CN110109451B - Novel geometric path tracking algorithm considering path curvature - Google Patents
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Abstract
The invention discloses a novel geometric path tracking algorithm considering path curvature, which comprises the following steps: s1, acquiring path discrete coordinate points at a fixed frequency by using a GPS to obtain a reference path point set P; s2, searching a path point p closest to the current automobile positioni(piBelongs to P); s3, calculating a path point p by using a least square methodiAt the corresponding path curvature ρi(ii) a S4, calculating rho according to the Ackerman steering geometric modeliCorresponding front wheel angle thetaρiAnd front wheel steering angleS5, calculating the current position and the path point p of the automobileiA course deviation yawrerr, a lateral deviation latErr; s6, according to the direction angle of the front wheelA course deviation yawErr and a transverse deviation Laterr are designed to a path tracking controller, and a desired direction angle of the front wheel is calculatedFurther, a desired rotation angle theta of the front wheel is obtainedt. The method is simple in algorithm, not only suitable for the technical field of simulation, but also capable of being realized on an embedded controller of a real vehicle, and has a good application prospect. Experiments prove that the method provided by the invention has small tracking error and stronger robustness.
Description
Technical Field
The invention relates to the technical field of unmanned vehicle path tracking, in particular to a novel geometric path tracking algorithm considering path curvature.
Background
The lateral control of the automobile is one of the key technologies for realizing the autonomous driving of the unmanned automobile. The path tracking controls the vehicle to travel along an expected path all the time through autonomous steering, meanwhile, the riding comfort and the traveling safety of the vehicle are guaranteed, the intelligent vehicle is a bridge for connecting upper-layer software and bottom-layer hardware of the intelligent vehicle, and the intelligent vehicle is a necessary link for achieving unmanned driving. The curvature-considered path tracking algorithm is that the front wheel rotation angle is estimated according to the curvature of the path to simulate the path change trend, then the negative feedback is used for eliminating the transverse deviation, and the heading deviation negative feedback is used for restraining the front wheel rotation angle to prevent overshoot.
At present, many researchers at home and abroad aim at the path tracking control of the unmanned automobile, mostly use transverse deviation and course deviation as the input of a controller, and use a feedback control method to realize the path tracking of the unmanned automobile. One of the most common path tracking methods is the geometry controller, which uses the geometric relationship of the path to the vehicle and to the vehicle itself to provide a control solution to the path tracking problem. The most representative geometry controller is a pure tracking algorithm, which is widely used due to its simple model, small calculation amount and good tracking effect.
The key to the pure tracking algorithm is the reasonable choice of look-ahead distance. The forward looking distance is too large, so that the transverse error of tracking is slowly eliminated, and an obvious road-reading phenomenon appears on a turning road section; the forward looking distance is too small, so that a good tracking effect is achieved at an extremely low speed, but an extremely serious oscillation phenomenon occurs at a high speed, so that the tracking effect is deteriorated. Therefore, many domestic and foreign scholars propose many improved algorithms based on the pure tracking algorithm to extend the stability of the pure tracking algorithm. Anibal Ollero proposes a tracking algorithm for adjusting the look-ahead distance based on fuzzy logic; the MIT team proposes a tracking algorithm that adaptively adjusts the forward apparent distance reference point based on vehicle speed. Since the control strategy does not consider the curvature of the path, the phenomenon of copying the near path occurs when the curvature of the path changes continuously, especially when the curvature is large.
