CN113448335A - Path planning method and device, vehicle and readable storage medium - Google Patents
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Abstract
The application provides a path planning method. The path planning method comprises the steps of obtaining a plurality of path points of a reference path generated based on a road reference line; calculating a plurality of initial control points according to the path points; adjusting the initial control points based on the objective function, the boundary constraint and the curvature constraint to generate target control points; and generating a final path according to the target control point. According to the path planning method, the path planning device, the vehicle and the computer-readable storage medium, the multiple path points of the reference path are obtained, the multiple control points are generated according to the path points, the control points are adjusted according to the objective function, the boundary constraint and the curvature constraint, and the final path is generated according to the target control points.
Description
Technical Field
The present disclosure relates to the field of image technologies, and in particular, to a path planning method, a path planning apparatus, a vehicle, and a computer-readable storage medium.
Background
With the development of artificial intelligence, unmanned vehicles have emerged, freeing the driver. At present, routes are planned according to road reference lines mostly by automatic driving vehicles, the road reference lines are generally subjected to intensive sampling, then a complete route is obtained through intermediate interpolation, and finally a route which is along the road reference lines or deviates from the road reference lines by a certain distance is generated, so that the safety of the generated route is low.
Disclosure of Invention
The embodiment of the application provides a path planning method, a path planning device, a vehicle and a computer readable storage medium.
The path planning method comprises the steps of obtaining a plurality of path points of a reference path generated based on a road reference line; calculating a plurality of initial control points according to the path points; adjusting the initial control points based on an objective function, a boundary constraint and a curvature constraint to generate target control points; and generating a final path according to the target control point.
In some embodiments, said calculating a plurality of initial control points from said path points comprises: and calculating a plurality of control points according to the path points and a first equation of the plurality of corresponding control points, and the derivative of the reference path and a second equation of the plurality of corresponding control points.
In some embodiments, said adjusting said initial control points to generate target control points based on an objective function, a boundary constraint, and a curvature constraint comprises: inputting the control points, the objective function, the boundary constraint, and the curvature constraint to a preset optimizer to output a plurality of target control points that minimize an output value of the objective function.
In some embodiments, the objective function includes a first portion, a second portion, a third portion and a fourth portion, the first portion is a distance minimum cost from the reference path, the second portion is a road centering cost, the third portion is a path second order smoothness cost, and the fourth portion is a path third order smoothness cost.
In some embodiments, the boundary constraints include boundary ranges, the boundary constraints being used to cause the control points to be located within corresponding boundary ranges, the boundary ranges corresponding to the control points being generated from at least one of road boundaries and obstacles.
In some embodiments, the boundary constraints further include a start point constraint and/or an end point constraint, the start point constraint being used to make the start point of the final path located at a preset start point position, and the end point constraint being used to make the end point of the final path located at the preset end point position.
In some embodiments, the curvature constraint includes a range of curvatures, the curvature constraint for causing the curvature of the waypoint to lie within the range of curvatures.
In some embodiments, the path planning method further includes obtaining a curvature of a reference point corresponding to the path point on the road reference line; and calculating the curvature of the path point according to the curvature of the reference point and the control point.
In some embodiments, the generating a final path from the target control point includes: generating a path function according to a preset curve parameter equation and a target control point, wherein the preset curve parameter equation comprises a uniform B spline curve; and generating the final path according to the path function.
The path planning device of the embodiment of the application comprises a first obtaining module, a first calculating module, an adjusting module and a generating module. The acquisition module is used for acquiring a plurality of path points of a reference path generated based on a road reference line; the calculation module is used for calculating a plurality of initial control points according to the path points; the adjusting module is used for adjusting the initial control point based on an objective function, a boundary constraint and a curvature constraint so as to generate a target control point; the generating module is used for generating a final path according to the target control point.
The vehicle of the embodiment of the present application includes a processor. The processor is used for acquiring a plurality of path points of a reference path generated based on a road reference line; calculating a plurality of initial control points according to the path points; adjusting the initial control points based on an objective function, a boundary constraint and a curvature constraint to generate target control points; and generating a final path according to the target control point.
