CN113467480B - Global path planning algorithm for unmanned equation - Google Patents
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Abstract
The invention discloses a global path planning algorithm for an unmanned equation, which comprises the following steps: 1. track boundary and centerline extraction: obtaining a pile barrel map of the track, obtaining ordered left and right pile barrel boundary discrete points and ordered central line discrete points of the track through a triangulation algorithm, obtaining continuous boundary and central line information through cubic spline interpolation, and calculating the distance between each discrete central point and the left and right boundary; the invention aims at the pile barrel track map of the FSAC, can accurately obtain the left and right boundaries and the central line of the track by using a triangulation algorithm, aims at the obtained central line and boundary conditions, aims at the minimum curvature, establishes an optimization model to solve and obtain a global minimum curvature path, and the global optimal path is suitable for the racing car to obtain good circle speed performance, and the obtained global optimal path is smooth and continuous and can be directly used as a target track for tracking the vehicle.
Description
Technical Field
The invention relates to the technical field of unmanned path planning, in particular to a global path planning algorithm for an unmanned equation.
Background
In recent years, due to the rapid development of informatization, unmanned research has become a great deal of popularity. In this context, the chinese society of automotive engineering began to hold the chinese college student's driverless equation (FSAC) with 2017. Trajectory planning is a key technology in unmanned vehicles, and directly affects the safety and smoothness of vehicle movement. The FSAC racing track is mainly formed by enclosing conical stake barrels, wherein the left side of the racing track is provided with a red stake barrel, and the right side is provided with a blue stake barrel
Current FSAC-based path planning studies are as follows: yan Guodong and the like propose a path planning algorithm based on a target bias-based bidirectional rapid search random tree RRT algorithm, and the algorithm has unknown application effect on a closed loop tubular race track environment in FSAC. Li Jiang et al propose a method for identifying a pile barrel and planning a path based on an unmanned equation, wherein a topological map is established by selecting a cone barrel with known color and coordinate position as a key node, and a running reference track is generated, but the detailed description is lacking. Outside the FSAC field, zheng Liang, zhang Xudong, etc., a local path planning algorithm is respectively provided by the Shixiaolu, etc., and is mainly used for path searching, obstacle avoiding, etc. It follows that there is less research on global path planning in FSAC.
The existing path planning algorithm cannot obtain a path which enables racing vehicles to run more quickly and stably in an FSAC race track. For FSAC games with the turn speed as the basis for judging the success or failure, the path planning algorithm directly influences the turn speed performance of the racing car in the track. The proposed path planning algorithm requires the completion of the global path planning of the racing car in the track, planning a race to achieve the fastest possible turn-up speed in the track. Since FSAC racetracks have many curves, in order to increase the speed of the vehicle over-bending, the racing car needs to pass the curve with as large a turning radius as possible, and therefore the minimum curvature is selected as the target of the global path planning.
Disclosure of Invention
The present invention is directed to a global path planning algorithm for an unmanned equation, so as to solve the problems set forth in the background art.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a global path planning algorithm for an unmanned equation, comprising the steps of:
1. track boundary and centerline extraction: obtaining a pile barrel map of the track, obtaining ordered left and right pile barrel boundary discrete points and ordered central line discrete points of the track through a triangulation algorithm, obtaining continuous boundary and central line information through cubic spline interpolation, and calculating the distance between each discrete central point and the left and right boundary;
2. establishing a global path optimization model: utilizing the discrete center points and the distances between the discrete center points and the left and right boundaries, which are obtained in the step one, taking the coordinates of the center points as an optimization object, taking the left and right boundaries as constraint conditions, establishing an optimization model, and finally converting the optimization model into a quadratic programming model for solving to obtain a final optimization result;
for the ith reference point on the centerline, r i Corresponding ith optimization point O i As reference point r i Moving the resulting point along the normal direction of the curve, then:
wherein the method comprises the steps ofo i，x And o i，y Respectively->Xy coordinates of>r i，x And r i，y Respectively->Xy coordinates of>Is a reference line +>Unit normal vector at n i，x And n i，y Respectively->Xy component, alpha i Is scalar, is used as an optimization parameter to characterize r i Along->Amount of movement, and alpha i ∈[-B i，r ，B i，l ]，B i，r B is the distance from the reference point to the right boundary i，l Distance from the left boundary for the reference point;
