CN107561943A - A kind of method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling - Google Patents

A kind of method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling Download PDF

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Publication number
CN107561943A
CN107561943A CN201710820692.8A CN201710820692A CN107561943A CN 107561943 A CN107561943 A CN 107561943A CN 201710820692 A CN201710820692 A CN 201710820692A CN 107561943 A CN107561943 A CN 107561943A
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automobile
equation
model
minimum time
inverse dynamics
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张丽霞
夏永凯
潘福全
张辉
冯停
罗淑兰
亓荣杰
路军
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Qingdao University of Technology
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Qingdao University of Technology
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Abstract

The present invention relates to vehicle handling stability field, and disclose a kind of automobile minimum time maneuver inverse dynamics mathematical modeling establishes method.It comprises the following steps：Step A：Establish automobile operation kinetic model；Step B：Automobile operation kinetic model is converted into Vehicle Handling Inverse Dynamics model；Step C：Establish automobile minimum time maneuver Optimal Control Model.The model advantage is that reverse pilot control input can be solved under conditions of default pilot model, so as to cleverly avoid the various problems of driver modeling, a new approaches are opened for automobile engineer, and theoretical foundation is provided in optimization Automobile Design and intelligent vehicle research, while the research for being alternatively pilotless automobile provides technical support or provides guidance for motor sport training.