A computer-readable storage medium embodying a computer program which, when executed by one or more processors, causes the processors to perform a path planning method. The path planning method comprises the steps of obtaining a plurality of path points of a reference path generated based on a road reference line; calculating a plurality of initial control points according to the path points; adjusting the initial control points based on an objective function, a boundary constraint and a curvature constraint to generate target control points; and generating a final path according to the target control point.
According to the path planning method, the path planning device, the vehicle and the computer-readable storage medium, the multiple path points of the reference path generated based on the road reference line are obtained, the multiple control points are generated according to the path points, then the control points are adjusted according to the objective function, the boundary constraint and the curvature constraint, and finally the final path is generated according to the target control points.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart diagram of a path planning method according to some embodiments of the present application;
FIG. 2 is a block diagram of a path planner according to some embodiments of the present application;
FIG. 3 is a schematic plan view of a vehicle according to certain embodiments of the present application;
FIG. 4 is a schematic flow chart diagram of a path planning method according to some embodiments of the present application;
FIG. 5 is a schematic diagram of a path planning method according to some embodiments of the present application;
fig. 6-8 are schematic flow charts of a path planning method according to some embodiments of the present disclosure;
FIGS. 9 and 10 are schematic diagrams of a scenario of a path planning method according to some embodiments of the present application;
FIG. 11 is a curvature profile of a final path and a reference path of certain embodiments of the present application; and
FIG. 12 is a schematic diagram of a connection between a processor and a computer readable storage medium according to some embodiments of the present application.
Detailed Description
Embodiments of the present application will be further described below with reference to the accompanying drawings. The same or similar reference numbers in the drawings identify the same or similar elements or elements having the same or similar functionality throughout. In addition, the embodiments of the present application described below in conjunction with the accompanying drawings are exemplary and are only for the purpose of explaining the embodiments of the present application, and are not to be construed as limiting the present application.
When path planning is performed, generally, a road reference line is collected for intensive sampling, then a complete path is obtained through modes such as intermediate interpolation, and if an obstacle exists on the road reference line or the road is tortuous, the generated path cannot well avoid the obstacle, and the path has poor smoothness and is not beneficial to driving safety.
Referring to fig. 1 to 3, a path planning method according to an embodiment of the present disclosure includes the following steps:
011: acquiring a plurality of path points of a reference path generated based on a road reference line;
012: calculating a plurality of initial control points according to the path points;
013: adjusting the initial control points based on the objective function, the boundary constraint and the curvature constraint to generate target control points;
014: and generating a final path according to the target control point.
The path planning apparatus 10 according to the embodiment of the present application includes a first obtaining module 11, a first calculating module 12, an adjusting module 13, and a generating module 14. The first obtaining module 11, the first calculating module 12 and the generating module 14 are configured to perform step 011, step 012, step 013 and step 014, respectively. That is, the first obtaining module 11 is configured to obtain a plurality of path points of a reference path generated based on a road reference line; the first calculating module 12 is configured to calculate a plurality of initial control points according to the path points; the adjusting module 13 is configured to adjust the initial control point based on the objective function, the boundary constraint and the curvature constraint to generate a target control point; the generating module 14 is configured to generate a final path according to the target control point.
The vehicle 100 of the embodiment of the present application includes a processor 20. The processor 20 is used for acquiring a plurality of path points of a reference path generated based on the road reference line; calculating a plurality of initial control points according to the path points; adjusting the initial control points based on the objective function, the boundary constraint and the curvature constraint to generate target control points; and generating a final path according to the target control point. That is, step 011, step 012, step 013, and step 014 may be implemented by processor 20. In other embodiments, the vehicle 100 is connected to a cloud (not shown), and the steps 011, 012, 013 and 014 can be implemented by the cloud.
Specifically, the vehicle 100 may embed a high-precision map of a current area, and obtain a road reference line (e.g., a road center line) from the high-precision map, and the vehicle 100 may generate a rough reference path in a Frenet coordinate system based on a preset path generation algorithm, and then obtain a plurality of path points on the reference path, where the path points include a first distance and a second distance (respectively (S, L)), the first distance S is an arc length distance from a foot point to a start point of the road reference line when the position of the vehicle 100 is projected onto the road reference line, and the second distance L is a normal distance from the position of the vehicle 100 and the foot point.