interpolation is carried out on the optimization points by using cubic spline interpolation, and taking the parameter t as the parameter of the ith section of spline, wherein x and y of the ith section of spline are expressed as follows, and abcd are polynomial coefficients respectively:
wherein parameter t of the ith spline i (s) is represented as follows:
s i，0 ，s i+1，0 the distance between the ith point and the (i+1) th point in the reference line is respectively, s is the distance between the current point and the reference line, so that when the current point is positioned at the ith point, t=0, and when the current point is positioned at the (i+1) th point, t=1, solving a linear equation set when t=0;
obtaining a linear equation set of spline parameters of an ith section of spline line of x and y coordinates according to the condition of cubic spline interpolation:
obtaining a linear equation set of N-segment spline lines according to the N-segment linear equation setWherein A is a coefficient matrix:
the spline coefficient result can be obtained by the linear equation set;
for the optimization of the minimum curvature path, taking the sum of the squares of curvature of N discrete points to obtain a minimum value as an optimization target, and selecting the sum of the squares of curvature as an optimization function, wherein the curvature for the ith point is as follows:
summing to obtain an optimized model:
wherein:
to optimize the point x coordinate second derivative vector,
to optimize the second derivative vector of the point y coordinate,
due to the optimization point O i At reference point r only i On the basis of small amplitude movement, the first derivatives of the curves corresponding to the optimization point and the reference point can be considered to be equal, and P is the same xx 、P xy And P yy All are constant matrices, at this time, the optimization model can be converted into quadratic programming, and the first-order derivative and the second-order derivative of the spline line at t=0 are respectively:
from the linear system of equations above:
wherein E is c The function of (a) is to extract spline parameter c from E, thus E c The method comprises the following steps:
next, the optimization points will be optimizedSubstitution can be obtained:
and, in addition, the method comprises the steps of,
let T c ＝2E c A -1 ，T x ＝2E c A -1 M x ，T y ＝2E c A-1M y Then:
as a further scheme of the invention: simplifying the optimization model to obtain a quadratic programming model, wherein G is a quadratic term matrix, c is a primary term vector, and const is a constant:
wherein:
as still further aspects of the invention: the optimized parameters can be obtained by solving a quadratic programming model of the model (10)By->Results of the optimization points can be obtained.
As still further aspects of the invention: solving the model by adopting a step-by-step iteration method, setting the iteration number as n, and taking a weighting parameter e n The method comprises the following steps:
as still further aspects of the invention: after weightingSubstituted into->New reference point ∈ ->And update->The constraint condition of (2) is carried out for the next optimization solution, and along with the updating of the reference point, better calculation is obtainedAs a result.
Compared with the prior art, the invention has the beneficial effects that:
the invention aims at the pile barrel track map of the FSAC, can accurately obtain the left and right boundaries and the central line of the track by using a triangulation algorithm, aims at the obtained central line and boundary conditions, aims at the minimum curvature, establishes an optimization model to solve and obtain a global minimum curvature path, and the global optimal path is suitable for the racing car to obtain good circle speed performance, and the obtained global optimal path is smooth and continuous and can be directly used as a target track for tracking the vehicle.
Drawings
Fig. 1 is a centerline plan view of a global path planning algorithm for an unmanned equation.
Fig. 2 is a schematic diagram of a global path planning algorithm for the drone equations.
Fig. 3 is a schematic diagram of spline parameters t in a global path planning algorithm for an unmanned equation.
Fig. 4 is a schematic structural diagram of a pile bucket in a global path planning algorithm for an unmanned equation.
Fig. 5 is a schematic diagram of the structure of the triangulation result in the global path planning algorithm for the drone equation.
Fig. 6 is a schematic diagram of a minimum curvature global path plan and centerline path contrast structure in a global path planning algorithm for an unmanned equation.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1 to 6, in an embodiment of the present invention, a global path planning algorithm for an unmanned equation includes the following steps:
1. track boundary and centerline extraction: obtaining a pile barrel map of the track, obtaining ordered left and right pile barrel boundary discrete points and ordered central line discrete points of the track through a triangulation algorithm, obtaining continuous boundary and central line information through cubic spline interpolation, and calculating the distance between each discrete central point and the left and right boundary;
2. establishing a global path optimization model: and (3) establishing an optimization model by using the discrete center points and the distances between the discrete center points and the left and right boundaries, taking the coordinates of the center points as optimization objects and the left and right boundaries as constraint conditions, and finally converting the optimization model into a quadratic programming model for solving to obtain a final optimization result.
