CN113401113A - Unmanned vehicle direct yaw moment control method and controller based on vehicle stable envelope line - Google Patents

Unmanned vehicle direct yaw moment control method and controller based on vehicle stable envelope line Download PDF

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CN113401113A
CN113401113A CN202110711327.XA CN202110711327A CN113401113A CN 113401113 A CN113401113 A CN 113401113A CN 202110711327 A CN202110711327 A CN 202110711327A CN 113401113 A CN113401113 A CN 113401113A
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vehicle
slip angle
center
yaw
yaw moment
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CN113401113B (en
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潘公宇
刘一
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Jiangsu University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units
    • B60W30/02—Control of vehicle driving stability
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/12—Lateral speed
    • B60W2520/125—Lateral acceleration

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Abstract

本发明公开了基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法及控制器，涉及电动汽车稳定性控制领域。由于质心侧偏角和横摆角速度对车辆稳定性的影响尤为重要，因此根据质心侧偏角和横摆角速度建立车辆稳定包络线。根据卡尔曼滤波得到实际车辆的质心侧偏角和横摆角速度；根据得到的质心侧偏角和横摆角速度结合车辆稳定包络线，建立滑模控制产生直接横摆力矩，使车辆的质心侧偏角和横摆角速度维持在车辆稳定线内，并设计趋近律减小滑模控制的抖振。最后将得到的直接横摆力矩通过横摆力矩分配器，进行驱动力或者制动力分配。本发明实现了汽车在高速转弯和避障条件下的行驶稳定性。

Figure 202110711327

The invention discloses a direct yaw moment control method and controller of an unmanned vehicle based on a vehicle stability envelope, and relates to the field of electric vehicle stability control. Since the influence of the center of mass slip angle and yaw angular velocity on vehicle stability is particularly important, the vehicle stability envelope is established according to the center of mass slip angle and yaw angular velocity. According to the Kalman filter, the center of mass slip angle and yaw angular velocity of the actual vehicle are obtained; according to the obtained center of mass slip angle and yaw angular velocity combined with the vehicle stability envelope, a sliding mode control is established to generate direct yaw moment, so that the center of mass side of the vehicle is The declination angle and yaw rate are maintained within the vehicle stability line, and a reaching law is designed to reduce the chattering of the sliding mode control. Finally, the obtained direct yaw moment is passed through the yaw moment distributor to distribute the driving force or braking force. The invention realizes the driving stability of the automobile under the conditions of high-speed turning and obstacle avoidance.

Figure 202110711327

Description

Unmanned vehicle direct yaw moment control method and controller based on vehicle stable envelope line
Technical Field
The invention relates to the field of unmanned vehicles, in particular to a method and a controller for controlling a direct yaw moment of an unmanned vehicle with a vehicle stable envelope line.
Background
At present, the new modernization is the irreversible trend of automobile development, and the intelligent unmanned automobile is a great technical innovation. The development of the unmanned automobile can effectively reduce traffic accidents and relieve traffic jam, and the unmanned automobile can generate greater social benefits with the continuous improvement of the intelligent degree. The intelligent electric automobile has the characteristics of parameter uncertainty, time randomness, strong nonlinearity and the like, and the design of a transverse motion control system has profound research significance.
The direct yaw moment control is an additional yaw moment generated by a difference in driving force or braking force between the left and right wheels of the vehicle to ensure lateral stability of the vehicle.
Disclosure of Invention
In order to solve the problem that the stability of the electric automobile is unstable due to excessive steering or insufficient steering under the extreme conditions of high speed, severe road and the like, the invention provides a method for controlling the stability envelope curve of the unmanned automobile direct yaw moment, which effectively improves the response speed and robustness of the system and improves the driving stability of the automobile under the extreme conditions of high speed, severe road and the like.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for controlling the direct yaw moment of the unmanned vehicle based on the vehicle stable envelope line comprises the following steps:
step one, establishing a vehicle stability envelope line according to a centroid side slip angle and a yaw velocity which influence the vehicle stability;
secondly, acquiring a mass center slip angle and a yaw angular velocity of the actual vehicle through designed Kalman filtering;
step three, designing direct yaw moment through sliding mode control to keep the mass center side slip angle and the yaw velocity of the vehicle in the stable envelope line of the vehicle;
designing an approach rate to reduce buffeting of sliding mode control and generate a direct yaw moment;
and step five, the yaw moment distributor calculates the driving force or braking moment of four wheels of the actual vehicle according to the direct yaw moment calculated in the step four, so that the vehicle is kept stable.
The unmanned vehicle direct yaw moment controller based on the vehicle stability envelope line comprises a vehicle stability envelope line generator, a Kalman filter, a sliding mode controller and a yaw moment distributor;
the vehicle stability envelope generator: establishing a vehicle stable envelope line according to the centroid side slip angle and the yaw angular speed;
the Kalman filter: estimating to obtain a mass center side slip angle and a yaw angular velocity of the actual vehicle according to the lateral acceleration and the yaw angular velocity obtained by the actual vehicle;
the sliding mode controller: according to the obtained centroid side drift angle and yaw angular velocity, combining with a vehicle stable envelope line, establishing sliding mode control to generate direct yaw moment, keeping the centroid side drift angle and yaw angular velocity of the vehicle in a vehicle stable line, and designing an approach law to reduce buffeting of the sliding mode control;
the yaw moment distributor: and (3) distributing the driving force or the braking force according to the direct yaw moment generated by the slip film controller, and calculating the driving force or the braking moment of four wheels of the actual vehicle to keep the vehicle stable.