The processor 20 can generate a final path according to the target control point and the parameter equation of the uniform B-spline curve, and the final path meets the boundary constraint and the curvature constraint, so that the final path is smoother, is farther away from the obstacle, and has better safety.
According to the path planning method, the path planning device 10 and the vehicle 100, the multiple path points of the reference path are obtained, the multiple control points are generated according to the path points, the control points are adjusted according to the objective function, the boundary constraint and the curvature constraint, and the final path is generated according to the target control points.
Referring to fig. 2, 3 and 4, in some embodiments, step 012 includes:
0121: a plurality of control points are calculated from the first equation for the path point and the corresponding plurality of control points and the second equation for the derivative of the reference path and the corresponding plurality of control points.
In certain embodiments, the first calculation module 12 is further configured to perform step 0121. That is, the first calculation module 12 is further configured to calculate the plurality of control points according to the first equation of the path point and the corresponding plurality of control points, and the second equation of the derivative of the reference path and the corresponding plurality of control points.
In some embodiments, processor 20 is further configured to calculate a plurality of control points based on the first equation for the path point and the corresponding plurality of control points and the second equation for the derivative of the reference path and the corresponding plurality of control points. That is, step 0121 may be implemented by processor 20.
Specifically, the number of the path points is n, and when a plurality of control points are calculated according to the path points, n first equations may be established according to a functional relationship between each path point and the plurality of control points for determining the path point:
wherein l0A path point corresponding to the starting point of the reference path, liRepresenting path points in the reference path,/n-1Indicating a path point, Q, corresponding to the end point of the reference pathiDenotes a control point, i is a natural number.
In the uniform 3 rd order B-spline curve, the number of control points is 2 more than the number of path points, therefore, n first equation associations cannot be solved for n +2 control points, and the derivative of the reference path and the corresponding control points can be usedThe functional relationship of the points, the second equation is again established, e.g. the derivative of the starting point satisfies the following functional relationship: referring to fig. 5, Δ s is a distance between two adjacent waypoints, and is a predetermined value.
The functional relationship between a waypoint and the plurality of control points used to determine the waypoint may be determined according to the parametric equation of a uniform 3 rd order B-spline curve. The parameter equation of the B spline curve is as follows:
wherein the content of the first and second substances,the q-order differential expression of the parametric equation for a B-spline curve can be obtained as follows:
in the path image in the Frenet coordinate system shown in fig. 5, an abscissa s is an arc length distance (i.e., a first distance) from a starting point of the path to a drop-foot point when the vehicle 100 is projected on the path in the Frenet coordinate system, and L is a normal distance (i.e., a second distance) between the vehicle 100 and the drop-foot point; s is located in each curve segment determined by the above parameter equation (e.g./in FIG. 5)0l1、l1l2Etc.) between the start and end points (s e s as shown in FIG. 5i,si+1]) At the determination of siCorresponding to liAnd si+1Corresponding to li+1Then, through s in [ s ]i,si+1]Obtaining the curve l by internal value takingili+1。
Mk+1Any element in the matrix can be represented by the formula:calculating to obtain; m isi,jRepresents Mk+1The ith, j-th element of the matrix ((k +1) × (k +1) square). Thus, the base matrix M of the uniform cubic B-spline curve can be obtained4:
In addition to this, the present invention is,
b(0)=[1 u u2u3 … uk]T;
b(1)=[0 1 2u 3u2 … kuk-1]T;
b(2)=[0 0 2 6u … k(k-1)uk-2]T;
b(3)=[0 0 0 6 …k(k-1)(k-2)uk-3]T;
the reference path is composed of a plurality of curves, the collected path points are nodes in the reference path, that is, the starting point or the end point of each curve, the path points can be obtained by sampling at equal distances, for example, one path point is collected on the reference path every Δ s (which is a predetermined value and can be determined according to the number of collected path points and the length of the reference path), and for the nodes, u is 0, so that the functional relationship between the path points and the control points of the B-spline curve for 3 times can be calculated according to the formula:
referring to fig. 2, 3 and 6, in some embodiments, step 013 includes the following steps:
0131: the control points, the objective function, the boundary constraint, and the curvature constraint are input to a preset optimizer to output a plurality of target control points that minimize an output value of the objective function.