Disclosure of Invention
In order to solve the problems, the invention discloses a novel geometric path tracking algorithm considering path curvature, which is characterized in that the corresponding automobile front wheel corner is calculated according to the curvature of a reference path to simulate the change trend of the reference path, the transverse deviation in the simulation process is eliminated by negative feedback, the course deviation is utilized to inhibit overshoot, the path tracking is finally realized, and the tracking precision and the tracking stability can be improved.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a novel geometric path tracking algorithm that takes into account path curvature, comprising the steps of:
s1, acquiring path discrete coordinate points at a fixed frequency by using a GPS to obtain a reference path point set P;
the GPS positioning precision is centimeter level, the reference path point set P is represented by plane right angle and is obtained by converting coordinates of longitude and latitude output by GPS into UTM coordinates (universal transverse axis mercator coordinates), so as to facilitate calculation of path curvature and positioning in a global coordinate system Xglobal-YglobalIs converted into a moving vehicle body coordinate system X _ v-X _ v.
S2, searching a path point p closest to the current automobile positioni(pi∈P);
The data in the reference path point set are arranged in sequence, only the nearest path point needs to be searched for the first time in a global search mode, and only local search is needed to be performed later, so that the advantages of saving computing resources and improving the search speed are achieved.
S3, calculating a path point p by using a least square methodiAt the corresponding path curvature ρi;
Respectively select points pi(xi,yi) Front and back 3 path points, 7 points pi(xi-3,yi-3),pi(xi-2,yi-2),pi(xi-1,yi-1),pi(xi,yi),pi(xi+1,yi+1),pi(xi+2,yi+2),pi(xi+3,yi+3). Wherein i>3
Using least square method to make cubic curve y ═ ai+bi·x+ci·x2+di·x3Fitting, i.e. solving the matrix b from a.x ═ b, since the above-mentioned overdetermined system of equations is not solved, it is possible to determine the matrix b from the matrix bApproximate solution using least square principleByTo obtain
obtaining a cubic curve y ═ ai0+bi0·x+ci0·x2+di0·x3
It should be noted that, the curve fitting method determines a curve fitting direction (along the x axis/y axis) by determining whether the x coordinate of the ordered path point changes monotonically (increases/decreases), specifically:
if x is satisfiedi-3>xi-2>xi-1>xi>xi+1>xi+2>xi+3The x coordinate of the ordered path point is monotonically decreased, if x is satisfiedi-3<xi-2<xi-1<xi<xi+1<xi+2<xi+3If the x coordinate of the ordered path point is monotonously increased, in the two cases, y is carried out along the x-axis direction as ai+bi·x+ci·x2+di·x3Fitting a curve;
otherwise, the x coordinate of the ordered path point is not monotonous, and in this case, x is carried out along the y-axis direction as ai+bi·y+ci·y2+di·y3And (6) fitting a curve.
When the curve fit is along the y-axis, the curvature solution and the waypoint heading solution are also adjusted accordingly.
It is emphasized that in a local path, the y coordinate of an ordered path point is necessarily monotonic when its x coordinate is not monotonic.
S4, calculating rho according to the Ackerman steering geometric modeliCorresponding front wheel angle thetaρiAnd front wheel steering angle
According to the ackermann steering principle, the geometrical relationship between the front wheel turning angle and the turning curvature can be expressed as:
tan(θρi)=L·ρi
thus, it is obtained:
θρi=arctan(L·ρi)
further, the direction angle of the front wheel is obtained
Wherein, thetaρiIs the steering angle of the front wheel, L is the wheel base, rhoiIs a path point piThe curvature of the (c) is such that,is the front wheel steering angle, yawcurrentThe current car heading angle.
S5, calculating the current position and the path point p of the automobileiA course deviation yawrerr, a lateral deviation latErr;
the first derivative of the cubic curve fitted in step S3 can be used to obtain the heading angle yaw of the path reference pointiNamely that
yawi=y′(xi)
Then, obtaining the course deviation:
yawErr=yawi-yawvehicle
wherein yawErr is the course deviation, yawiFor path referencePoint course angle, yawvehicleIs the vehicle heading angle.
For determining the lateral deviation, the coordinates (x) of the path reference point in the global coordinate system are determinedR,yR) Coordinate (x) converted to vehicle body coordinate systemr,yr) The conversion formula can be expressed as:
wherein (x)vehicle,yvehicle) Is the position coordinate of the automobile under the UTM coordinate.