Further, the vehicle stability envelope is specifically:
and in a coordinate system with the yaw velocity of the vehicle as a vertical axis and the centroid slip angle as a horizontal axis, the stable state of the vehicle is quickly determined through the envelope line of one parallelogram. If the yaw angle and the centroid slip angle of the vehicle are within the parallelogram, the vehicle state is stable; if the vehicle yaw rate and the centroid slip angle are outside the parallelogram, then the vehicle condition is not stable.
Further, the kalman filter is designed as follows:
and establishing a linear two-degree-of-freedom vehicle dynamic equation containing parameter uncertainty and interference and noise influence according to Newton's law.
Figure RE-GDA0003222431600000021
Figure RE-GDA0003222431600000022
Wherein beta is the vehicle mass center slip angle, r is the yaw angular velocity, m and IZRespectively vehicle mass and moment of inertia,/FAnd lRFront axle and rear axle respectivelyDistance of heart, vxFor vehicle longitudinal speed, delta front wheel angle, CFAnd CRRespectively, front and rear wheel cornering stiffnesses.
And establishing a discrete system state equation and an observation equation by using the model.
x(k+1)＝Ax(k)+Bδ(k)+ω(k)#(11)
y(k)＝Hx(k)+Dδ(k)+v(k)#(12)
Wherein the system n-dimensional state vector
Figure RE-GDA0003222431600000023
System state transition matrix
Figure RE-GDA0003222431600000031
Figure RE-GDA0003222431600000032
Random disturbance of system
Figure RE-GDA0003222431600000033
Systematic observation vector
Figure RE-GDA0003222431600000034
Observation matrix
Figure RE-GDA0003222431600000035
Figure RE-GDA0003222431600000036
System observation noise
Figure RE-GDA0003222431600000037
State one-step prediction
Figure RE-GDA0003222431600000038
And (3) state estimation calculation:
Figure RE-GDA0003222431600000039
a filter gain matrix:
Figure RE-GDA00032224316000000310
where R is the observed noise covariance matrix.
Estimating an error variance matrix:
P(k)＝[1-K(k)H(k)]P(k)-#(15)
one-step prediction error matrix:
P(k)-＝A(k)P(k)AT(k)+Q#(16)
and calculating the estimation of the state value by recursion of the observed value obtained by the real vehicle.
Further, the sliding mode controller is designed as follows:
defining a sliding surface s1Comprises the following steps:
Figure RE-GDA00032224316000000311
where rho is [0,1 ]]To design the parameters, | Δ rmaxTo the maximum absolute value of the set yaw-rate error, | Δ β tintmaxThe maximum absolute value of the slip angle error.
Differential sliding surface s1Obtaining:
Figure RE-GDA00032224316000000312
with a two-degree-of-freedom vehicle model (1), additional moments applied in the lateral direction can be obtained with respect to
Figure RE-GDA00032224316000000313
The formula of (a):
Figure RE-GDA00032224316000000314
substituting (19) into (18) to obtain
Figure RE-GDA00032224316000000315
Order to
Figure RE-GDA00032224316000000316
Can obtain
Figure RE-GDA00032224316000000317
Figure RE-GDA0003222431600000041
In order to reduce buffeting of sliding mode control, the invention designs an approach law with an exponential term:
Figure RE-GDA0003222431600000042
wherein 0<p1<1，p2>0。
Figure RE-GDA0003222431600000043
Wherein 0<c0<1，c1>0， c2>0 and c2E.g. N. H (S) is a positive value and does not affect the stability of the system. When the system is far from the sliding surface p1H, (S) becomes smaller, p2The ratio/H (S) is increased, thereby increasing the approaching speed and increasing the convergence speed to the sliding surface. When the system is close to the sliding surface p1H, (S) and p2The/h(s) are small, and therefore a small control gain is obtained, thereby reducing chattering.
Combining equations (22) and (21), the control rate is obtained as follows:
Figure RE-GDA0003222431600000044
further, the yaw moment distributor is specifically designed as follows:
the longitudinal force distribution of the vehicle tire is distributed according to the axle load proportion, and the front and rear axle load values are as follows:
Figure RE-GDA0003222431600000045
in the formula axFor longitudinal acceleration, FZF，FZRThe vertical load of the front and rear shafts is adopted, and h is the height of the mass center of the whole vehicle.
The longitudinal force of each wheel should satisfy the following conditions while satisfying the yaw moment and the total longitudinal force requirement:
Figure RE-GDA0003222431600000046
the four tire forces are obtained according to the yaw moment and the vertical load, and the longitudinal force of each wheel distributed according to the load ratio is as follows:
Figure RE-GDA0003222431600000047
in the formula Fx1、Fx2、Fx3、Fx4The longitudinal forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively, FxThe total longitudinal driving force is determined by the pedal opening, B is the wheel base, and L is the wheel base.
The invention has the beneficial effects that:
1. the invention establishes a vehicle stability envelope curve based on a two-degree-of-freedom vehicle model and a Pacejka tire model to obtain a centroid side deviation angle and yaw velocity envelope curve which can enable the vehicle to maintain stable, and the vehicle can maintain stable as long as the centroid side deviation angle and the yaw velocity of the actual vehicle are in the envelope curve. The problem of obtaining ideal slip angle and yaw rate under the limit working condition is solved.
2. The method comprises the steps of obtaining the mass center slip angle and the yaw angular velocity of an actual vehicle through designed Kalman filtering; the problem that the centroid slip angle is difficult to measure is solved.
