And obtaining a reference vehicle speed observation value according to a maximum wheel speed method:
(17) in the formula (I), wherein,
the angular velocity of rotation of each wheel.
According to the longitudinal acceleration of the vehicle measured by the sensor and the kinematic relationship, a reference vehicle speed observer is designed as follows:
(18) (ii) a In the formula, the state vector
Observation vector
. In-process noise qsAnd observation noise rsAnd can be automatically adjusted according to the current vehicle state. The system matrix and the observation matrix are respectively:
whereinTIs the sampling time.
When the wheels are locked or the vertical jumping is large, the difference between the wheel speed and the vehicle speed is overlarge. And (4) adjusting the process noise and the measurement noise in real time by considering the acceleration of the wheel and the vertical motion state of the wheel. When the wheel is locked, the wheel speed is zero, and the confidence coefficient of the observed value is set to be zero at the moment; when the vertical displacement of the wheel is large, the wheel speed is changed greatly, and the wheel speed confidence coefficient is correspondingly reduced.
And S130, based on the principle of sliding mode control, taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed and the target slip rate of each wheel as input, and outputting the corrected braking torque of each wheel.
The "target slip ratio" refers to a slip ratio that the wheel is expected to achieve, and can be generally set empirically, such as 0.2.
From the reference vehicle speed and the wheel speed of the wheel, an actual slip rate of the wheel can be calculated, the actual slip rate = (reference vehicle speed-wheel speed of the wheel)/reference vehicle speed. According to the vertical movement displacement of each wheel, based on the principle of sliding mode control, the torque required to be applied when the actual slip ratio is controlled to be close to the target slip ratio is the required braking torque.
According to the wheel slip rate correction method, a 4+2 n-degree-of-freedom complete vehicle dynamic model is built, only the four degrees of freedom of the vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the rolling direction and n degrees of freedom of rotation of n wheels are considered in a general dynamic model, so that the method is only suitable for the situation of running on a flat road surface, and the complete vehicle dynamic model also considers n degrees of freedom of the n wheels in the vertical direction, so that the method is not only suitable for the situation of running on the flat road surface, but also is particularly suitable for the situation of running on a bumpy road surface. And secondly, determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamics model, so that the obtained vertical motion displacement and the reference vehicle speed of each wheel are more accurate and reliable, and the vertical motion displacement and the reference vehicle speed of each wheel are used as reference quantities for wheel slip rate correction control. And finally, outputting the corrected braking torque based on the principle of sliding mode control, thereby realizing the reliable control of the slip rate of the vehicle in the emergency braking process under the road surface (particularly the bumpy road surface), controlling the actual slip rate near the target slip rate, improving the emergency braking strength, avoiding the occurrence of dangerous accidents caused by insufficient braking force and ensuring the braking safety.
Example 2
As shown in fig. 3, the present embodiment provides another wheel slip ratio correction method, and is a further optimization of S130 in embodiment 1. Referring to fig. 3, the method comprises the steps of:
s110, a 4+2 n-degree-of-freedom vehicle dynamics model is built, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the heeling direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom.
And S120, determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamic model.
S110 and S120 are the same as those in embodiment 1, and are not described again here.
S131, determining a braking torque expression of each wheel according to the vertical movement displacement of each wheel.
Preferably, the determining the braking torque expression of each wheel according to the vertical movement displacement of each wheel comprises:
determining the relationship between the vertical motion displacement of each wheel and a correction threshold according to the vertical motion displacement of each wheel, and whether each wheel jumps off the ground;
and determining the braking torque expression of each wheel according to the relationship and whether each wheel jumps away from the ground.
In the preferred embodiment, the relationship between the vertical motion displacement of the wheel and a correction threshold (the correction threshold is a wheel vertical displacement threshold determined according to multiple simulation and test results when the braking torque calculated by the traditional sliding mode controller is corrected) is considered, whether the wheel jumps away from the ground is determined, and a braking torque expression is determined according to the relationship, wherein the expression division is scientific and reasonable, and the expressions corresponding to different bumping degrees are provided, so that the control is more accurate.