Then the lateral deviation is obtained:
S6, according to the direction angle of the front wheelA course deviation yawErr and a transverse deviation Laterr are designed to a path tracking controller, and a desired direction angle of the front wheel is calculatedFurther, the expected rotation angle theta of the front wheel is obtainedt。
The path tracking controller may be represented as:
whereinThe desired front wheel heading angle (the angle of the front wheel to true north), to mimic the trend of path changes,
k1a lateral deviation correction coefficient for eliminating the lateral deviation,
k2is a course deviation correction systemAnd a number of the front wheel turning angle suppressing means for suppressing the overshoot.
The invention has the beneficial effects that:
a novel geometric path tracking algorithm considering curvature is provided for an unmanned automobile, the path curvature is used for calculating a front wheel corner to simulate the path change trend, the transverse deviation is adjusted by negative feedback, and the transverse deviation exceeding is restrained by the transverse deviation negative feedback. Experiments prove that the path tracking algorithm provided by the invention has better applicability to curve paths. The method has the advantages of simple algorithm principle and low calculation complexity, is suitable for the technical field of simulation, can be realized on an embedded controller of a real vehicle, and has good application prospect.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention.
Fig. 2 is a schematic view of an ackermann steering model.
Fig. 3, 4 and 5 show simulation results of the path tracking controller according to the present invention.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
The general design idea of the invention is as follows: and calculating the corresponding automobile front wheel corner according to the curvature of the reference path to simulate the change trend of the reference path, eliminating the transverse deviation in the simulation process by using negative feedback, and inhibiting overshoot by using course deviation to finally realize path tracking.
An embodiment of the invention comprises the following steps:
s1, acquiring path discrete coordinate points at fixed frequency by using a GPS to obtain a reference path point set P;
the GPS positioning precision is centimeter level, the reference path point set P is represented by a plane right angle, and coordinates are converted into UTM coordinates through longitude and latitude output by the GPS(Universal Cross-axis mercator coordinates) to facilitate the computation of path curvature and to be located in the global coordinate System Xglobal-YglobalIs converted into a moving vehicle body coordinate system X _ v-X _ v.
S2, searching a path point p closest to the current automobile positioni(pi∈P);
The data in the reference path point set are arranged in sequence, only the nearest path point needs to be searched for the first time in a global search mode, and only local search is needed to be performed later, so that the advantages of saving computing resources and improving the search speed are achieved.
S3, calculating a path point p by using a least square methodiAt the corresponding path curvature ρi;
Respectively select points pi(xi,yi) Front and back 3 path points, 7 points pi(xi-3,yi-3),pi(xi-2,yi-2),pi(xi-1,yi-1),pi(xi,yi),pi(xi+1,yi+1),pi(xi+2,yi+2),pi(xi+3,yi+3). Wherein i>3。
Using least square method to make cubic curve y ═ ai+bi·x+ci·x2+di·x3Fitting, i.e. obtaining the matrix b from a.x ═ b, and since the system of overdetermined equations is not solved, the approximate solution is obtained using the principle of least squaresByTo obtain
obtaining a cubic curve of y ═ ai0+bi0·x+ci0·x2+di0·x3
It should be noted that, the curve fitting method determines a curve fitting direction (along the x axis/y axis) by determining whether the x coordinate of the ordered path point changes monotonically (increases/decreases), specifically:
if x is satisfiedi-3>xi-2>xi-1>xi>xi+1>xi+2>xi+3The x coordinate of the ordered path point is monotonically decreased, if x is satisfiedi-3<xi-2<xi-1<xi<xi+1<xi+2<xi+3If the x coordinate of the ordered path point is monotonously increased, in the two cases, y is carried out along the x-axis direction as ai+bi·x+ci·x2+di·x3Fitting a curve;
otherwise, the x coordinate of the ordered path point is not monotonous, and in this case, x is carried out along the y-axis direction as ai+bi·y+ci·y2+di·y3And (6) fitting a curve.
