CN104859661A - Vehicle cornering time optimization algorithm - Google Patents

Abstract

The invention provides a vehicle cornering time optimization algorithm. As a driver firstly gives a control turning angle according to the running road profile and motion state of a vehicle, the motion state of the vehicle in running is obtained by a vehicle-mounted sensor; direction deviation and lateral displacement deviation between a vehicle running trajectory and a track center line are obtained by a Kalman filter according to the motion state of the longitudinal vehicle in running on the basis of predetermined rules; an additional turning angle is obtained by a controller according to the motion state, direction deviation and lateral displacement deviation on the basis of the optimal control algorithm; and the optimal turning angle of front wheels of the vehicle is determined by both the control turning angle and the additional turning angle. According to the invention, the optimized turning angle is obtained through computation, so that the vehicle turns a corner in a shorter time. Thus, the time for a racing driver to complete the whole race is shortened, and a good grade is achieved.

Description

Curved time-optimized algorithm crossed by vehicle

Technical field

The present invention relates to a kind of vehicle and cross curved time algorithm, be specifically related to a kind of vehicle and cross curved time-optimized algorithm.

Background technology

Racing car is the motion using automobile to do race.In 1895, this motion first time occurred in France.Nowadays, it has become the competitive sports that the whole world attracts maximum spectators to watch.

In F1 formula car or intelligent vehicle contest, individual pen time minimum is the ultimate aim that players is pursued.In the automobile race of most of form, when racing car enters straight way link, except driver needs the skilled gearshift time of holding the best, the performance of racing car itself also has a great impact car speed.After entering various bend, brake, throttle, direction, gear link will be accomplished perfection by driver simultaneously, just can throw other opponents away, obtain leading.Thus for a car racing driver, can excessively curved skill play a part key for the triumph that finally obtain match.Therefore, how completing curved sooner, is the problem faced by each car racing driver.

Summary of the invention

The present invention carries out to solve above-mentioned problem, and object is to provide a kind of and reduces racing car and cross the vehicle of curved time and pass curved time-optimized algorithm.

The invention provides a kind of vehicle and cross curved time-optimized algorithm, for obtaining the front-wheel optimum corner of described vehicle when vehicle is crossed curved along predetermined track thus making described Ackermann steer angle period of service minimum, it is characterized in that, comprise the following steps: step 1, chaufeur is according to the given control corner of speed and direction of predetermined track and vehicle operating; Step 2, the operating speed of onboard sensor collection vehicle and tyre slip angle; Step 3, Kalman filter to obtain deviation in direction between the line of centers in vehicle operating track and predetermined track and side travel deviation based on pre-defined rule according to speed; Step 4, controller obtains additional rotation angle according to speed, deviation in direction and side travel deviation based on optimal control algorithm; Step 5, control corner is added with additional rotation angle and obtains the optimum corner of front-wheel.

Cross curved time-optimized algorithm at vehicle provided by the present invention, can also have such feature: wherein, speed comprises: yaw velocity, longitudinal velocity and side velocity.

Cross curved time-optimized algorithm at vehicle provided by the present invention, can also have such feature: wherein, step 3 comprises the following steps:

Step 3-1, Kalman filter gathers line of centers information and the boundary information in described planning track,

Step 3-2, Kalman filter to obtain described deviation in direction between the line of centers in described vehicle operating track and described planning track and described side travel deviation based on pre-defined rule according to described speed and described line of centers information and boundary information.

Cross curved time-optimized algorithm at vehicle provided by the present invention, can also have such feature: wherein, described step 4 comprises the following steps:

Step 4-1: the increment obtaining described vehicle movement distance according to described speed, described tyre slip angle, described deviation in direction and described side travel deviation,

Step 4-2: set up secondary objective function according to described increment, described secondary objective function J is:

Wherein, q ₁and q ₂represent coefficient of weight, δ is the optimum corner of front-wheel, and Δ ψ is deviation in direction, and Δ y is side travel deviation, r _rfor the radius of described racing track line of centers camber,

Step 4-3: the described secondary objective function be simplified according to described side velocity, described yaw velocity, described deviation in direction and described side travel deviation:

Step 4-4: by solving Riccati equation, obtains feedback gain K _lQG, described solution Riccati equation is:

A ^TP+PA-(PB+N)R ^-1(B ^TP+N ^T)+Q＝0

Wherein, r=1, N=0, v _xfor longitudinal velocity, a _yfor lateral acceleration, C _yffor front-wheel cornering stiffness, C _yrfor trailing wheel cornering stiffness, q ₃and q ₄represent coefficient of weight, a be automobile barycenter to front axle distance, b be automobile barycenter to rear axle distance, I is Vehicular yaw rotor inertia, and m is car mass, and P is the solution of Riccati equation,

Step 4-5: obtain described additional rotation angle based on pre-defined rule according to described feedback gain, described additional rotation angle is:

δ _LOG＝-K _LOGΔx

Wherein, Δ x=x-x ₀, x ₀=[0,0, ψ ^*, Y ^*], Y ^*for planning track, ψ ^*for planning track tangent line and and X-axis between angle, X-axis is the coordinate axle under inertial coordinates system.

The effect of invention

Curved time-optimized algorithm is crossed according to vehicle involved in the present invention, because chaufeur is first according to road shape and the given control corner of state of kinematic motion of vehicle traveling, onboard sensor obtains the state of kinematic motion in vehicle operating, Kalman filter obtains deviation in direction between vehicle operating track and racing track line of centers and side travel deviation according to the state of kinematic motion in vehicle operating based on pre-defined rule, controller is according to state of kinematic motion, deviation in direction and side travel deviation obtain additional rotation angle based on optimal control algorithm, control corner and additional rotation angle determine the optimum corner of front-wheel of vehicle jointly, vehicle of the present invention is crossed curved time-optimized algorithm and is made vehicle period of service when crossing curved short by calculating optimization corner, thus shortening car racing driver completes the time needed for whole schedules, the achievement obtained.

Accompanying drawing explanation

Fig. 1 is the diagram of circuit that in embodiments of the invention, curved time-optimized algorithm crossed by vehicle;

Fig. 2 is vehicle dynamic model figure in embodiments of the invention;

Fig. 3 is the geometric relationship figure of vehicle on planning track in embodiments of the invention;

Fig. 4 is that in embodiments of the invention, intelligent vehicle model 2m/s crosses curved distance base diagram;

Fig. 5 is that in embodiments of the invention, intelligent vehicle model 3m/s crosses curved distance base diagram;

Fig. 6 is the yaw velocity-time chart in embodiments of the invention in intelligent vehicle model driving process;

Fig. 7 is the side velocity-time chart in embodiments of the invention in intelligent vehicle model driving process;

Fig. 8 is front wheel angle-time chart in embodiments of the invention; And

Fig. 9 is side slip angle-time chart in embodiments of the invention.

Detailed description of the invention

The technological means realized to make the present invention, creation characteristic, reach object and effect is easy to understand, following examples are crossed curved time-optimized algorithm to vehicle of the present invention by reference to the accompanying drawings and are specifically addressed.

Fig. 1 is the diagram of circuit that in embodiments of the invention, curved time-optimized algorithm crossed by vehicle.

As shown in Figure 1, in the present embodiment, vehicle crosses curved time-optimized algorithm 100 for calculating the optimum corner of the front-wheel of vehicle in excessively curved process, thus it is curved that vehicle was completed within the shortest time.The concrete steps that curved time-optimized algorithm 100 crossed by vehicle are as follows:

Step S1, the road shape travelled according to vehicle and state of kinematic motion, chaufeur controls corner δ to one, vehicle _lM, then, enter step S2.

Step S2, onboard sensor obtains the yaw velocity of vehicle operating, longitudinal velocity and side velocity.

The present embodiment adopts non-linear auto model to design curved optimum corner, and this non-linear auto model is two degrees of freedom single-track vehicle handling dynamics model.Specific as follows:

Fig. 2 is vehicle dynamic model figure in embodiments of the invention.