Preferably, determining each wheel braking torque expression based on the relationship and whether each wheel is jumping off the ground comprises:
if the vertical movement displacement of the wheel is lower than the correction threshold, determining that the wheel braking torque expression is a basic braking torque; the basic braking torque is based on a sliding mode control principle, and the basic braking torque is output by taking the reference vehicle speed, the wheel speed of a wheel and the target slip ratio as input;
if the vertical movement displacement of the wheel is larger than the correction threshold and the wheel does not jump off the ground, determining a wheel braking torque expression according to the basic braking torque, the maximum braking torque allowed by the vehicle, the vertical movement displacement of the wheel and the correction coefficient;
and if the wheel jumps away from the ground, determining a wheel braking torque expression according to the basic braking torque, the maximum allowable braking torque of the vehicle, the static radius of the wheel, the rolling radius of the wheel and the correction coefficient.
The maximum braking torque allowed by the vehicle is related to the vehicle type, and the vehicle leaving parameters are set.
When the vehicle runs on a bumpy road surface, if the wheels completely jump off the ground, the ground braking force is 0, and at the moment, if the ideal slip rate is still used for control, the target slip rate can be achieved only by applying extremely small braking pressure. When the wheels contact the ground again, the ground braking force increases, and the braking pressure needs to be increased in time to reach the target slip ratio. However, due to the hysteresis of the actual brake system, the wheel will jump off the ground again when the brake pressure has not yet reached the target value. The above steps are repeated in a circulating way, so that the situation of braking force loss during emergency braking under a bumpy road surface is easily caused. Therefore, preferably, the respective wheel braking torque expressions are as follows:
wherein M isbi ′For corrected individual wheel braking torque, MbiFor basic braking torque of each wheel, zuiFor each wheel vertical motion displacement, kappa is a correction coefficient (the correction coefficient refers to the ratio of the additionally applied braking torque to the tire vertical displacement, and the magnitude of the correction coefficient is determined according to multiple simulation and test results), R0Is the wheel resting radius and R is the wheel rolling radius.
When the wheel jumping amount is lower than the set correction threshold, braking is carried out by the braking torque (namely basic braking torque) calculated by the normal sliding mode controller; when the wheel jumping amount exceeds the correction threshold and the ground is not jumped off, the applied braking torque is linearly increased according to the wheel jumping amount; and when the wheel completely jumps away from the ground, braking by using the calculated maximum braking torque so as to realize quick response of the braking torque after the wheel contacts the ground again.
It will be appreciated that the vertical displacement of the wheel just as it jumps off the ground is R0-R+ε。
And S132, determining the corrected braking torque of each wheel according to the braking torque expression of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio based on the principle of sliding mode control.
Specifically, the determining the corrected braking torque of each wheel according to each wheel braking torque expression, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio based on the principle of sliding mode control includes:
designing a sliding mode controller, taking the reference vehicle speed, the wheel speed and the target slip ratio of each wheel as input, and outputting the basic braking torque of each wheel;
and determining the braking torque of each wheel according to the basic braking torque of each wheel and each wheel braking torque expression.
Fig. 4 is a schematic diagram of a brake dynamics model according to the present embodiment. The sliding mode controller is designed as follows:
each wheel having a longitudinal slip ratio of
(19) Whereinv x As the longitudinal speed of the vehicle, ωiR is the wheel speed of each wheel, and R is the rolling radius of each wheel; derived from the above formula
(20) (ii) a The rotational motion equation (4) of each wheel and the longitudinal motion differential equation of the whole vehicle are obtained
(21) Substituting into the above-mentioned formula (20) after derivation to obtain
(21) In which F isxiFor longitudinal forces of each wheel, IwThe moment of inertia of each wheel.
The deviation formula of the target slip rate and the actual slip rate is
（22），eiFor slip ratio deviation, λiTo actual slip ratio, λidThe target slip ratio is obtained.
Considering the high-frequency jitter easily caused by sliding mode control, the following proportional integral sliding mode surface is established according to the slip rate deviation
(23) In the formulaγThe coefficient is obtained by multiple simulation experiments. The derivative of the above formula is obtained and substituted into the derivative of formula (22)
（24）。
By substituting formula (21) for formula (24)
（25）。
Selecting a control rate of
(26) In which epsilon1、ε2Psi and psi are constants, and the constants are obtained through multiple simulation experiments.