When the curve fit is along the y-axis, the curvature solution and the waypoint heading solution are also adjusted accordingly.
It is emphasized that in a local path, the y coordinate of an ordered path point is necessarily monotonic when its x coordinate is not monotonic.
S4, calculating rho according to the Ackerman steering geometric modeliCorresponding front wheel angle thetaρiAnd front wheel steering angle
According to the ackerman steering principle, the geometrical relationship between the front wheel turning angle and the turning curvature can be expressed as:
tan(θρi)=L·ρi
thus, it is obtained:
θρi=arctan(L·ρi)
further, the direction angle of the front wheel is obtained
Wherein, thetaρiIs the steering angle of the front wheel, L is the wheel base, rhoiIs a path point piThe curvature of the (c) is such that,is the front wheel steering angle, yawcurrentThe current car heading angle.
S5, calculating the current position and the path point p of the automobileiA course deviation yawrerr, a lateral deviation latErr;
the first derivative of the cubic curve fitted in step S3 can be used to obtain the heading angle yaw of the path reference pointiNamely, it is
yawi=y′(xi)
Then, obtaining the course deviation:
yawErr=yawi-yawvehicle
wherein yawErr is the course deviation, yawiIs the path reference point course angle, yawvehicleIs the vehicle heading angle.
For determining the lateral deviation, the coordinates (x) of the path reference point in the global coordinate system are determinedR,yR) Coordinate (x) converted into vehicle body coordinate systemr,yr) The conversion formula can be expressed as:
wherein (x)vehicle,yvehicle) The position coordinates of the automobile in the UTM coordinate system.
Then the lateral deviation is obtained:
S6, according to the direction angle of the front wheelA course deviation yawErr and a transverse deviation Laterr are designed to a path tracking controller, and a desired direction angle of the front wheel is calculatedFurther, a desired rotation angle theta of the front wheel is obtainedt。
The path tracking controller may be represented as:
whereinThe desired front wheel heading angle (the angle of the front wheel to true north), to mimic the trend of path changes,
k1a lateral deviation correction coefficient for eliminating the lateral deviation,
k2the correction coefficient is used to restrain the front wheel angle and prevent overshoot.
The simulation results show that: when the initial transverse deviation is 1 meter, the tracking average transverse deviation is 11.19cm, and the course deviation is 2.86 degrees; when the initial transverse deviation is-1 meter, the tracking average transverse deviation is 11.13cm, and the course deviation is 2.88 degrees; when there is no initial lateral deviation, the tracking average lateral deviation is 2.21cm and the heading deviation is 0.85 °. Simulation test results show that the path tracking algorithm has a good tracking effect.
The technical means disclosed in the invention scheme is not limited to the technical means disclosed in the above embodiment, and also includes the technical scheme formed by any improvement of the above technical features.
Claims (6)
1. A novel geometric path tracking algorithm that takes into account path curvature, comprising the steps of:
s1, acquiring path discrete coordinate points at a fixed frequency by using a GPS to obtain a reference path point set P;
s2, searching a path point p closest to the current automobile positioni(pi∈P);
S3, calculating a path point p by using a least square methodiAt the corresponding path curvature ρi;
S4, calculating rho according to the Ackerman steering geometric modeliCorresponding front wheel corner thetaρiAnd front wheel steering angle
S5, calculating the current position and the path point p of the automobileiA course deviation yawrerr, a lateral deviation latErr;
s6, according to the direction angle of the front wheelAutomobile current course angle yawvehicleCourse deviation yawar and lateral deviation latErr design path tracking controller:whereinFor desired direction angle, k, of the front wheel1For the lateral deviation correction coefficient, k2Calculating the expected turning angle of the front wheel for the course deviation correction coefficient
2. A novel geometric path-tracking algorithm taking into account path curvature according to claim 1, characterized in that: in the step S1, the step of,
the GPS positioning accuracy is centimeter level, the reference path point set P is represented by plane right angle and obtained by converting coordinates into universal transverse axis mercator coordinates through longitude and latitude output by GPS, and the purpose is to calculate path curvature and position the path in a global coordinate system X convenientlyglobal-YglobalIs converted into a moving vehicle body coordinate system X _ v-X _ v.