As shown in Figure 2, the X-axis of earth coordinate system (i.e. inertial coordinates system), Y-axis is vertical with X-axis, non-linear auto model; Two degree of freedom are respectively sideway movement and weaving.The equation of motion that vehicle travels on road is:

Wherein, m is car mass, v _xfor longitudinal velocity, v _yfor side velocity; for yaw velocity; A be automobile barycenter to front axle distance, be vehicle parameter, b be automobile barycenter to rear axle distance, be vehicle parameter, F _yffor the total side force of front-wheel, F _yrfor the total side force of trailing wheel, I is Vehicular yaw rotor inertia.

The present embodiment obtains the total side force of front-wheel and the total side force of trailing wheel by setting up tire model." magic formula " tire model is as follows:

F _yi＝2D _isin(C _yiarctan(B _yiα _i-E _yi(B _yiα _i-arctan(B _yiα _i)))) (2)

In order to simplify non-linear tire force, it is approximately linear time-varying (LTV) model here.Launching at each current time by Taylor's formula, retain first order component, high order component is cast out, then tire force can be converted into simple LTV expression formula:

F _yi(t)＝C _yi(t)α _i(t)+D _yi(t) (3)

Wherein, C _yit () is time dependent tire cornering stiffness, D _yit () is the tire force when sideslip angle is zero, α _ilower expression tyre slip angle, subscript i comprises f and r, and f represents front-wheel, and r represents trailing wheel, and subscript y represents lateral.

Front and rear wheel sideslip angle is calculated by following formula:

Wherein, α _ffor front wheel side drift angle; α _rfor rear wheel-side drift angle; δ is the optimum corner of front-wheel, as the input of model.

Onboard sensor can detect the state of kinematic motion of automobile, and wherein the state of kinematic motion of vehicle comprises: yaw velocity side velocity v _ywith longitudinal velocity v _x.Then, step S3 is entered.

Step S3, Kalman filter to obtain deviation in direction between the line of centers in vehicle operating track and described planning track and side travel deviation according to running state based on pre-defined rule.

The key of controller to obtain vehicle deviation in direction in the process of moving and side travel deviation.

Conveniently calculate, Δ y and Δ ψ linearization.Line of centers information and the boundary information in planning track is collected by Kalman filter.

Fig. 3 is the geometric relationship figure of vehicle on planning track in embodiments of the invention.

As shown in Figure 3, X-axis and Y-axis are the coordinate axle under earth coordinate system (i.e. inertial coordinates system), and empty camber line is the line of centers in planning track, and real camber line is the border in planning track, r _rfor the radius of described racing track line of centers camber, to plan that the line of centers in track is for line of reference, in T time, the distance travelled along line of reference is ds _r, and interior automobile advance is ds=VT ≈ uT during this period of time, wherein, V is the speed of vehicle, and u is the average velociity in vehicle T time.D ψ _rfor in time T, vehicle to be advanced ds relative to the line of centers in planning track _rapart from corresponding angle.

Vehicle is along line of centers advance ds _rwith X-axis forward angle ψ _r:

Then deviation in direction Δ ψ is defined as yaw angle ψ and ψ _rdifference:

Wherein, ψ _rfor track is planning centerline tangent direction and the X-axis forward angle in track.

In order to by side travel error linear, when the speed of a motor vehicle is constant, only depend on corner.Side travel error delta y can be approximated to be:

Δy＝v _ycos(Δψ)+v _xsin(Δψ) (8)

In order to keep vehicle in planning track, boundary condition is defined as following form:

Wherein, w _rfor planning the width in track, w is the half of car gage.

According to above-mentioned pre-defined rule, Kalman filter can draw vehicle deviation in direction Δ ψ under steam and side travel deviation delta y.Then, step S4 is entered.

Step S4, controller obtains additional rotation angle according to side velocity, yaw velocity, deviation in direction and the side travel deviation application theory of optimal control.

Cross curved time-optimized in, if larger along the distance passed through with reference to route within the regular hour, can think in whole process it is shorten the time.

The increment of distance is obtained according to the side travel error between the predicted state of vehicle front wheel angle and vehicle and racing track line of reference:

Formula (10) meets with Δ y < < r _r.

When Δ s maximizes, namely in the set time, the distance that automobile travels along road line of reference is more, then automobile advance on bend more, the whole mistake curved time will shorten.So the present invention proposes secondary objective function:

Wherein, q ₁and q ₂represent coefficient of weight, δ is that front-wheel optimizes corner.