Replacing the formula (26) with the formula (25), and obtaining the braking torque of each wheel through arrangement
（27）。
Considering that the sliding mode controller adopts sgn function to easily cause severe buffeting, the shaking elimination is carried out by utilizing saturation function, and the saturation function is defined as
（28）。
And analyzing the stability of the sliding mode control algorithm by utilizing the Lyapunov law, and simultaneously solving the stable condition. Selecting the Lyapunov equation as
(29). Is differentiated from the equation
(30). When selecting epsilon1>0，ε2>At the time of 0, the number of the first,
(31) namely, the sliding mode controller has stability.
In the embodiment, a braking torque expression is determined firstly, and then the braking torque of each corrected wheel is determined based on the principle of sliding mode control, the expression and the like, so that the accurate control of the braking torque is realized. The relationship between the vertical movement displacement of the wheels and the correction threshold is considered, whether the wheels jump off the ground or not is considered, the braking torque expression is determined according to the relationship, the expression division is scientific and reasonable, and the expressions corresponding to different bumping degrees are provided, so that the control is more accurate.
Example 3
As shown in fig. 5, the present embodiment provides a wheel slip ratio correction apparatus including:
the dynamic model building module 101 is used for building a 4+2 n-degree-of-freedom vehicle dynamic model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the heeling direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom;
the wheel vertical motion displacement and reference vehicle speed determining module 102 is used for determining the vertical motion displacement and the reference vehicle speed of each wheel based on a state observer and the whole vehicle dynamic model;
and the braking torque output module 103 is used for outputting the corrected braking torque of each wheel by taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio as input based on the principle of sliding mode control.
Further, the dynamic model building module 101 is further configured to determine a vertical motion differential equation of the vehicle body and the wheels according to the sprung mass, the wheel mass, the vertical displacement of the vehicle center of mass, the vertical motion displacement of the wheels, the vertical unevenness of the ground and the suspension force; determining pitching motion and rolling motion differential equations of the vehicle body according to the rotational inertia of the vehicle body around the y axis, the rotational inertia of the vehicle body around the x axis, the pitch angle acceleration of the vehicle body, the roll angle acceleration of the vehicle body, the longitudinal acceleration of the vehicle body, the lateral acceleration of the vehicle body, the vertical distance from the center of mass of the vehicle to a pitching center and the vertical distance from the center of mass of the vehicle to a rolling center; and determining a wheel rotational motion equation according to the rotational inertia of the wheel, the rotational angular speed of the wheel, the longitudinal reaction force of the ground to the wheel, the braking moment of the wheel and the rolling radius of the wheel.
Further, the wheel vertical motion displacement and reference vehicle speed determining module 102 is further configured to perform state observation on the vehicle centroid vertical displacement, the vehicle body pitch angle and the vehicle body roll angle based on a state observer, and obtain an observed value; determining vertical movement displacement of each wheel according to the whole vehicle dynamic model, the observed value and the dynamic stroke of each suspension; and determining the reference vehicle speed according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body, the angular acceleration of each wheel and the vertical motion displacement of each wheel on the basis of the state observer.
Further, the braking torque output module 103 is further configured to determine a braking torque expression of each wheel according to the vertical movement displacement of each wheel; and determining the corrected braking torque of each wheel according to the braking torque expression of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio based on the principle of sliding mode control.
The wheel slip ratio correction device is used for executing the wheel slip ratio correction method, and therefore at least has functional modules and beneficial effects corresponding to the method.
Example 4
As shown in fig. 6, the present embodiment provides an electronic apparatus including:
at least one processor; and
a memory communicatively coupled to at least one of the processors; wherein,
the memory stores instructions executable by at least one of the processors to enable the at least one of the processors to perform the method described above. The at least one processor in the electronic device is capable of performing the above method and thus has at least the same advantages as the above method.
Optionally, the electronic device further includes an interface for connecting the components, including a high-speed interface and a low-speed interface. The various components are interconnected using different buses and may be mounted on a common motherboard or in other manners as desired. The processor may process instructions for execution within the electronic device, including instructions stored in or on the memory to display Graphical information for a GUI (Graphical User Interface) on an external input/output device, such as a display device coupled to the Interface. In other embodiments, multiple processors and/or multiple buses may be used, along with multiple memories and multiple memories, as desired. Also, multiple electronic devices may be connected, with each device providing portions of the necessary operations (e.g., as a server array, a group of blade servers, or a multi-processor system). In fig. 6, one processor 201 is taken as an example.