3. For the ith reference point on the centerline, r i Corresponding ith optimization point O i As reference point r i Moving the resulting point along the normal direction of the curve, then:
wherein the method comprises the steps ofo i，x And o i，y Respectively->Xy coordinates of (c). />r i，x And r i，y Respectively->Xy coordinates of (c). />Is a reference line +>Unit normal vector at n i，x And n i，y Respectively->Xy component, alpha i Is scalar, is used as an optimization parameter to characterize r i Along->Amount of movement, and alpha i ∈[-B i，r ，B i，l ]，B i，r B is the distance from the reference point to the right boundary i，l Is the distance of the reference point from the left boundary.
Then constructing a mathematical model, and combining the global curvature with the optimization parameter alpha i By means of the method, the extremum of the mathematical model can be solved, and a solution of the optimized parameters can be obtained, namely a global minimum curvature result is obtained.
In order to ensure continuity and smoothness of an optimization result, a cubic spline interpolation is used for interpolating an optimization point, a parameter t is taken as a parameter of an ith section of spline, and x and y of the ith section of spline are expressed as follows, wherein abcd is a polynomial coefficient respectively:
wherein parameter t of the ith spline i (s) is represented as follows:
s i，0 ，s i+1，0 the distances between the i-th point and the i+1th point in the reference line are respectively, s is the distance between the current point and the reference line, and therefore, when the current point is located at the i-th point, t=0. When the current point is located at the i+1th point position, t=1. Solving the linear equation set at t=0 can simplify the calculation amount.
Obtaining a linear equation set of spline parameters of an ith section of spline line of x and y coordinates according to the condition of cubic spline interpolation:
obtaining a linear equation set of N-segment spline lines according to the N-segment linear equation setWherein A is a coefficient matrix:
from this linear system of equations, spline line coefficient results can be obtained.
For the optimization of the minimum curvature path, taking the sum of the squares of curvature of N discrete points to obtain a minimum value as an optimization target, and selecting the sum of the squares of curvature as an optimization function, wherein the curvature for the ith point is as follows:
summing to obtain an optimized model:
wherein:
to optimize the point x coordinate second derivative vector.
To optimize the second derivative vector of the point y coordinate.
Due to the optimization point O i At reference point r only i On the basis of small amplitude movement, the first derivatives of the curves corresponding to the optimization point and the reference point can be considered to be equal, and P is the same xx 、P xy And P yy All are constant matrices, at this time, the optimization model can be converted into quadratic programming, and the first-order derivative and the second-order derivative of the spline line at t=0 are respectively:
from the linear system of equations of equation (4):
wherein E is c The function of (a) is to extract spline parameter c from E, thus E c The method comprises the following steps:
next, the optimization points will be optimizedSubstitution can be obtained:
wherein,
let T c ＝2E c A -1 ，T x ＝2E c A -1 M x ，T y ＝2E c A -1 M y Then:
substituting the formula (9) into the formula (5) and then simplifying to obtain a quadratic programming model, wherein G is a quadratic term matrix, c is a primary term vector, and const is a constant:
wherein:
the optimized parameters can be obtained by solving a quadratic programming model of the model (10)By->Results of the optimization points can be obtained.
Since the first-order derivatives of the curves corresponding to the previous optimization point and the reference point are considered to be equal, under the condition that the movement amplitude of the optimization point is large, the error is obviously increased, in order to reduce the influence caused by the approximation error, a step-and-step iteration method is adopted to solve the model, the iteration number is set to be n, and the weighting parameter e is taken n The method comprises the following steps:
after weightingSubstituted into->New reference point ∈ ->And update->And (3) carrying out the next optimization solution, and obtaining a better result along with the updating of the reference point. Finally, setting iteration solution times n=2, and selecting an iteration parameter e 1 ＝0.5，e 2 Good results were obtained with =1.