Description

A kind of method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling
Technical field
The present invention relates to vehicle handling stability field, and in particular to a kind of automobile minimum time maneuver inverse dynamics mathematical modeling Method for building up.
Background technology
Vehicle handling stability of running at high speed can decide vehicle safety and cornering ability, and the security of automobile is one Social foci.Therefore the control stability for automobile of running at high speed turns into the focus of automotive research.Vehicle handling stability, it is Refer under conditions of driver does not feel overstrain, fatigue, automobile can be given according to driver by steering system and steered wheel Fixed direction (straight line or turning) traveling；And when by external interference (road injustice, crosswind, goods or passenger's unbalance loading), automobile Interference can be resisted and keep the performance of stable traveling.Vehicle handling stability energy research method includes open-loop method and closed loop at present Method.Open-loop method does not account for the feedback of driver, and Pilot Model Parameters are not easy to determine in closed-loop policy.In order to solve to close " bottleneck " problem of driver modeling in ring method, the present invention is using Vehicle Handling Inverse Dynamics model to vehicle handling stability Studied.The Vehicle Handling Inverse Dynamics model be reversely solved by running car motion state driver manipulation it is defeated Enter, introduce various constraintss on this basis, establish Optimal Control Model, steering wheel is solved by specified maneuvering performance Handle input, when specified maneuvering performance completes the motion of two-track line for the most short time, then as automobile minimum time maneuver reserve motion Mechanical model.In the research of minimum time maneuver problem, the mathematical modeling assumed condition established in the past from reality farther out, and is studied Method is not perfect enough, and achievement in research is dfficult to apply to reality.Therefore, the present invention establishes automobile minimum time maneuver Optimal Control Model and changed Before kind the shortcomings that mathematical modeling.
The content of the invention
Present invention aims to overcome that the shortcomings of the prior art, seeks a kind of automobile minimum time maneuver inverse dynamics mathematics The method for building up of model.Solved after founding mathematical models, driver side can be obtained to disk handle input, driver is overtaken other vehicles During how to manipulate steering wheel provide directive function, or pilotless automobile research provide technical support or for match Car training provides guidance.
To reach above-mentioned purpose, technical scheme provides a kind of automobile minimum time maneuver inverse dynamics mathematical modeling Method for building up, comprise the following steps：Step A：Establish automobile operation kinetic model；Step B：Automobile operation kinetic model It is converted into Vehicle Handling Inverse Dynamics model；Step C：Establish automobile minimum time maneuver Optimal Control Model.
Idiographic flow processing procedure：According to the minimum time maneuver inverse dynamics model and solution procedure of foundation, phase is write out The program answered, input automobile side angle speed v, longitudinal velocity u, yaw velocity ωr, center-of-mass coordinate y, these states of course angle θ The initial value of variable, by the calculating of optimum control, iteration, finally give control variable vehicle front corner δ and front-wheel drive Power Fxf, and automobile side angle speed v, longitudinal velocity u, yaw velocity ωr, center-of-mass coordinate y, course angle θ are entirely being moved through Numerical value in journey.
Compared with prior art, the present invention has advantages below：Can under conditions of default pilot model reverse solution Go out driver's steering wheel handle input, so as to cleverly avoid the various problems of driver modeling in direct problem.Solution is drawn Driver's steering wheel handle input how driver's overtaking process is manipulated steering wheel provide directive function, while be alternatively nothing The research of people's driving provides technical support or provides guidance for motor sport training.One is opened for automobile engineer New approaches, and provide theoretical foundation in optimization Automobile Design and intelligent vehicle research.
Brief description of the drawings
The overview flow chart of the method for building up of Fig. 1 automobile minimum time maneuver inverse dynamics mathematical modelings of the present invention.
Fig. 2 is 3DOF car model of the present invention.
Embodiment
The present invention will be further described with reference to the accompanying drawings and detailed description：
A kind of method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling, specifically includes following steps：
Step A：Automobile operation kinetic model is established, is considering lateral movement, weaving and the lengthwise movement of automobile On the basis of, force analysis, the 3DOF motion state of automobile equation of foundation, i.e. automobile operation kinetic simulation are carried out to vehicle Type：
Assuming that tire model is linear tire, then front-wheel lateral deviation power F in formula 1yfWith trailing wheel lateral deviation power FyrFor：
When not considering that automotive suspension vertical vibration and automobile roll influence, wheel load is present such as before and after automobile in formula 2 Lower relation：
Wherein：V is automobile side angle speed；U is the longitudinal velocity of automobile；ωrFor the yaw velocity of automobile；M is vehicle Gross mass；IzIt is vehicle around vertical axis rotary inertia；A, b are respectively distance of the vehicle barycenter to antero posterior axis；δ is front wheel angle； FyfFor front-wheel lateral deviation power；FyrFor trailing wheel lateral deviation power；FxfFor front wheel drive force/brake force (Fxf>=0 is driving force, Fxf<0 is system Power)；FxrFor rear wheel drive force/brake force；FfFor rolling resistance (Ff=fmg, f are coefficient of rolling resistance)；FwFor air drag (Fw=CDA (3.6u) 2/21.15, CDFor coefficient of air resistance, A is front face area)；Pavement friction factor；FzfHung down for front-wheel Straight power；FzrFor trailing wheel vertical force；hgFor automobile height of center of mass；