3. According to the invention, the direct yaw moment is designed through sliding mode control to keep the mass center side slip angle and the yaw velocity of the vehicle in the stable envelope curve of the vehicle, so that the control failure caused by inaccurate modeling and external environment condition change of the system is solved, and the rapidity and the robustness of the system are improved.
4. According to the method, the buffeting of the sliding mode control is reduced by designing the approach rate, a direct yaw moment is generated, and the buffeting problem in the sliding mode control is solved.
5. The method is easy to realize and is suitable for wide popularization and application.
Drawings
Fig. 1 is a schematic diagram of a direct yaw moment control method for an electric vehicle based on a vehicle stability envelope according to the present invention.
Fig. 2 is a vehicle stability envelope of the present invention vehicle direct yaw moment control method based on the vehicle stability envelope.
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in fig. 1, the direct yaw moment controller of the electric vehicle based on the vehicle stability envelope of the present invention is implemented by a vehicle stability envelope generator, a sliding mode controller, a yaw moment divider, and a kalman filter. And a vehicle stability envelope generator that establishes a vehicle stability envelope based on the centroid slip angle and the yaw rate. The Kalman filter is used for obtaining lateral acceleration and yaw angular velocity through the actual vehicle and inputting the lateral acceleration and the yaw angular velocity into the Kalman filter to obtain a mass center lateral deviation angle and the yaw angular velocity of the actual vehicle; and the sliding mode controller is used for establishing sliding mode control to generate direct yaw moment according to the obtained mass center side offset angle and yaw velocity in combination with the vehicle stable envelope line, so that the mass center side offset angle and the yaw velocity of the vehicle are maintained in the vehicle stable line, and a closing law is designed to reduce buffeting of the sliding mode control. And a yaw moment distributor for distributing the driving force or the braking force by passing the obtained direct yaw moment through the yaw moment distributor. The invention realizes the driving stability of the automobile under the conditions of high-speed turning and obstacle avoidance.
As shown in fig. 2, a vehicle stability envelope is constructed for the centroid slip angle and yaw rate.
The invention relates to an electric vehicle direct yaw moment control method based on a vehicle stable envelope line, which comprises the following concrete implementation steps:
1) generating a vehicle stability envelope
The slip angle β and the yaw rate r of the vehicle state have a crucial effect on the stability of the vehicle. The vehicle stability envelope curve is shown in fig. 1, and as long as the centroid side offset angle beta and the yaw rate r of the vehicle running are within the range of the envelope curve, the running stability of the vehicle can be ensured. The beta-r borderline formula is as follows:
Figure RE-GDA0003222431600000061
Figure RE-GDA0003222431600000062
a1＝tanαr,peak#(3)
Figure RE-GDA0003222431600000063
Figure RE-GDA0003222431600000064
CD and AB are the left boundary and the right boundary of the vehicle stable envelope line mass center side deflection angle respectively, and BC and AD are the upper boundary and the lower boundary of the vehicle stable envelope line yaw angular speed respectively. lRIs the distance of the center of mass to the rear wheel, vxIs the longitudinal velocity, αr,peakMu is the road surface friction coefficient for the maximum slip angle of the rear wheel.
Since the rear wheel is more easily saturated than the front wheel due to the large load on the rear wheel, the stability margin is determined by the rear wheel force peak, and the rear wheel maximum slip angle formula is as follows:
Figure RE-GDA0003222431600000065
where μ is the road surface coefficient of friction. Bringing r into the CD and AB segments, maximum slip angle betamaxAnd minimum slip angle betaminCan be expressed as:
Figure RE-GDA0003222431600000066
Figure RE-GDA0003222431600000067
2) designing a Kalman filter
The centroid slip angle is particularly important for stability under extreme conditions. At present, a highly integrated sensor can measure the yaw velocity of a vehicle in the running process, but the centroid slip angle cannot be directly measured, so that the centroid slip angle is estimated through Kalman filtering.
The algorithm is as follows:
and establishing a linear two-degree-of-freedom vehicle dynamic equation containing parameter uncertainty and interference and noise influence according to Newton's law.
Figure RE-GDA0003222431600000071
Figure RE-GDA0003222431600000072
Wherein beta is the vehicle mass center slip angle, r is the yaw angular velocity, m and IzRespectively vehicle mass and moment of inertia,/FAnd lRDistances from the front and rear axes, respectively, to the center of mass, vxIs a longitudinal direction of the vehicleThe speed of the moving-direction is controlled,
Figure RE-GDA0003222431600000073
for lateral acceleration, delta front wheel angle, CFAnd CRRespectively, front and rear wheel cornering stiffnesses.
And establishing a discrete system state equation and an observation equation by using the model.
x(k+1)＝Ax(k)+Bδ(k)+ω(k)#(11)
y(k)＝Hx(k)+Dδ(k)+v(k)#(12)
Wherein the system n-dimensional state vector
Figure RE-GDA0003222431600000074
System state transition matrix
Figure RE-GDA0003222431600000075
Figure RE-GDA0003222431600000076
Systematic observation vector
Figure RE-GDA0003222431600000077
Observation matrix
Figure RE-GDA0003222431600000078
Figure RE-GDA0003222431600000079
Random disturbance of system
Figure RE-GDA00032224316000000710
System observation noise
Figure RE-GDA00032224316000000711
ω1(k)、ω2(k)、v1(k)、v2(k) The white noise is independent and normally distributed, and the delta t is the system sampling time.