The memory 202 is a computer-readable storage medium, and can be used for storing software programs, computer-executable programs, and modules, such as program instructions/modules corresponding to the wheel slip ratio correction method in the embodiment of the present invention (for example, the dynamic model building module 101, the wheel vertical motion displacement and reference vehicle speed determination module 102, and the braking torque output module 103 in the wheel slip ratio correction device). The processor 201 executes various functional applications of the device and data processing, i.e., implements the above-described wheel slip ratio correction method, by executing software programs, instructions, and modules stored in the memory 202.
The memory 202 may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data created according to the use of the terminal, and the like. Further, the memory 202 may include high speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid state storage device. In some examples, the memory 202 may further include memory located remotely from the processor 201, which may be connected to the device over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The electronic device may further include: an input device 203 and an output device 204. The processor 201, the memory 202, the input device 203 and the output device 204 may be connected by a bus or other means, and fig. 6 illustrates the connection by a bus as an example.
The input device 203 may receive input numeric or character information, and the output device 204 may include a display device, an auxiliary lighting device (e.g., an LED), a tactile feedback device (e.g., a vibration motor), and the like. The display device may include, but is not limited to, a Liquid Crystal Display (LCD), a Light Emitting Diode (LED) display, and a plasma display. In some implementations, the display device can be a touch screen.
Example 5
The present embodiment provides a medium having stored thereon computer instructions for causing the computer to perform the method described above. The computer instructions on the medium for causing a computer to perform the method described above thus have at least the same advantages as the method described above.
The medium of the present invention may take the form of any combination of one or more computer-readable media. The medium may be a computer readable signal medium or a computer readable storage medium. The medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the medium include: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF (Radio Frequency), etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + +, or the like, as well as conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
It should be understood that various forms of the flows shown above, reordering, adding or deleting steps, may be used. For example, the steps described in the present application may be executed in parallel, sequentially, or in different orders, as long as the desired results of the technical solutions disclosed in the present application can be achieved, and the present invention is not limited herein.
The above-described embodiments should not be construed as limiting the scope of the present application. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions may be made in accordance with design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. A method of correcting a wheel slip ratio, comprising the steps of:
building a 4+2 n-degree-of-freedom complete vehicle dynamics model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the side tilting direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom;
determining vertical motion displacement and reference vehicle speed of each wheel based on a state observer and the whole vehicle dynamics model;
and based on the principle of sliding mode control, taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip rate as input, and outputting the corrected braking torque of each wheel.
2. The method for correcting the wheel slip ratio according to claim 1, wherein the building of the 4+2 n-degree-of-freedom full vehicle dynamic model comprises:
determining a whole vehicle dynamic model with 1+ n degrees of freedom of a vehicle body vertical direction and n wheel vertical directions according to the sprung mass, the wheel mass, the vehicle mass center vertical displacement, the wheel vertical motion displacement, the vertical unevenness of the ground and the suspension force;
determining a whole vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body rolling according to the rotational inertia of the vehicle body around the y axis, the rotational inertia of the vehicle body around the x axis, the vehicle body pitch angle acceleration, the vehicle body roll angle acceleration, the vehicle body longitudinal acceleration, the vehicle body lateral acceleration, the vertical distance from the vehicle mass center to the pitching center and the vertical distance from the vehicle mass center to the rolling center;
determining a whole vehicle dynamic model with one degree of freedom in the longitudinal direction of the vehicle body according to the mass of the whole vehicle, the longitudinal acceleration of the vehicle body and the longitudinal reaction force of the ground on each wheel;
determining a whole vehicle dynamic model with n degrees of freedom of rotation of n wheels according to the moment of inertia of the wheels, the rotating angular speed of the wheels, the longitudinal reaction force of the ground to the wheels, the braking moment of the wheels and the rolling radius of the wheels;
and determining the 4+2 n-degree-of-freedom complete vehicle dynamic model according to the complete vehicle dynamic model with 1+ n degrees of freedom of the vertical vehicle body and the vertical n wheels, the complete vehicle dynamic model with two degrees of freedom of vehicle body pitching and vehicle body side tilting, the complete vehicle dynamic model with one degree of freedom of the longitudinal vehicle body and the complete vehicle dynamic model with n degrees of freedom of the rotation of the n wheels.
