CN109916421B - Path planning method and device - Google Patents
Path planning method and device Download PDFInfo
- Publication number
- CN109916421B CN109916421B CN201910201609.8A CN201910201609A CN109916421B CN 109916421 B CN109916421 B CN 109916421B CN 201910201609 A CN201910201609 A CN 201910201609A CN 109916421 B CN109916421 B CN 109916421B
- Authority
- CN
- China
- Prior art keywords
- circle
- distance
- vehicle
- end point
- center
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention provides a path planning method, which comprises the following steps: acquiring a reference path; determining a first distance when a first obstacle exists in a circle with the diameter of the distance between the starting point and the first end point; setting a first father circle and a first end circle by taking the starting point and the first distance as radii respectively; determining a second parent circle from the child circles of the first parent circle; when the coincidence degree of the mth father circle and the first end circle is larger than a preset first threshold value, generating a first list and a second list; at the current moment, acquiring a first parameter of the vehicle, and calculating a second parameter at the next moment according to the first parameter, so as to determine a first track set; processing the first track set according to the first list and the second list; evaluating the tracks in the processed first track set through a heuristic value function to determine a first target track; and when the distance difference between the end point and the end point of the nth target track is smaller than a preset second threshold value, generating a target path. Therefore, the reasonability and the real-time performance of the path are guaranteed.
Description
Technical Field
The invention relates to the technical field of data processing, in particular to a path planning method and device.
Background
With the development of artificial intelligence technology and modern manufacturing industry, the automatic driving technology gradually advances people's daily life, and the travel mode of people is changed profoundly. The unmanned technology can be briefly divided into perception, prediction, positioning, decision, planning and control. The planning usually refers to a path planning method, and the main task is to plan a path which is convenient for the controller to execute and has no collision according to the current vehicle information and reasonable exploration environment space.
The main difficulties of path planning are adaptability to complex environments and real-time computing. The former requires that the path planning method not only can be effective in a simple driving scene, but also has completeness of solution in a complex environment. The latter requires that the solution time of the path planning method is limited to ensure real-time planning of the driving process.
Current path planning algorithms generally fall into two categories, graph search and random sampling.
A Graph is a concept in Graph Theory (GT) that represents a class of topologies represented by a number of discrete nodes and edges connecting the nodes. The primary condition of the graph search algorithm is to convert the real world into a graph, the conversion method comprises a visual graph method, a space dispersion method, a Thiessen polygon mapping method and the like, and the graph search algorithm can be divided into a depth priority algorithm and a breadth priority algorithm according to a graph traversal mode. Two of the most well-known in the planning field are Dijkstra and a-algorithms, respectively, based on graph-based search methods. The graph search algorithm mainly guides search by using a heuristic function on a graph, and then searches for a path from a starting point to an end point, wherein the design of the heuristic function is mostly related to the distance from the starting point to a current point and the distance from the end point to the current point.
The random sampling algorithm is a classic tree search algorithm, and the most notable of them is the fast expanding random tree method (RRT). The RRT algorithm expands a tree structure from a starting point to the outside, and the expanding direction of the tree structure is determined by randomly collecting points in a planning space. This method is probabilistic and non-optimal. The random sampling algorithm has the problems of path mutation and the like, and a path which accords with vehicle dynamics needs to be generated through subsequent optimization.
The graph search algorithm based on the heuristic function has high requirements on the design of the heuristic function, the algorithm A guides the path search direction to be as close to the end point as possible through the heuristic function, and the method is very similar to a greedy idea. However, in many scenarios, the shortest route is often not the most reasonable route in the field of automatic driving, and these routes have the defects of being too close to an obstacle, and turning too sharply. A series of algorithms based on the A-frame have low space utilization rate, the requirements of a planned path on sensing precision and control precision are high, and the comfort is not good due to similar paths.
The random sampling-based method has certain uncertainty inevitably existing in the path, and the randomness of the sampling points causes the fluctuation characteristic of the original path, so most random sampling-based methods need further optimization of the path, which greatly increases the time consumption of the algorithm and can not meet the real-time path planning requirement of unmanned vehicles.
Disclosure of Invention
The embodiment of the invention aims to provide a path planning method and a path planning device, which are used for solving the problems of poor comfort, time-consuming algorithm and the like caused by path mutation, and the requirements of a planned path on perception accuracy and control accuracy in the conventional calculation.
To solve the above problem, in a first aspect, the present invention provides a path planning method, including:
acquiring a reference path of a vehicle, wherein the reference path comprises a starting point and an end point;
taking a first end point on the reference path; the first end point is located between the start point and the end point;
judging whether an obstacle exists in a circle with the diameter of the distance between the starting point and the first end point;
when a first obstacle exists, determining a first distance between the starting point and the first obstacle; the first obstacle is the obstacle closest to the starting point in the obstacles; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle;
setting a first father circle by taking the starting point as a circle center and the first distance as a radius;
setting a first end point circle by taking the first end point as a circle center and the first distance as a radius;
determining the distance between each of a plurality of circles on the circumference and the nearest barrier to the circle by taking the point on the circumference of the first father circle as the center of the circle, and generating a child distance set;
calculating the geometric distance between each of a plurality of centers of circles on the circumference and the first end point, and generating a geometric distance set;
calculating a set of heuristic values of the sub-circles corresponding to the circle centers according to the sub-distance set and the geometric distance set; the radius of the sub-circle is the difference between the distance between the circle center and the nearest barrier and the safety distance of the vehicle;
determining a child circle corresponding to the minimum heuristic value in the heuristic value set as a second parent circle;
when the coincidence degree of the mth father circle and the first end circle is larger than a preset first threshold value, generating a first list and a second list; the first list comprises circle center positions and radiuses of the first father circle to the mth father circle; the second list includes positions and radii from a sub-circle centered on the circumference of the first parent circle to a center of a sub-circle centered on the circumference of the mth parent circle; m is an integer greater than 2;
at the current moment, acquiring a first parameter of the vehicle;
calculating a second parameter of the vehicle at the next moment according to the first parameter at the current moment and the dynamic model of the vehicle;
calculating a first track set of the vehicle from the current moment to the next moment according to the first parameter and the second parameter;
processing the first track set according to the first list and the second list to generate a processed first track set;
evaluating the tracks in the first track set after processing through a heuristic value function;
determining a first target track from the processed first track set according to the evaluation result;
when the distance difference between the end point of the nth target track and the end point is smaller than a preset second threshold value, processing the first target track to the nth target track to generate a target path; n is an integer greater than 2.