Vehicle dynamic model gets system state variables write as state space equation, form is as follows:

Wherein,

c _yffor front-wheel cornering stiffness, C _yrfor trailing wheel cornering stiffness.

Introduce process noise w to formula (12) entrance point, its state space equation can be changed into following form:

Wherein G=B, w are Gaussian sequence.

Measurement equation z with sensor noise v can have following form to represent;

z＝Hx+v

Wherein, z=[ψ Δ ψ Δ y], v=[v _ψv _{Δ ψ}v _{Δ y}].

Calculating K alman gain, supposes that the covariance of process disturbance is set as 10 ², yaw velocity lateral deviation Δ y, is set as 0.01 with the noise of deviation in direction Δ ψ ².Estimated valve after can being optimized by " Kalman " function in Matlab/simulink software

Secondary objective function (11) can turn to:

At condition Δ y < < r _runder:

Can obtain according to the theory of optimal control:

R＝1,N＝0

Wherein, a _yfor lateral acceleration.

Can by separating Riccati equation, solve the Optimal Feedback of quadratic model object function, Riccati equation is:

A ^TP+PA-(PB+N)R ^-1(B ^TP+N ^T)+Q＝0 (15)

Wherein, P is the solution of Riccati equation, and " LQR " function in Matlab instrument can be utilized to solve.

Solve formula (15), feedback gain K can be obtained _lOG, controller exports additional rotation angle δ _lOG, additional rotation angle δ _lOGexpression formula is as follows:

δ _LQG＝-K _LQGΔx (16)

Wherein, Δ x=x-x ₀, x ₀for desired ride state, x ₀=[0,0, ψ ^*, Y ^*], Y ^*for planning track, ψ ^*for planning track tangential direction and X-axis forward angle.Then, step S5 is entered.

Step S5, control corner is added with additional rotation angle and obtains the optimum corner of front-wheel.

In order to verify the validity of designed control algorithm, according to theory of similarity BuckinghamPi principle, test with Freescale model of mind car.

Vibration equivalence: according to dimensional method, for a certain physical phenomenon, if two equal by the demensionless number Π that the physical system of differential equation is corresponding, so the differential equation of two physical systems has identical solution.By measuring the basic specification of Freescale intelligent vehicle model parameter and real vehicle is as shown in table 1.

Table 1 model car and certain real vehicle basic specification

By above-mentioned physical quantity composition nondimensionalization item, can obtain:

In table 1, the dimension of parameter is as shown in table 2.

Table 2 vehicle basic specification dimension

Wherein: Π _iScalefor the dimensionless item of intelligent vehicle model, Π _iRealfor the dimensionless item of real vehicle, subscript i=1,2,3.The dimensionless item deviation of model car and real vehicle is less, then can think and intelligent vehicle model and real vehicle vibration equivalence according to the ratio of length dimension, be about 1:10.

In order to Reality simulation situation, the single-point optimum proposed according to Guo Konghui academician is here taken aim at curvature pilot model in advance and is simulated to the control corner δ of one, vehicle expection _rM.According to " principle of least error ", chaufeur expects an optimal trajectory curvature 1/R ^*, meet when automobile is passed by preview distance d (after namely taking aim at time T in advance), vehicle is after taking aim at time T in advance, and the lateral coordinates y (t+T) of vehicle is consistent with this place desired trajectory lateral coordinates f (t+T):

Optimum lateral acceleration is:

Optimal curvature is:

Chaufeur bearing circle angle is input as:

Consider reaction and perform time delay, chaufeur steering wheel angle is input as:

Wherein, K _hfor steering angle gain, τ _rfor chaufeur reflection time delay, τ _hfor driver's operation time delay.

Test results: on open smooth ground, laid racing track.Record the sensing data that is arranged on intelligent vehicle mould and expend time in.

Fig. 4 is that in embodiments of the invention, intelligent vehicle model 2m/s crosses curved distance base diagram.

" S " that racing track is made up of two tangent quarter circular arc curved and two sections of straight line racing tracks are formed.According to the data of record, when the speed of a motor vehicle is 2m/s, corresponding real vehicle speed is 20m/s, with the position every 1 second record intelligent vehicle mould.