State one-step prediction
Figure RE-GDA00032224316000000712
And (3) state estimation calculation:
Figure RE-GDA00032224316000000713
a filter gain matrix:
K(k)＝P(k)-H(k)T[H(k)P(k)-H(k)T+R]-1
where R is the observed noise covariance matrix.
Estimating an error variance matrix:
P(k)＝[1-K(k)H(k)]P(k)-#(15)
one-step prediction error matrix:
P(k)-＝A(k)P(k)AT(k)+Q#(16)
wherein Q is the covariance of the random perturbation of the system.
And calculating the estimation of the state value by recursion of the observed value obtained by the real vehicle.
3) Design sliding mode controller
The sliding mode controller generates a direct yaw moment, so that the mass center side offset angle and the yaw velocity of the vehicle are maintained in a vehicle stable envelope line, the purpose of keeping the vehicle stable is achieved, and buffeting of sliding mode control is reduced through a designed approach law. Defining a sliding surface s1Comprises the following steps:
Figure RE-GDA0003222431600000081
where rho is [0,1 ]]To design the parameters, | Δ rmaxTo the maximum absolute value of the set yaw-rate error, | Δ β tintmaxThe maximum absolute value of the slip angle error.
Differential sliding surface s1Obtaining:
Figure RE-GDA0003222431600000082
wherein (r, beta) is a point outside the stable envelope line, (r)safe,βsafe) To the nearest point on the stability envelope.
With a two-degree-of-freedom vehicle model (1), additional moments applied in the lateral direction can be obtained with respect to
Figure RE-GDA00032224316000000811
The formula of (a):
Figure RE-GDA0003222431600000083
wherein FFy、FRyFront and rear wheel side forces, M, respectivelyzIs the yaw moment.
Substituting (19) into (18) to obtain
Figure RE-GDA0003222431600000084
Order to
Figure RE-GDA0003222431600000085
Can obtain
Figure RE-GDA0003222431600000086
Figure RE-GDA0003222431600000087
In order to reduce buffeting of sliding mode control, the invention designs an approach law with an exponential term:
Figure RE-GDA0003222431600000088
wherein 0<p1<1，p2>0。
Figure RE-GDA0003222431600000089
Wherein 0<c0<1，c1>0， c2>0 and c2E.g. N. H (S) is a positive value and does not affect the stability of the system. When the system is far from the sliding surface p1H, (S) becomes smaller, p2The ratio/H (S) is increased, thereby increasing the approaching speed and increasing the convergence speed to the sliding surface. When the system is close to the sliding surface p1H, (S) and p2The/h(s) are small, and therefore a small control gain is obtained, thereby reducing chattering.
Combining equations (22) and (21), the control rate is obtained as follows:
Figure RE-GDA00032224316000000810
4) distributor for designing transverse moment
The direct yaw moment output by the sliding mode controller generates driving force or braking force of wheels through the yaw moment distributor.
The vehicle tire longitudinal force distribution is generally distributed in axle load proportion. The front and rear axle load values are as follows:
Figure RE-GDA0003222431600000091
in the formula axFor longitudinal acceleration, FZF，FZRThe vertical load of the front shaft and the rear shaft is adopted, and h is the height of the mass center of the whole vehicle.
The longitudinal force of each wheel should satisfy the following conditions while satisfying the yaw moment and the total longitudinal force requirement:
Figure RE-GDA0003222431600000092
in combination (24) (25), the longitudinal forces of the individual wheels, distributed according to the load ratio, are obtained as follows:
Figure RE-GDA0003222431600000093
in the formula Fx1、Fx2、Fx3、Fx4The longitudinal forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively, FxThe total longitudinal driving force is determined by the pedal opening, and B is the wheel track.
The above-listed series of detailed descriptions are merely specific illustrations of possible embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent means or modifications that do not depart from the technical spirit of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1.基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，包括如下步骤：1. the direct yaw moment control method of unmanned vehicle based on vehicle stability envelope, is characterized in that, comprises the steps: S1、根据影响车辆稳定的质心侧偏角和横摆角速度建立车辆稳定包络线；S1. Establish a vehicle stability envelope according to the center of mass slip angle and yaw rate that affect vehicle stability; S2、获取实际车辆的质心侧偏角和横摆角速度；S2. Obtain the side-slip angle and yaw rate of the actual vehicle; S3、设计直接横摆力矩的滑模控制器，将车辆的质心侧偏角和横摆角速度保持在车辆稳定包络线内；S3. Design a sliding mode controller with direct yaw moment to keep the vehicle's center of mass slip angle and yaw rate within the vehicle's stability envelope; S4、设计趋近率减小滑模控制器的抖振，生成直接横摆力矩；S4. The design approach rate reduces the chattering of the sliding mode controller and generates direct yaw moment; S5、根据步骤S3、S4生成的直接横摆力矩，求出实际车辆四个车轮的驱动力或者制动力矩，使车辆维持稳定。