In certain embodiments, the adjusting module 13 is further configured to perform step 0131. That is, the adjusting module 13 is further configured to input the control points, the objective function, the boundary constraint, and the curvature constraint to a preset optimizer to output a plurality of target control points that minimize the output value of the objective function.
In some embodiments, the processor 20 is further configured to input the control points, the objective function, the boundary constraints, and the curvature constraints to a preset optimizer to output a plurality of target control points that minimize an output value of the objective function. That is, step 0131 may be implemented by processor 20.
Specifically, optimization of the control points can be achieved by setting optimization conditions through an optimizer. The optimizer may be, for example, non-linear optimization software such as Ipopt, NLopt, snpot, etc.
After the objective function, the control points, the boundary constraint and the curvature constraint are all input into the optimizer, the optimizer can automatically calculate and output the optimized control points which enable the output value of the objective function to be minimum and meet the boundary constraint and the curvature constraint.
The objective function is: wherein the first part For the minimum distance cost from the reference path, the second part i is 0n-3Qi +2-Qi2 Δ s2 for road centering cost, and the third part is road centering costIs the path second order smoothness cost; fourth sectionThe third order smoothness cost of the path. Omegaref、ωdl、ωddl、ωdddlWeight coefficients respectively representing the terms, ω, of the vehicle 100 under different scenesref、ωdl、ωddl、ωdddlIn contrast, e.g. for scenes with higher smoothness requirements, ω will beddl、ωdddlHigher weight setting of (c), e.g. in a centrally demanding scenario, ωdlThe weight setting is higher, so that the path optimization effect under different scenes is improved.
The boundary constraint comprises a boundary range, the boundary constraint is used for enabling the control point to be located in the corresponding boundary range, and the boundary range corresponding to the control point is generated according to the road boundary. The boundary range may also take into account more factors, such as obstacles, to generate a more accurate boundary range from the road boundary and the obstacles.
For example, the boundary range of each control point is: li,min≤Qi≤li,max,li,minAnd li,maxThe information such as the road boundary corresponding to the control point and the obstacles near the control point is calculated, so that the control point is ensured to be always positioned in the road boundary, and the obstacles can be well bypassed according to the final path generated by the control point, and the driving safety is ensured.
In addition, the boundary constraint may further include a start point constraint and/or an end point constraint, by which a start point of the final path may be located at a preset start point position; with the end point constraint, the end point of the final path may be located at the preset end point position, so that the start point and the end point of the final path are the start point and the end point of the travel of the vehicle 100, respectively.
For example, the starting point constraint may be to locate the starting point of the final path at the starting point of the reference path, and the starting point constraint may be performed by a functional relationship between the path point and the control point:for another example, the end point constraint may not be set, or may be set so that the end point of the final path is located at the end point of the reference path, and the end point constraint may be performed by a functional relationship between the path point and the control point:
the curvature constraints include a range of curvatures, and the curvature k (i) corresponding to each path point lies within the range of curvatures: kappamin≤k(i)≤kmaxFor example κmin=-0.2,κmaxThe curvature of the final path is always within the curvature range, and the final path is smoother.
Referring again to fig. 2, 3 and 7, in some embodiments, the path planning method further includes:
015: acquiring the curvature of a reference point corresponding to the path point on a road reference line;
016: and calculating the curvature of the path point according to the curvature of the reference point and the control point.
In some embodiments, the path planning apparatus further includes a second obtaining module 15 and a second calculating module 16, and the second obtaining module 15 and the second calculating module 16 are respectively configured to perform steps 015 and 016. That is, the second obtaining module 15 is configured to obtain the curvature of a reference point corresponding to the path point on the road reference line; the second calculation module 16 is used for calculating the curvature of the path point according to the curvature of the reference point and the control point.
In some embodiments, the processor 20 is further configured to obtain a curvature of a reference point corresponding to the waypoint on the road reference line; the curvature of the upper path point is calculated based on the curvature of the reference point, the path point, and the control point. That is, step 015 and step 016 may be implemented by the processor 20.