Initial time, vehicle travels on straight racing track, after enter bend, finally roll bend away from and enter straight racing track.Result shows, intelligent vehicle model in, low speed driving time, when entering bend and coming off the curve, all against racing track edge and travel, at the transition phase of " S " bend, approximate with straight-line pass.The driving trace of vehicle decreased curved total kilometrage, whole process 20s consuming time, and when not having system optimizing control, whole process then needs 21.1s, thus can reduce over the curved time.

Verify further designed controller, when the speed of a motor vehicle is increased to 3m/s, corresponding real vehicle is 30m/s, when namely running at high speed.In this case, controller needs to ensure that vehicle passes through bend smoothly within racing track width range.

Fig. 5 is that in embodiments of the invention, intelligent vehicle model 3m/s crosses curved distance base diagram.

As shown in Figure 5, intelligent vehicle model in traveling in the near future, predict front bend at hand, in advance vehicle is controlled, control it and provide turn sign, allow vehicle first lanes laterally, and against racing track with speed faster and enter first bend, at the transition phase of two bends, almost pass through with straight line track, finally against bend and show greatly a constant corner and come off the curve.

Fig. 6 is the yaw velocity-time chart in embodiments of the invention in intelligent vehicle model driving process; Fig. 7 is the side velocity-time chart in embodiments of the invention in intelligent vehicle model driving process; Fig. 8 is front wheel angle-time chart in embodiments of the invention; Fig. 9 is side slip angle-time chart in embodiments of the invention.

As Fig. 6, Fig. 7, Fig. 8 and Fig. 9, curve 10 represents intelligent vehicle model and does not use vehicle of the present invention to cross curved time-optimized algorithm, curve 20 represents intelligent vehicle model and uses vehicle of the present invention to cross curved time-optimized algorithm, as can be seen from Fig. 6, Fig. 7, Fig. 8 and Fig. 9, cross in curved time-optimized algorithm at use vehicle of the present invention, little than when not having a controller of the overshoot of system dynamic response, whole process about 13.3s consuming time, and under the effect not having controller, consuming time is 14.2s, and therefore designed controller efficiently reduced the curved time.

Test results shows, the curved time-optimized control algorithm of designed mistake, under the prerequisite ensureing vehicle run stability, can effectively reduce over the curved time.

The effect of embodiment and effect

Curved time-optimized algorithm crossed by vehicle involved by the present embodiment, because chaufeur is first according to road shape and the given control corner of state of kinematic motion of vehicle traveling, onboard sensor obtains the state of kinematic motion in vehicle operating, Kalman filter obtains deviation in direction between vehicle operating track and racing track line of centers and side travel deviation according to the state of kinematic motion in vertical vehicle operating based on pre-defined rule, controller is according to state of kinematic motion, deviation in direction and side travel deviation obtain additional rotation angle based on optimal control algorithm, control corner and additional rotation angle determine the optimum corner of front-wheel of vehicle jointly, vehicle of the present invention is crossed curved time-optimized algorithm and is made vehicle period of service when crossing curved short by calculating optimization corner, thus shortening car racing driver completes the time needed for whole schedules, the achievement obtained.

Above-mentioned embodiment is preferred case of the present invention, is not used for limiting the scope of the invention.

Claims (4)

1. a curved time-optimized algorithm crossed by vehicle, for obtaining the front-wheel optimum corner of described vehicle when vehicle is crossed curved along predetermined track thus making described Ackermann steer angle period of service minimum, it is characterized in that, comprises the following steps:

Step 1, chaufeur is according to the given control corner of speed and direction of described predetermined track and described vehicle operating;

Step 2, onboard sensor gathers speed in described vehicle operating and tyre slip angle;

Step 3, Kalman filter to obtain deviation in direction between the line of centers in described vehicle operating track and described predetermined track and side travel deviation based on pre-defined rule according to described speed;

Step 4, controller obtains additional rotation angle according to described speed, described deviation in direction and described side travel deviation based on optimal control algorithm;

Step 5, described control corner is added with described additional rotation angle and obtains the optimum corner of described front-wheel.

2. curved time-optimized algorithm crossed by vehicle according to claim 1, it is characterized in that:

Wherein, described speed comprises: yaw velocity, longitudinal velocity and side velocity.