S5. According to the direct yaw moment generated in steps S3 and S4, the actual driving force or braking moment of the four wheels of the vehicle is obtained, so that the vehicle can be maintained stable. 2.根据权利要求1所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S1中建立的车辆稳定包络线具体为：2. the unmanned vehicle direct yaw moment control method based on the vehicle stability envelope according to claim 1, is characterized in that, the vehicle stability envelope established in the described S1 is specifically: 以车辆横摆角速度为纵轴，质心侧偏角为横轴的坐标系中，通过一个平行四边的包络线形快速确定车辆的稳定状态，如果车辆横摆角度和质心侧偏角在平行四边形之内，则表示车辆状态稳定；如果车辆横摆角速度和质心侧偏角在平行四边形之外，则表示车辆状态不稳定；In a coordinate system with the vehicle yaw rate as the vertical axis and the center of mass slip angle as the horizontal axis, the stable state of the vehicle is quickly determined through a parallelogram envelope. If the vehicle yaw angle and the center of mass slip angle are between the parallelogram If the vehicle yaw rate and the center of mass slip angle are outside the parallelogram, it means the vehicle state is unstable; 为使得质心侧偏角β和横摆角速度r在此范围内，设计β-r边界线的公式如下：In order to make the center of mass slip angle β and the yaw rate r within this range, the formula for designing the β-r boundary line is as follows:
Figure FDA0003133061350000011
Figure FDA0003133061350000011
Figure FDA0003133061350000012
Figure FDA0003133061350000012
 a1＝tan αr，peak#(3)a 1 =tan α r, peak #(3)
Figure FDA0003133061350000013
Figure FDA0003133061350000013
Figure FDA0003133061350000014
Figure FDA0003133061350000014
 其中lR为质心至后轮的距离，vx为纵向速度，αr，peak为后轮最大侧偏角，μ是路面摩擦系数；where l R is the distance from the center of mass to the rear wheel, v x is the longitudinal speed, α r, peak is the maximum slip angle of the rear wheel, and μ is the road friction coefficient; 由于后轮的载荷大，后轮相比于前轮更容易饱和，因此，稳定性边界由后轮力峰值决定，后轮最大侧偏角公式如下：Due to the large load on the rear wheels, the rear wheels are more likely to be saturated than the front wheels. Therefore, the stability boundary is determined by the peak force of the rear wheels. The formula for the maximum rear wheel slip angle is as follows:
Figure FDA0003133061350000015
Figure FDA0003133061350000015
 其中μ是路面摩擦系数，将r带入CD和AB段，最大滑移角βmax和最小滑移角βmin可以表示为：where μ is the friction coefficient of the road surface, and taking r into the CD and AB segments, the maximum slip angle β max and the minimum slip angle β min can be expressed as:
Figure FDA0003133061350000021
Figure FDA0003133061350000021
Figure FDA0003133061350000022
Figure FDA0003133061350000022
 3.根据权利要求1所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S2中，质心侧偏角通过设计的卡尔曼滤波估算得到，具体过程如下：3. the direct yaw moment control method of unmanned vehicle based on vehicle stability envelope according to claim 1, is characterized in that, in described S2, the center of mass slip angle is estimated by the Kalman filter of design, and concrete The process is as follows: 根据牛顿定律，建立包含参数不确定以及干扰、噪声影响的线性二自由度车辆动力学方程：According to Newton's law, a linear two-degree-of-freedom vehicle dynamics equation including parameter uncertainty, interference and noise effects is established:
Figure FDA0003133061350000023
Figure FDA0003133061350000023
Figure FDA0003133061350000024
Figure FDA0003133061350000024
 其中，β为车辆质心侧偏角，r为横摆角速度，m和IZ分别为车辆质量和转动惯量，lF和lR分别为前轴和后轴到质心的距离，vx为车辆纵向速度，
Figure FDA0003133061350000025
为侧向加速度，，δ前轮转角，CF和CR分别为前后轮侧偏刚度；Among them, β is the side slip angle of the center of mass of the vehicle, r is the yaw rate, m and I Z are the vehicle mass and moment of inertia, respectively, l F and l R are the distances from the front and rear axles to the center of mass, and v x is the longitudinal direction of the vehicle speed,
Figure FDA0003133061350000025
is the lateral acceleration, δ is the front wheel angle, CF and CR are the cornering stiffness of the front and rear wheels, respectively; 将上述模型建立离散系统状态方程和观测方程：The above model is used to establish the discrete system state equation and observation equation: x(k+1)＝Ax(k)+Bδ(k)+ω(k)#(11)x(k+1)=Ax(k)+Bδ(k)+ω(k)#(11) y(k)＝Hx(k)+Dδ(k)+v(k)#(12)y(k)=Hx(k)+Dδ(k)+v(k)#(12) 其中，系统n维状态向量
Figure FDA0003133061350000026
系统状态转移矩阵
Figure FDA0003133061350000027
系统随机扰动
Figure FDA0003133061350000028
系统观测向量
Figure FDA0003133061350000029
观测矩阵
Figure FDA00031330613500000210
系统观测噪声
Figure FDA00031330613500000211
ω1(k)、ω2(k)、v1(k)、v2(k)为相互独立正态分布的白噪声，Δt为系统采样时间；Among them, the n-dimensional state vector of the system
Figure FDA0003133061350000026
System State Transition Matrix
Figure FDA0003133061350000027
System random disturbance
Figure FDA0003133061350000028