Step B：Automobile operation kinetic model is converted into Vehicle Handling Inverse Dynamics model, specifically includes following processing：
Step B1 introduces front wheel angle equation, by front-wheel side drift angleWith trailing wheel side drift angleBring relational expression δ=L/R+ (α into respectively1-α2) in, obtaining front wheel angle equation is：
Wherein：α1For front-wheel side drift angle；α2For trailing wheel side drift angle；R is motor turning radius；
Front wheel angle is by state ω it can be seen from δ expression formular/ u and input path 1/R are together decided on；
Step B2 introduces driving force equation group, to calculate motor racing track, establishes ground reference coordinate system Oxy(Fig. 2), Wherein the center-of-mass coordinate of automobile is x, and y, vehicle axis system x' axles and the angle of ground reference coordinate system x-axis are that course angle is θ, then Movement Locus Equation is：
In the case of minimum time maneuver, automobile is in driving condition, now there is Fxr=0, formula 2 and formula 3 are substituted into, is arranged ：
Simultaneous formula 1 and formula 5, are obtained
Formula 1 is substituted into formula 7, obtained
Fxf[sinδ-sin(δ+θ)]+Fyf[cosδ-cos(δ+θ)]+Fyr(1-cosθ)+(Ff+Fw) formula 8 of sin θ=0
Simultaneous formula 6 and formula 8, obtain driving force equation group：
Formula 9 is as regarded state as known quantity, three equations, three function Fxf、Fyf、Fyr, can be to implicit function Fxf、Fyf、Fyr Solved；
Step B3 introduces course angle equation, course angle θ, side slip angle β and the yaw velocity ω of vehiclerBetween deposit Relational expression is：
To the derivation of formula 10, obtain
Wherein：β=v/u is side slip angle；
Formula 1 is substituted into formula 11, arranges to obtain course angle equation
Step B4 introduces motor racing radius equation, and can obtain motor turning radius by Movement Locus Equation formula 5 is：
Simultaneous formula 5 and formula 13, obtain motor racing radius equation：
It can be seen that motor turning radius is determined, according to formula 5, to obtain by motion state from the expression formula of motor racing radius
Step C：Automobile minimum time maneuver Optimal Control Model is established on the basis of step B, specifically includes following processing： Various constraintss are introduced on the basis of Vehicle Handling Inverse Dynamics model, with vehicle front corner δ and front wheel drive force FxfFor Variable is controlled, two-track line process is completed as control targe using the shortest time, Optimal Control Model is established, minimum time maneuver problem is turned Optimal control problem is turned to, optimal control problem is converted into nonlinear programming problem with direct collocation method, it is secondary with sequence Planing method solves to the nonlinear programming problem after conversion, specifically includes following steps：
C1：Introduce performance indications：According to the theory of optimal control, shortest time performance is described with mathematic(al) representation and refers to Mark：
Wherein：t0For initial time；tfFor terminal juncture；Z is control variable；
C2：Domination set is introduced, automobile minimum time maneuver Optimal Control Model is anti-using the two-track line after optimizing as domination set Ask driver's steering wheel angle to input, initially set up road model, establish driver's acceptable path input set, generally examine Worry is fitted with low order smooth function, therefore the state variable of the Vehicle Handling Inverse Dynamics model should be by two-track line boundary Constraint, the state variable y (x) of the Vehicle Handling Inverse Dynamics model should be by the boundary constraint of two-track line：
f1(x)≤y(x)≤f2(x) formula 17
Wherein：f1(x), f2(x) it is respectively upper and lower two-track line equation,
Road model is specially
The longitudinal velocity u of the Vehicle Handling Inverse Dynamics model is constrained by automobile max. speed；Front wheel angle δ by The constraint of physiological driver's limit.
C3：Various constraintss are introduced, are specifically included：
(1) rollover constraint：The model that the present invention establishes does not consider the effect of suspension, therefore ignores the shadow at automobile side inclination angle Ring, automobile is determined for automotive structural parameter, the condition turned on one's side only requires side force or side acceleration reaches and necessarily faced Dividing value, therefore the acceleration threshold value that automobile is not turned on one's side is provided, acceleration threshold value is：ay≤3m/s
(2) front-wheel drive force constraint：For verified automobile when doing minimum time maneuver, automobile is constantly in driving condition, this When, rear wheel drive force Fxr=0, front wheel drive force will be limited by ground adhesive rate, and front wheel drive force is constrained to：
Front wheel drive force is also constrained by the maximum driving force that power drive system provides.According to engine speed and vapour The relation of the relation of car travel speed, engine output torque and driving force, by engine test bench characteristic curve, can obtain maximum The relation of driving force and automobile driving speed.
(3) boundary condition：Automobile original state when doing the motion of two-track line is fixed, and the SOT state of termination will be by lateral displacement Constraint, therefore the boundary condition of setting models is wanted, the model boundary condition is：
V (0)=v0, ωr(0)=ωr0, y (0)=y0, θ (0)=θ0, u (0)=u0, y (xf)=yf。
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto, Any one skilled in the art in the technical scope of present disclosure, technique according to the invention scheme and its Inventive concept is subject to equivalent substitution or change, should all be included within the scope of the present invention.