3. The method for correcting the wheel slip ratio according to claim 1, wherein the determining the vertical kinematic displacement of each wheel and the reference vehicle speed based on the state observer and the entire vehicle dynamics model comprises:
based on a state observer, carrying out state observation on the vertical displacement of the mass center of the vehicle, the pitch angle of the vehicle body and the roll angle of the vehicle body to obtain an observed value;
determining vertical movement displacement of each wheel according to the whole vehicle dynamic model, the observed value and the dynamic stroke of each suspension;
and determining the reference vehicle speed according to the wheel speed of each wheel, the longitudinal acceleration of the vehicle body, the angular acceleration of each wheel and the vertical motion displacement of each wheel on the basis of the state observer.
4. The wheel slip ratio correction method according to any one of claims 1 to 3, wherein outputting the braking torque of each wheel with the vertical movement displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel, and the target slip ratio as inputs based on the principle of sliding mode control comprises:
determining a braking moment expression of each wheel according to the vertical movement displacement of each wheel;
and determining the corrected braking torque of each wheel according to the braking torque expression of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip ratio based on the principle of sliding mode control.
5. The method of modifying wheel slip ratio of claim 4, wherein said determining each wheel braking torque expression based on each said wheel vertical motion displacement comprises:
determining the relationship between the vertical motion displacement of each wheel and a correction threshold according to the vertical motion displacement of each wheel, and whether each wheel jumps off the ground;
and determining the braking torque expression of each wheel according to the relationship and whether each wheel jumps away from the ground.
6. The wheel slip ratio correction method according to claim 5, wherein determining each wheel braking torque expression based on the relationship and whether each of the wheels jumps off the ground includes:
if the vertical movement displacement of the wheel is lower than the correction threshold, determining that the wheel braking torque expression is a basic braking torque; the basic braking torque is based on a sliding mode control principle, and the basic braking torque is output by taking the reference vehicle speed, the wheel speed of a wheel and the target slip ratio as input;
if the vertical movement displacement of the wheel is larger than the correction threshold and the wheel does not jump off the ground, determining a wheel braking torque expression according to the basic braking torque, the maximum braking torque allowed by the vehicle, the vertical movement displacement of the wheel and the correction coefficient;
and if the wheel jumps away from the ground, determining a modified wheel braking torque expression according to the basic braking torque, the maximum allowable braking torque of the vehicle, the static radius of the wheel, the rolling radius of the wheel and the modification coefficient.
7. The wheel slip ratio correction method according to claim 5 or 6, wherein the respective wheel braking torques are:
if the vertical movement displacement of the wheel is less than or equal to the correction threshold, the braking torque of the wheel is the basic braking torque;
if the vertical movement displacement of the wheel is larger than the correction threshold and the wheel does not jump off the ground, the braking torque of the wheel is the sum of the basic braking torque and a first correction torque, and the first correction torque is the product of the vertical movement displacement of the wheel, a correction coefficient and the maximum allowable braking torque of the vehicle;
if the wheel jumps off the ground, the wheel braking torque is the sum of the basic braking torque and a second correction torque, which is the product of the value of the wheel resting radius minus the wheel rolling radius, the correction factor and the maximum braking torque allowed by the vehicle.
8. A wheel slip ratio correction apparatus, characterized by comprising:
the dynamic model building module is used for building a 4+2 n-degree-of-freedom vehicle dynamic model, wherein the 4+2 n-degree-of-freedom comprises four degrees of freedom of a vehicle body in the vertical direction, the longitudinal direction, the pitching direction and the heeling direction, and the vertical direction and the rotation of n wheels are 2n degrees of freedom;
the wheel vertical motion displacement and reference vehicle speed determining module is used for determining the vertical motion displacement and the reference vehicle speed of each wheel based on the state observer and the whole vehicle dynamic model;
and the braking torque output module is used for outputting the corrected braking torque of each wheel by taking the vertical motion displacement of each wheel, the reference vehicle speed, the wheel speed of each wheel and the target slip rate as input on the basis of the principle of sliding mode control.
9. An electronic device, comprising:
at least one processor, and a memory communicatively coupled to at least one of the processors;
wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-7.
10. A medium having stored thereon computer instructions for causing a computer to perform the method of any one of claims 1-7.
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| CN114291093A (en) * | 2021-11-30 | 2022-04-08 | 安徽海博智能科技有限责任公司 | Layered correction control method and system for cooperative automatic driving of vehicle and road |
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