3. A novel geometric path-tracking algorithm taking into account path curvature according to claim 1, characterized in that: in the step S3, in the above step,
calculation of Path points p Using the least squares methodi(piE P) corresponding path curvature PiThe specific process is as follows:
respectively select point pi(xi,yi) The simulation proves that the better fitting result is obtained when N is 3 for each of the front and back N path points, and the following description is given by taking N as 3, and the 7 (2N +1) path points are p respectivelyi(xi-3,yi-3),pi(xi-2,yi-2),pi(xi-1,yi-1),pi(xi,yi),pi(xi+1,yi+1),pi(xi+2,yi+2),pi(xi+3,yi+3) Wherein i>3;
Using least square method to make cubic curve y ═ ai+bi·x+ci·x2+di·x3Fitting, i.e. obtaining the matrix b from a.x ═ b, and since the system of overdetermined equations is not solved, the approximate solution is obtained using the principle of least squaresByTo obtain
obtaining a cubic curve of y ═ ai0+bi0·x+ci0·x2+di0·x3,
4. A novel geometric path-tracking algorithm taking into account path curvature according to claim 3, characterized in that: in the step S3, the curve fitting method adopts an ordered discrete point fitting method: determining the curve fitting direction along the x axis or the y axis by judging whether the x coordinate value of the ordered path point changes monotonously;
in particular to a method for preparing a high-performance nano-silver alloy,
if x is satisfiedi-3>xi-2>xi-1>xi>xi+1>xi+2>xi+3The x coordinate of the ordered path point is monotonically decreasing, if x is satisfiedi-3<xi-2<xi-1<xi<xi+1<xi+2<xi+3If the x coordinate of the ordered path point is monotonically increasing, in both cases, y is carried out along the x-axis direction as ai+bi·x+ci·x2+di·x3Fitting a curve;
otherwise, the x coordinate of the ordered path point does not change monotonically, and in this case, x is carried out along the y-axis direction as ai+bi·y+ci·y2+di·y3Fitting a curve;
when the curve fitting is along the y axis, the curvature solving and the path point course solving also need to be correspondingly adjusted;
when the x coordinate value of the ordered path point does not change monotonically in the local path, the y coordinate thereof changes monotonically without fail.
5. A novel geometric path-tracking algorithm taking into account path curvature according to claim 1, characterized in that: in the step S4, in the above step,
according to the ackermann steering geometry principle, the geometrical relationship between the front wheel turning angle and the turning curvature can be expressed as:
tan(θρi)=L·ρi
thus, it is obtained:
θρi=arctan(L·ρi)
further, obtain
6. A novel geometric path-tracking algorithm taking into account path curvature according to claim 1, characterized in that: in the step S5, in the above step,
the first derivative of the cubic curve fitted in step S3 can be used to obtain the heading angle yaw of the path reference pointiNamely, it is
yawi=y′(xi)
Then, obtaining the course deviation:
yawErr=yawi-yawvehicle
wherein yawErr is the course deviation, yawiIs the path reference point course angle, yawvehicleIs the angle of the course of the automobile,
coordinate (x) of path reference point in global coordinate systemR,yR) Coordinate (x) converted to vehicle body coordinate systemr,yr) The conversion formula can be expressed as:
wherein (x)vehicle,yvehicle) Is the position coordinate of the automobile under the mercator coordinate of the transverse axis,
then the lateral deviation is obtained:
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