System observation vector
Figure FDA0003133061350000029
observation matrix
Figure FDA00031330613500000210
System observation noise
Figure FDA00031330613500000211
ω 1 (k), ω 2 (k), v 1 (k), and v 2 (k) are white noises with independent normal distribution, and Δt is the system sampling time; 状态一步预测State one-step prediction
Figure FDA00031330613500000212
Figure FDA00031330613500000212
 状态估算计算：State estimation calculation:
Figure FDA0003133061350000031
Figure FDA0003133061350000031
 滤波增益矩阵：Filter gain matrix: K(k)＝P(k)-H(k)T[H(k)P(k)-H(k)T+R]-1 K(k)=P(k)-H(k) T [H(k)P(k) - H(k) T +R] -1 其中R为观测噪声协方差矩阵；where R is the observation noise covariance matrix; 估计误差方差阵：Estimated error variance matrix: P(k)＝[1-K(k)H(k)]P(k)-#(15)P(k)=[1-K(k)H(k)]P(k) - #(15) 一步预测误差方阵：One-step prediction error square matrix: P(k)-＝A(k)P(k)AT(k)+Q#(16)P(k) - =A(k)P(k)A T (k)+Q#(16) 通过实车得到的观测值递推计算出状态值的估算。The estimation of the state value is calculated recursively through the observed values obtained from the real vehicle. 4.根据权利要求1所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S2中，所述横摆角速度由传感器获取。4 . The direct yaw moment control method for an unmanned vehicle based on the vehicle stability envelope according to claim 1 , wherein, in the S2 , the yaw angular velocity is acquired by a sensor. 5 . 5.根据权利要求1所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S3设计直接横摆力矩的滑模控制器的具体过程如下：5. the direct yaw moment control method of unmanned vehicle based on vehicle stability envelope according to claim 1, is characterized in that, the concrete process of the sliding mode controller of described S3 design direct yaw moment is as follows: 定义滑动面s1为：The sliding surface s1 is defined as:
Figure FDA0003133061350000032
Figure FDA0003133061350000032
 其中ρ∈[0，1]为设计参数，|Δr|max为设定的横摆角速度误差的最大绝对值，|Δβ|max为滑移角误差的最大绝对值；where ρ∈[0,1] is the design parameter, |Δr| max is the maximum absolute value of the set yaw rate error, and |Δβ| max is the maximum absolute value of the slip angle error; 微分滑动面s1得到：Differentiating the sliding surface s 1 yields:
Figure FDA0003133061350000033
Figure FDA0003133061350000033
 结二自由度车辆模型(1)，在横向施加额外的力矩，可以得到关于
Figure FDA0003133061350000039
的公式：Combining the two-degree-of-freedom vehicle model (1), with additional moment applied in the lateral direction, it can be obtained about
Figure FDA0003133061350000039
The formula:
Figure FDA0003133061350000034
Figure FDA0003133061350000034
 将(19)代入(18)得到Substitute (19) into (18) to get
Figure FDA0003133061350000035
Figure FDA0003133061350000035
 令
Figure FDA0003133061350000036
可以得到中间值
Figure FDA0003133061350000037
make
Figure FDA0003133061350000036
Intermediate value can be obtained
Figure FDA0003133061350000037
Figure FDA0003133061350000038
Figure FDA0003133061350000038
 6.根据权利要求5所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S4的趋紧率为具有指数项的趋紧率，具体如下：6. the direct yaw moment control method of unmanned vehicle based on vehicle stability envelope according to claim 5, is characterized in that, the tightening rate of described S4 has the tightening rate of exponential term, is specifically as follows:
Figure FDA0003133061350000041
Figure FDA0003133061350000041
 其中0＜p1＜1，p2＞0，
Figure FDA0003133061350000042
其中0＜c0＜1，c1＞0，c2＞0并且c2∈N，H(S)为正值，不影响系统稳定性；where 0<p 1 <1, p 2 >0,
Figure FDA0003133061350000042
Where 0<c 0 <1, c 1 >0, c 2 >0 and c 2 ∈ N, H(S) is a positive value, which does not affect the system stability; 当系统远离滑动面时，p1H(S)变小，p2/H(S)变大，提高接近速度，并加快向滑动面的收敛速度；When the system moves away from the sliding surface, p 1 H(S) becomes smaller and p 2 /H(S) becomes larger, which increases the approach speed and accelerates the convergence speed to the sliding surface; 当系统靠近滑动面时，p1H(S)和p2/H(S)都很小，获得较小的控制增益，以减小抖振；When the system is close to the sliding surface, both p 1 H(S) and p 2 /H(S) are small, and a small control gain is obtained to reduce chattering; 合并等式(22)和(21)，得到控制率如下：Combining equations (22) and (21), the control rate is obtained as follows:
Figure FDA0003133061350000043
Figure FDA0003133061350000043
 7.根据权利要求6所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制方法，其特征在于，所述S5的具体过程如下：7. the unmanned vehicle direct yaw moment control method based on vehicle stability envelope according to claim 6, is characterized in that, the concrete process of described S5 is as follows: 车辆轮胎纵向力分配按照轴载比例分配，前后轴载荷值如下：The longitudinal force distribution of the vehicle tires is distributed according to the axle load ratio, and the front and rear axle load values are as follows:
Figure FDA0003133061350000044
Figure FDA0003133061350000044
 式中ax为纵向加速度，FZF，FZR为前后轴垂直载荷，h为整车质心高度；where a x is the longitudinal acceleration, F ZF and F ZR are the vertical loads of the front and rear axles, and h is the height of the center of mass of the vehicle; 各轮的纵向力在满足横摆力矩和总纵向力需求的同时，还应该满足下列条件：The longitudinal force of each wheel should meet the following conditions while meeting the requirements of yaw moment and total longitudinal force:
Figure FDA0003133061350000045
Figure FDA0003133061350000045
 结合(24)(25)得到按载荷比分配的各个车轮纵向力如下：Combined with (24) and (25), the longitudinal forces of each wheel distributed according to the load ratio are obtained as follows:
Figure FDA0003133061350000046
Figure FDA0003133061350000046
 式中Fx1、Fx2、Fx3、Fx4分别为左前轮、右前轮、左后轮、右后轮的纵向力，Fx为总的纵向驱动力，由踏板开度决定，B为轮距。In the formula, F x1 , F x2 , F x3 , and F x4 are the longitudinal forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, Fx is the total longitudinal driving force, which is determined by the pedal opening, and B is wheelbase. 8.基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制器，其特征在于，包括车辆稳定包络线生成器、卡尔曼滤波器、滑模控制器、横摆力矩分配器；8. The unmanned vehicle direct yaw moment controller based on the vehicle stability envelope is characterized in that, comprising a vehicle stability envelope generator, a Kalman filter, a sliding mode controller, and a yaw moment distributor; 所述车辆稳定包络线生成器：根据质心侧偏角和横摆角速度建立车辆稳定包络线；The vehicle stability envelope generator: establishes the vehicle stability envelope according to the center of mass slip angle and the yaw rate; 所述卡尔曼滤波器：根据实际车辆得到侧向加速度和横摆角速度估算得到实际车辆的质心侧偏角和横摆角速度；The Kalman filter: obtains the side-slip angle and the yaw angular velocity of the actual vehicle by estimating the lateral acceleration and yaw angular velocity obtained from the actual vehicle; 所述滑模控制器：根据得到的质心侧偏角和横摆角速度结合车辆稳定包络线，建立滑模控制产生直接横摆力矩，使车辆的质心侧偏角和横摆角速度维持在车辆稳定线内，并设计趋近律减小滑模控制的抖振；The sliding mode controller: According to the obtained center of mass slip angle and yaw angular velocity combined with the vehicle stability envelope, a sliding mode control is established to generate direct yaw moment, so that the center of mass slip angle and yaw angular velocity of the vehicle are maintained at the vehicle stability. within the line, and design the reaching law to reduce the chattering of the sliding mode control; 所述横摆力矩分配器：根据滑膜控制器生成的直接横摆力矩，进行驱动力或者制动力分配，求出实际车辆四个车轮的驱动力或者制动力矩，使车辆维持稳定。The yaw moment distributor: According to the direct yaw moment generated by the synovial controller, the driving force or braking force is distributed, and the actual driving force or braking torque of the four wheels of the vehicle is obtained, so as to maintain the stability of the vehicle. 9.根据权利要求8所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制器，其特征在于，所述车辆稳定包络线具体为：9. The unmanned vehicle direct yaw moment controller based on the vehicle stability envelope according to claim 8, wherein the vehicle stability envelope is specifically: 以车辆横摆角速度为纵轴，质心侧偏角为横轴的坐标系中，通过一个平行四边的包络线形快速确定车辆的稳定状态，如果车辆横摆角度和质心侧偏角在平行四边形之内，则表示车辆状态稳定；如果车辆横摆角速度和质心侧偏角在平行四边形之外，则表示车辆状态不稳定；In a coordinate system with the vehicle yaw rate as the vertical axis and the center of mass slip angle as the horizontal axis, the stable state of the vehicle is quickly determined by a parallelogram envelope. If the vehicle yaw angle and the center of mass slip angle are between the parallelogram If the yaw rate and the center of mass slip angle of the vehicle are outside the parallelogram, it means that the vehicle is unstable; 所述卡尔曼滤波器设计如下：The Kalman filter is designed as follows: 根据牛顿定律，建立包含参数不确定以及干扰、噪声影响的线性二自由度车辆动力学方程；According to Newton's law, establish a linear two-degree-of-freedom vehicle dynamics equation including parameter uncertainty, interference and noise effects;
Figure FDA0003133061350000051
Figure FDA0003133061350000051
Figure FDA0003133061350000052
Figure FDA0003133061350000052
 其中，β为车辆质心侧偏角，r为横摆角速度，m和IZ分别为车辆质量和转动惯量，lF和lR分别为前轴和后轴到质心的距离，vx为车辆纵向速度，δ前轮转角，CF和CR分别为前后轮侧偏刚度；Among them, β is the side slip angle of the center of mass of the vehicle, r is the yaw rate, m and I Z are the vehicle mass and moment of inertia, respectively, l F and l R are the distances from the front and rear axles to the center of mass, and v x is the longitudinal direction of the vehicle speed, δ front wheel angle, C F and C R are the cornering stiffness of the front and rear wheels, respectively; 将上述模型建立离散系统状态方程和观测方程：The above model is used to establish the discrete system state equation and observation equation: x(k+1)＝Ax(k)+Bδ(k)+ω(k)#(11)x(k+1)=Ax(k)+Bδ(k)+ω(k)#(11) y(k)＝Hx(k)+Dδ(k)+v(k)#(12)y(k)=Hx(k)+Dδ(k)+v(k)#(12) 其中，系统n维状态向量
Figure FDA0003133061350000061
系统状态转移矩阵
Figure FDA0003133061350000062
系统随机扰动
Figure FDA0003133061350000063
系统观测向量
Figure FDA0003133061350000064
观测矩阵
Figure FDA0003133061350000065
系统观测噪声
Figure FDA0003133061350000066
Among them, the n-dimensional state vector of the system
Figure FDA0003133061350000061
System State Transition Matrix
Figure FDA0003133061350000062
System random disturbance