3. curved time-optimized algorithm crossed by vehicle according to claim 1, it is characterized in that:

Wherein, step 3 comprises the following steps:

Step 3-1, Kalman filter gathers line of centers information and the boundary information in described planning track,

Step 3-2, Kalman filter to obtain described deviation in direction between the line of centers in described vehicle operating track and described planning track and described side travel deviation based on pre-defined rule according to described speed and described line of centers information and boundary information.

4. curved time-optimized algorithm crossed by vehicle according to claim 2, it is characterized in that:

Wherein, described step 4 comprises the following steps:

Step 4-1: the increment obtaining described vehicle movement distance according to described speed, described tyre slip angle, described deviation in direction and described side travel deviation,

Step 4-2: set up secondary objective function according to described increment, described secondary objective function J is:

$J=\mathrm{\&Sigma;}{q}_1({\mathrm{\&Delta;yd\&psi;}}^2-q_2{r}_r\mathrm{d\&psi;}\frac{{\mathrm{\&Delta;\&psi;}}^2}{2}+{\mathrm{\&delta;}}^2)$

Wherein, q ₁and q ₂represent coefficient of weight, δ is the optimum corner of front-wheel, and Δ ψ is deviation in direction, and Δ y is side travel deviation, r _rfor the radius of described racing track line of centers camber,

Step 4-3: the described secondary objective function be simplified according to described side velocity, described yaw velocity, described deviation in direction and described side travel deviation:

$J=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(q_{1}d{\mathrm{\&psi;}}_r^2{\mathrm{\&Delta;y}}^2+\frac{1}{2}{q}_2{r}_{r}d{\mathrm{\&psi;}}_r{\mathrm{\&Delta;\&psi;}}^2+{\mathrm{\&delta;}}^2)$

Step 4-4: by solving Riccati equation, obtains feedback gain K _lQG, described solution Riccati equation is:

A ^TP+PA-(PB+N)R ^-1(B ^TP+N ^T)+Q＝0

Wherein, $A=\left[\begin{array}{cccc}-\frac{a^2{C}_{\mathrm{yf}}+b^2{C}_{\mathrm{yr}}}{{\mathrm{Iv}}_x}& -\frac{({\mathrm{aC}}_{\mathrm{yf}}-{\mathrm{bC}}_{\mathrm{yr}})}{{\mathrm{Iv}}_x}& 0& 0\\ -\frac{({\mathrm{aC}}_{\mathrm{yf}}-{\mathrm{bC}}_{\mathrm{yr}})}{{\mathrm{mv}}_x}-v_x& -\frac{C_{\mathrm{yf}}+C_{\mathrm{yr}}}{{\mathrm{mv}}_x}& 0& 0\\ 1& 0& 0& 0\\ 0& 1& v_x& 0\end{array}\right],$ $B={\left[\begin{array}{cccc}\frac{{\mathrm{aC}}_{\mathrm{yf}}}{I}& \frac{C_{\mathrm{yf}}}{m}& 0& 0\end{array}\right]}^{\&prime;},Q=\left[\begin{array}{cccc}{q}_1& 0& 0& 0\\ 0& q_2& 0& 0\\ 0& 0& q_3\frac{a_y^2{T}^2}{{v_x}^2}& 0\\ 0& 0& 0& \frac{1}{2}{q}_4{v}_{x}T\end{array}\right],$ R=1, N=0, v _xfor longitudinal velocity, a _yfor side direction and speed, C _yffor front-wheel cornering stiffness, C _yrfor trailing wheel cornering stiffness, q ₃and q ₄represent coefficient of weight, a be automobile barycenter to front axle distance, b be automobile barycenter to rear axle distance, I is Vehicular yaw rotor inertia, and m is car mass, and P is the solution of Riccati equation,

Step 4-5: obtain described additional rotation angle based on pre-defined rule according to described feedback gain, described additional rotation angle is:

δ _LOG＝-K _LOGΔx

Wherein, Δ x=x-x ₀, x ₀=[0,0, ψ ^*, Y ^*], Y ^*for planning track, ψ ^*for the angle between planning track tangent line and X-axis, X-axis is the coordinate axle under inertial coordinates system.