Specifically, to implement the curvature constraint, the processor 20 needs to calculate the curvature of each waypoint and make the curvature of the waypoint lie within the curvature range. The curvature of each path point determined by the control point sees k (i) the calculation formula is as follows:
wherein k isriThe curvature of the path point at the matched point on the road reference line, the reference point on the road reference line and the curvature thereof are preset values, and the processor 20 can directly obtain the curvature. And then, carrying out functional relation between the path points and the control points of the 3-time B-spline curve obtained by the calculation:the curvature at the path point can be determined by substituting the formula. The curvature of the path point is determined according to a formula formed by the control points, and the curvature of the path point is in a curvature range, so that the control points are also restricted by the curvature range, and the control points are adjusted through curvature restriction.
Referring to fig. 2, 3 and 8, in some embodiments, step 014 includes the steps of:
0141: generating a path function according to a preset curve parameter equation and the target control point, wherein the preset curve parameter equation comprises a uniform B spline curve; and
0142: and generating a final path according to the path function.
In certain embodiments, generation module 14 is further configured to perform steps 0141 and 0142. That is, the generating module 14 is further configured to generate a path function according to a preset curve parameter equation and the target control point, where the preset curve parameter equation includes a uniform B-spline curve; and generating a final path according to the path function.
In some embodiments, the processor 20 is further configured to generate a path function according to a preset curve parameter equation and the target control point, the preset curve parameter equation including a uniform B-spline curve; and generating a final path according to the path function. That is, steps 0141 and 0142 may be implemented by processor 20.
Specifically, the preset curve parameter equation may be a parameter equation of a uniform B-spline curve:after the target control point is determined, the parameter equation of the uniform B spline curve can be determined according to the control point, so that the s is in the [ s ]i,si+1]Obtaining the curve l by internal value takingili+1Thereby generating a B-spline curve between each two waypoint to form the final path.
A comparison of the final path M3, the reference path M2 and the road reference line M1 generated from the control points adjusted by the objective function, the boundary constraint and the curvature constraint is shown in fig. 9 and 10, where fig. 10 is a detailed enlarged view of the region M in fig. 9, and it can be seen that the final path M3 is smoother and more distant from the obstacle Z than the reference path M2. Thus, the security of the final path m1 is good.
In addition, referring to fig. 11, according to the curvature distribution diagrams of the final path m3 and the reference path m2, it can be seen that the curvatures of the final path m3 are both located between the intervals [ -0.2,0.2], so that the curvature constraint is satisfied, and the smoothness is good.
Referring to fig. 12, a computer readable storage medium 300 storing a computer program 302 according to an embodiment of the present disclosure, when the computer program 302 is executed by one or more processors 20, the processor 20 may execute the path planning method according to any of the above embodiments.
For example, referring to fig. 1, the computer program 302, when executed by the one or more processors 20, causes the processors 20 to perform the steps of:
011: acquiring a plurality of path points of a reference path generated based on a road reference line;
012: calculating a plurality of initial control points according to the path points;
013: adjusting the initial control points based on the objective function, the boundary constraint and the curvature constraint to generate target control points;
014: and generating a final path according to the target control point.
For another example, referring to fig. 4, when the computer program 302 is executed by the one or more processors 20, the processors 20 may further perform the steps of:
0121: a plurality of control points are calculated from the first equation for the path point and the corresponding plurality of control points and the second equation for the derivative of the reference path and the corresponding plurality of control points.
In the description herein, references to the description of the terms "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example" or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more program modules for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes additional implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
Although embodiments of the present application have been shown and described above, it is to be understood that the above embodiments are exemplary and not to be construed as limiting the present application, and that changes, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
Claims (12)
1. A method of path planning, comprising:
acquiring a plurality of path points of a reference path generated based on a road reference line;
calculating a plurality of initial control points according to the path points;
adjusting the initial control points based on an objective function, a boundary constraint and a curvature constraint to generate target control points;
and generating a final path according to the target control point.
2. The path planning method according to claim 1, wherein the calculating a plurality of initial control points according to the path points comprises:
and calculating a plurality of control points according to the path points and a first equation of the plurality of corresponding control points, and the derivative of the reference path and a second equation of the plurality of corresponding control points.
3. The path planning method according to claim 1, wherein the adjusting the initial control points based on the objective function, the boundary constraint, and the curvature constraint to generate target control points comprises:
inputting the control points, the objective function, the boundary constraints, and the curvature constraints to a preset optimizer to output a plurality of adjusted control points that minimize an output value of the objective function.