Figure FDA0003133061350000063
System observation vector
Figure FDA0003133061350000064
observation matrix
Figure FDA0003133061350000065
System observation noise
Figure FDA0003133061350000066
 状态一步预测State one-step prediction
Figure FDA0003133061350000067
Figure FDA0003133061350000067
 状态估算计算：State estimation calculation:
Figure FDA0003133061350000068
Figure FDA0003133061350000068
 滤波增益矩阵：Filter gain matrix: K(k)＝P(k)-H(k)T[H(k)P(k)-H(k)T+R]-1 K(k)=P(k) - H(k) T [H(k)P(k) - H(k) T +R] -1 其中R为观测噪声协方差矩阵；where R is the observation noise covariance matrix; 估计误差方差阵：Estimated error variance matrix: P(k)＝[1-K(k)H(k)]P(k)-#(15)P(k)=[1-K(k)H(k)]P(k) - #(15) 一步预测误差方阵：One-step prediction error square matrix: P(k)-＝A(k)P(k)AT(k)+Q#(16)P(k) - =A(k)P(k)A T (k)+Q#(16) 通过实车得到的观测值递推计算出状态值的估算。The estimation of the state value is calculated recursively through the observed values obtained from the real vehicle. 10.根据权利要求8所述的基于车辆稳定包络线的无人驾驶汽车直接横摆力矩控制器，其特征在于，所述滑模控制器设计：10. The unmanned vehicle direct yaw moment controller based on the vehicle stability envelope according to claim 8, wherein the sliding mode controller is designed: 定义滑动面s1为：The sliding surface s1 is defined as:
Figure FDA0003133061350000069
Figure FDA0003133061350000069
 其中ρ∈[0，1]为设计参数，|Δr|max为设定的横摆角速度误差的最大绝对值，|Δβ|max为滑移角误差的最大绝对值；where ρ∈[0,1] is the design parameter, |Δr| max is the maximum absolute value of the set yaw rate error, and |Δβ| max is the maximum absolute value of the slip angle error; 微分滑动面s1得到：Differentiating the sliding surface s 1 yields:
Figure FDA00031330613500000610
Figure FDA00031330613500000610
 结二自由度车辆模型(1)，在横向施加额外的力矩，可以得到关于
Figure FDA00031330613500000611
的公式：Combining the two-degree-of-freedom vehicle model (1), with additional moment applied in the lateral direction, it can be obtained about
Figure FDA00031330613500000611
The formula:
Figure FDA0003133061350000071
Figure FDA0003133061350000071
 将(19)代入(18)得到Substitute (19) into (18) to get
Figure FDA0003133061350000072
Figure FDA0003133061350000072
 令
Figure FDA0003133061350000073
可以得到
Figure FDA0003133061350000074
make
Figure FDA0003133061350000073
can get
Figure FDA0003133061350000074
Figure FDA0003133061350000075
Figure FDA0003133061350000075
 为了减小滑模控制的抖振，本发明设计具有指数项的趋近律：In order to reduce the chattering of the sliding mode control, the present invention designs a reaching law with an exponential term:
Figure FDA0003133061350000076
Figure FDA0003133061350000076
 其中0＜p1＜1，p2＞0。
Figure FDA0003133061350000077
其中0＜c0＜1，c1＞0，c2＞0并且c2∈N，H(S)为正值，不影响系统稳定性，当系统远离滑动面时p1H(S)变小，p2/H(S)变大，从而提高了接近速度，并加快了向滑动面的收敛速度，当系统靠近滑动面时p1H(S)和p2/H(S)都很小，因此获得了较小的控制增益，从而减小抖振；where 0<p 1 <1, and p 2 >0.
Figure FDA0003133061350000077
where 0<c 0 <1, c 1 >0, c 2 >0 and c 2 ∈N, H(S) is a positive value, which does not affect the system stability. When the system moves away from the sliding surface, p 1 H(S) becomes is small, p 2 /H(S) becomes larger, which improves the approach speed and accelerates the convergence speed to the sliding surface. When the system approaches the sliding surface, both p 1 H(S) and p 2 /H(S) are very high. small, so a small control gain is obtained, thereby reducing chattering; 合并等式(22)和(21)，得到控制率如下：Combining equations (22) and (21), the control rate is obtained as follows:
Figure FDA0003133061350000078
Figure FDA0003133061350000078
 所述横摆力矩分配器具体设计如下：The specific design of the yaw moment distributor is as follows: 车辆轮胎纵向力分配按照轴载比例分配，前后轴载荷值如下：The longitudinal force distribution of the vehicle tires is distributed according to the axle load ratio, and the front and rear axle load values are as follows:
Figure FDA0003133061350000079
Figure FDA0003133061350000079
 式中ax为纵向加速度，FZF，FZR为前后轴垂直载荷，h为整车质心高度；where a x is the longitudinal acceleration, F ZF and F ZR are the vertical loads of the front and rear axles, and h is the height of the center of mass of the vehicle; 各轮的纵向力在满足横摆力矩和总纵向力需求的同时，还应该满足下列条件：The longitudinal force of each wheel should meet the following conditions while meeting the requirements of yaw moment and total longitudinal force:
Figure FDA00031330613500000710
Figure FDA00031330613500000710
 根据横摆力矩和垂直载荷求得四个轮胎力得到按载荷比分配的各个车轮纵向力如下：According to the yaw moment and vertical load, the four tire forces are obtained, and the longitudinal forces of each wheel distributed according to the load ratio are as follows:
Figure FDA0003133061350000081
Figure FDA0003133061350000081
 式中Fx1、Fx2、Fx3、Fx4分别为左前轮、右前轮、左后轮、右后轮的纵向力，Fx为总的纵向驱动力，由踏板开度决定，B为轮距。In the formula, F x1 , F x2 , F x3 , and F x4 are the longitudinal forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively, F x is the total longitudinal driving force, which is determined by the pedal opening, B for the wheelbase.
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