The triangulation algorithm is as shown in fig. 1:
a) As shown in the figure, a local pile bucket race track map is constructed, and all pile bucket points are contained;
b) Inserting a first pile barrel point, and connecting the insertion point with an end point to form a triangle chain;
c) Inserting the next point, if the triangle circumscribed circle in the original triangle chain contains the inserted point, then the triangles are called influencing triangles;
d) Deleting all public edges affecting the triangle, and reconnecting the newly inserted points to each node to form a new triangle chain;
e) Repeating the steps c and d, and sequentially inserting all pile barrel points to obtain a complete triangular chain;
f) All lines containing three vertexes of the original super triangle are deleted, as for the reserved points, according to the vehicle position and direction, the red pile barrel and the blue pile barrel are sequentially connected to obtain the left and right boundaries of the final track, the midpoints of the connecting lines of the pile barrels with different colors can be regarded as the center of the track, and the center points of the track are also sequentially connected to obtain the center line of the track.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (5)
1. A global path planning algorithm for an unmanned equation, comprising the steps of:
1. track boundary and centerline extraction: obtaining a pile barrel map of the track, obtaining ordered left and right pile barrel boundary discrete points and ordered central line discrete points of the track through a triangulation algorithm, obtaining continuous boundary and central line information through cubic spline interpolation, and calculating the distance between each discrete central point and the left and right boundary;
2. establishing a global path optimization model: utilizing the discrete center points and the distances between the discrete center points and the left and right boundaries, which are obtained in the step one, taking the coordinates of the center points as an optimization object, taking the left and right boundaries as constraint conditions, establishing an optimization model, and finally converting the optimization model into a quadratic programming model for solving to obtain a final optimization result;
for the ith reference point on the centerline, r i Corresponding ith optimization point O i As reference point r i Moving the resulting point along the normal direction of the curve, then:
wherein the method comprises the steps ofo i,x And o i,y Respectively->Xy coordinates of>r i,x And r i,y Respectively isXy coordinates of>Is a reference line +>Unit normal vector at n i,x And n i,y Respectively->Xy component, alpha i Is scalar, is used as an optimization parameter to characterize r i Along->Amount of movement, and alpha i ∈[-B i,r ,B i,l ]，B i,r B is the distance from the reference point to the right boundary i,l Distance from the left boundary for the reference point;
interpolation is carried out on the optimization points by using cubic spline interpolation, and taking the parameter t as the parameter of the ith section of spline, wherein x and y of the ith section of spline are expressed as follows, and abcd are polynomial coefficients respectively:
wherein parameter t of the ith spline i (s) is represented as follows:
s i,0 ,s i+1,0 the distance between the ith point and the (i+1) th point in the reference line is respectively, s is the distance between the current point and the reference line, so that when the current point is positioned at the ith point, t=0, and when the current point is positioned at the (i+1) th point, t=1, solving a linear equation set when t=0;
obtaining a linear equation set of spline parameters of an ith section of spline line of x and y coordinates according to the condition of cubic spline interpolation:
obtaining a linear equation set of N-segment spline lines according to the N-segment linear equation setWherein A is a coefficient matrix:
the spline coefficient result can be obtained by the linear equation set;
for the optimization of the minimum curvature path, taking the sum of the squares of curvature of N discrete points to obtain a minimum value as an optimization target, and selecting the sum of the squares of curvature as an optimization function, wherein the curvature for the ith point is as follows:
summing to obtain an optimized model:
wherein:
to optimize the point x coordinate second derivative vector,
to optimize the second derivative vector of the point y coordinate,
due to the optimization point O i At reference point r only i On the basis of small amplitude movement, the first derivatives of the curves corresponding to the optimization point and the reference point can be considered to be equal, and P is the same xx 、P xy And P yy All are constant matrices, at this time, the optimization model can be converted into quadratic programming, and the first-order derivative and the second-order derivative of the spline line at t=0 are respectively:
from the above linear system of equations:
wherein E is c The function of (a) is to extract spline parameter c from E, thus E c The method comprises the following steps:
next, the optimization points will be optimizedSubstitution can be obtained:
and, in addition, the method comprises the steps of,
let T c ＝2E c A -1 ，T x ＝2E c A -1 M x ，T y ＝2E c A -1 M y Then:
2. the global path planning algorithm for an unmanned equation of claim 1, wherein the quadratic programming model is obtained by simplifying the optimization model, wherein G is a quadratic term matrix, c is a first order term vector, const is a constant:
wherein:
3. a global path planning algorithm for an unmanned equation according to claim 2, wherein the optimization parameters are obtained by solving the quadratic programming model in claim 2By-> Results of the optimization points can be obtained.
4. A global path gauge for an unmanned equation according to claim 3The dividing algorithm is characterized in that a step-by-step iteration method is adopted to solve a model, the iteration number is set as n, and a weighting parameter e is taken n The method comprises the following steps:
5. the global path planning algorithm for an unmanned aerial vehicle of claim 4, wherein the weighted sum isSubstituted into->New reference point ∈ ->And update->And (3) carrying out the next optimization solution, and obtaining a result along with updating of the reference point.
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