4. The path planning method according to claim 1, wherein the objective function includes a first part, a second part, a third part and a fourth part, the first part is a distance minimum cost from the reference path, the second part is a road centering cost, the third part is a path second order smoothness cost, and the fourth part is a path third order smoothness cost.
5. The path planning method according to claim 1, wherein the boundary constraint includes a boundary range, and the boundary constraint is used to make the control points located in a corresponding boundary range, and the boundary range corresponding to the control points is generated according to a road boundary.
6. The path planning method according to claim 5, wherein the boundary constraints further include a start point constraint and/or an end point constraint, the start point constraint being used to make the start point of the final path located at a preset start point position, and the end point constraint being used to make the end point of the final path located at a preset end point position.
7. A path planning method according to claim 1, wherein the curvature constraints comprise a range of curvatures, the curvature constraints being used to bring the curvature of the path point within the range of curvatures.
8. The path planning method according to claim 7, further comprising:
acquiring the curvature of a reference point corresponding to the path point on the road reference line;
and calculating the curvature of the path point according to the curvature of the reference point and the control point.
9. The path planning method according to claim 1, wherein the generating a final path according to the target control point comprises:
generating a path function according to a preset curve parameter equation and a target control point, wherein the preset curve parameter equation comprises a uniform B spline curve; and
and generating the final path according to the path function.
10. A path planning apparatus, comprising:
the device comprises a first acquisition module, a second acquisition module and a third acquisition module, wherein the first acquisition module is used for acquiring a plurality of path points of a reference path generated based on a road reference line;
the first calculation module is used for calculating a plurality of initial control points according to the path points;
an adjusting module, configured to adjust the initial control point based on an objective function, a boundary constraint, and a curvature constraint to generate a target control point;
and the generating module is used for generating a final path according to the target control point.
11. A vehicle, comprising a processor configured to:
acquiring a plurality of path points of a reference path generated based on a road reference line;
calculating a plurality of initial control points according to the path points;
adjusting the initial control points based on an objective function, a boundary constraint and a curvature constraint to generate target control points;
and generating a final path according to the target control point.
12. A computer-readable storage medium containing a computer program which, when executed by a processor, causes the processor to carry out the path planning method of any one of claims 1-9.
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Cited By (11)
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CN113932826A (en) * | 2021-10-13 | 2022-01-14 | 北京经纬恒润科技股份有限公司 | Optimization method and system for vehicle navigation path |
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CN114114930A (en) * | 2022-01-28 | 2022-03-01 | 清华大学 | Method, device, equipment and medium for generating local reference path of automobile |
CN114114930B (en) * | 2022-01-28 | 2022-04-19 | 清华大学 | Method, device, equipment and medium for generating local reference path of automobile |
WO2024031959A1 (en) * | 2022-08-10 | 2024-02-15 | 美的集团(上海)有限公司 | Obstacle avoidance robot, control method and control device thereof, and readable storage medium |
CN115077534B (en) * | 2022-08-11 | 2022-11-15 | 合肥井松智能科技股份有限公司 | AGV path planning method based on B spline curve |
CN115077534A (en) * | 2022-08-11 | 2022-09-20 | 合肥井松智能科技股份有限公司 | AGV path planning method based on B spline curve |
CN115357032A (en) * | 2022-10-20 | 2022-11-18 | 上海仙工智能科技有限公司 | NURBS-based mobile robot path generation method, system and storage medium |
CN115357032B (en) * | 2022-10-20 | 2023-01-31 | 上海仙工智能科技有限公司 | NURBS-based mobile robot path generation method, system and storage medium |
CN117311368A (en) * | 2023-11-23 | 2023-12-29 | 武汉光昱明晟智能科技有限公司 | Automatic pre-marking robot system and operation method thereof |
CN117311368B (en) * | 2023-11-23 | 2024-04-09 | 武汉光昱明晟智能科技有限公司 | Automatic pre-marking robot system and operation method thereof |
CN117533317A (en) * | 2023-12-12 | 2024-02-09 | 北京斯年智驾科技有限公司 | Tractor reversing path smoothing method, system, device and storage medium |
CN117533317B (en) * | 2023-12-12 | 2024-05-17 | 北京斯年智驾科技有限公司 | Tractor reversing path smoothing method, system, device and storage medium |
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