Claims (8)

  1. A kind of 1. modeling legislation of automobile minimum time maneuver inverse dynamics mathematical modeling, it is characterised in that：Comprise the following steps：
    Step A：Establish automobile operation kinetic model；
    Step B：Automobile operation kinetic model is converted into Vehicle Handling Inverse Dynamics model；
    Step C：Establish automobile minimum time maneuver Optimal Control Model.
  2. 2. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 1, it is characterised in that described Step A：Automobile operation kinetic model is established, is specifically included：Step A1：Consider the lateral movement of automobile, weaving and On the basis of lengthwise movement, 3DOF motion state of automobile equation is established；Step A2：Establish linear tire equation and motion Equation of locus；Step A3：On the basis of longitudinal axle load displacement is considered, automobile operation kinetic model is established.
  3. 3. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 2, it is characterised in that In step A1, specifically include：Assuming that tire cornering characteristics are in the range of linearity, the differential equation of motion of automobile is reduced to side To motion, the car model of weaving and lengthwise movement 3DOF, and then establish its differential equation of motion；
    In step A2, specifically include：When automobile side angle acceleration is less than 0.4g, tire can be approximately considered and be in linear model Enclose, establish front and back wheel lateral deviation power equation；Establish ground reference coordinate systemO xy , and then establish kinematic trajectory equation；
    In step A3, specifically include：When not considering that automotive suspension vertical vibration and automobile roll influence, before and after automobile The relation of wheel load establishes longitudinal loading equation of transfer.
  4. 4. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 3, it is characterised in that institute Stating 3DOF motion state of automobile equation in step A1 is：
    ；
    Front and back wheel lateral deviation power equation and kinematic trajectory equation are respectively in step A2：
    ；
    ；
    Longitudinal loading equation of transfer is in step A3：
    ；
    The method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 3, it is characterised in that described Step B:Automobile operation kinetic model is converted into Vehicle Handling Inverse Dynamics model, specifically includes：Step B1：Incoming direction Disk corner；Step B2：Introduce driving force equation group；Step B3：Introduce course angle equation；Step B4:Introduce motor racing radius Equation；Most automobile operation kinetic model is converted into Vehicle Handling Inverse Dynamics model at last.
  5. 5. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 4, it is characterised in that In step B1, specifically include：Determine to turn to angle equation according to front and back wheel side drift angle；In step B2, specifically include：In steepest Under operating situation, automobile is in driving condition, now hasF xr =0, bring into step A2 and step A3 equation, carry out equation and ask Solution, finally gives driving force equation group；In step B3, specifically include：The course angle of vehicleθ, side slip angleβWith yaw angle Speedω r Between relational expression be present, to being brought into after its derivation in step A1 equations, arrangement obtains course angle side Journey；In step B4, specifically include：Motor turning radius item in angle equation be present according to turning to, introduce automobile radius expression formula, Motor turning radius is determined by movement locus, and then determines motor racing radius equation.
  6. 6. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 5, it is characterised in that institute Stating the steering angle equation determined in step B1 according to front and back wheel side drift angle is：
    Driving force equation group is in step B2：
    ；
    Course angle equation is in step B3：
    ；
    Course angle equation is in step B4：
    ；
    The method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 5, it is characterised in that described Step C：Automobile minimum time maneuver Optimal Control Model is established, is specifically included：Step C1：Introduce performance indications；Step C2：Introduce control System collection；Step C3：Introduce various constraintss；Finally establish automobile minimum time maneuver Optimal Control Model.
  7. 7. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 6, it is characterised in that In step C1, specifically include：According to the theory of optimal control, shortest time performance indications can be described with mathematic(al) representation；
    In step C2, specifically include：The model that the present invention establishes carrys out reverse driving using the two-track line after optimizing as domination set Member's handle input, therefore road model should be established first, driver's acceptable path input set is established, is generally considered with low Rank smooth function is fitted, therefore the dominant vector of the Vehicle Handling Inverse Dynamics model should be by the pact of two-track line boundary Beam；
    In step C3, specifically include：（1）Rollover constraint：The model that the present invention establishes does not consider the effect of suspension, therefore ignores The influence at automobile side inclination angle, automobile is determined for automotive structural parameter, the condition turned on one's side is only required side force or laterally added Speed reaches certain critical value, therefore provides the acceleration threshold value that automobile is not turned on one's side；（2）Front-wheel drive force constraint： For verified automobile when doing minimum time maneuver, automobile is constantly in driving condition, now, rear wheel drive force Fxr=0, front wheel drive force To be limited by ground adhesive rate；（3）Boundary condition：Automobile original state when doing the motion of two-track line is fixed, the SOT state of termination To be constrained by lateral displacement, therefore want the boundary condition of setting models.
  8. 8. the method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling according to claim 7, it is characterised in that institute The mathematic(al) representation for stating performance indications in step C1 is：
    ；
    The constraint of road model and two-track line boundary is respectively in step C2：
    ；
    f1(x)≤Z(x)≤f2(x)；
    Automobile is not turned on one's side in step C3 acceleration threshold value, front-wheel drive force constraint, boundary condition are respectively：
    a y ≤3m/s 2 ；
    ；
    ,,,,,。
CN201710820692.8A 2017-09-13 2017-09-13 A kind of method for building up of automobile minimum time maneuver inverse dynamics mathematical modeling Pending CN107561943A (en)

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CN108725453A (en) * 2018-06-11 2018-11-02 南京航空航天大学 Control system and its switch mode are driven altogether based on pilot model and manipulation the man-machine of inverse dynamics
CN110155081A (en) * 2019-05-28 2019-08-23 南京航空航天大学 A kind of adaptive obstruction-avoiding control system of intelligent driving automobile

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CN108717268A (en) * 2018-06-22 2018-10-30 南京航空航天大学 Automatic Pilot minimum time maneuver control system and its control method based on optimum control and safe distance
CN110155081A (en) * 2019-05-28 2019-08-23 南京航空航天大学 A kind of adaptive obstruction-avoiding control system of intelligent driving automobile

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Application publication date: 20180109