In a possible implementation manner, the obtaining the reference path of the vehicle specifically includes:
receiving a starting point of a journey and an end point of the journey sent by a server;
calling an environment map file according to the starting point of the travel and the end point of the travel;
and generating a reference path according to the starting point of the journey, the end point of the journey and the environment map file.
In a possible implementation manner, the calculating, according to the subset distance set and the geometric distance set, a set of heuristic values of a plurality of sub-circles corresponding to circle centers specifically includes:
by the formula f = d end -R calculating heuristic values of a plurality of sub-circles corresponding to the center of the circle;
wherein d is end The geometric distance from the center of the circle to the first end point is shown, and R is the radius of the sub-circle.
In one possible implementation, the geometric distance includes one of an euler distance, a manhattan distance, and a durbin distance.
In a possible implementation manner, the first parameter includes an x coordinate, a y coordinate, an orientation, a vehicle speed, and a steering wheel angle of the vehicle at a current time, and the calculating a second parameter of the vehicle at a next time according to the first parameter at the current time specifically includes:
calculating a second parameter of the vehicle at the next time by the following formula:
x t+Δt ＝x t +vcosθcosβΔt
y t+Δt ＝y t +vsinθcosβΔt
θ t+Δt ＝θ t +vsinβΔt/l
v t+Δt ＝v t +aΔt
β t+Δt ＝β t +ωΔt
wherein x is t For the x coordinate, y coordinate of the vehicle at the current moment t Is a vehicle is inY-coordinate of previous time, theta t Is the orientation of the vehicle at the present moment, v t Speed of the vehicle at the present moment, beta t The steering wheel angle of the vehicle at the current moment; x is the number of t+Δt Is the x coordinate, y of the vehicle at the next moment t+Δt Is the y-coordinate, theta, of the vehicle at the next instant t+Δt Is the orientation of the vehicle at the next moment, v t+Δt Is the speed of the vehicle at the next moment, β t+Δt The steering wheel angle for the vehicle at the next moment; and l is the vehicle wheel base.
In a possible implementation manner, the processing the first track set according to the second list to generate a processed first track set specifically includes:
and deleting the tracks outside the sub-circle in the first track set according to the position and the radius from the sub-circle taking the circumference of the first father circle as the center of the circle to the center of the sub-circle taking the circumference of the mth father circle as the center of the circle.
In a possible implementation manner, the evaluating, by a heuristic function, the tracks in the first track set after the processing specifically includes:
calculating a heuristic value of each track in the processed first track set through f = g + h;
when the heuristic value of the track is minimum, determining the track as a first target track;
wherein f is a heuristic value of each trajectory, and g is a distance from the starting point to a position where the vehicle is located at the next moment; h comprises a circle center guide item and an end point guide item.
In one possible implementation, the formula h = l next +l 1 +l 2 ...l dist H is calculated;
wherein l next A circle center guide item which represents the distance from the position of the vehicle at the next moment to the nearest circle center, l 1 +l 2 ...l dist The vehicle navigation system is an end point guide item and represents the distance from the circle center closest to the position of the vehicle at the next moment to the next circle center, the distance from the next circle center to the next circle center, \ 823030, and the sum of the distances from the last circle center to the end point.
In a possible implementation manner, before generating the first list and the second list when the coincidence degree of the mth parent circle and the end circle is greater than a preset first threshold, the method further includes:
and when the heuristic values of all the sub-circles of a certain parent circle are equal, returning to the parent circle at the upper level of the parent circle, and deleting the position and the radius of the center of the parent circle from the first list.
In a second aspect, the present invention provides a path planning apparatus, including:
an acquisition unit configured to acquire a reference path of a vehicle, the reference path including a start point and an end point;
the setting unit is used for taking a first end point on the reference path; the first end point is located between the start point and the end point;
a determination unit configured to determine whether or not an obstacle exists in a circle having a diameter equal to a distance between the start point and the first end point;
a determining unit configured to determine, when a first obstacle exists, a first distance between the starting point and the first obstacle; the first obstacle is the obstacle closest to the starting point in the obstacles; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle;
the setting unit is further configured to set a first father circle by taking the starting point as a circle center and the first distance as a radius;
the setting unit is further used for setting a first end point circle by taking the first end point as a circle center and the first distance as a radius;
the determining unit is further configured to determine, with a point on the circumference of the first parent circle as a center, a distance between each of a plurality of circles on the circumference and a nearest obstacle to the center, and generate a child distance set;
a calculation unit, configured to calculate a geometric distance between each of a plurality of centers of circles on the circumference and the first end point, and generate a set of geometric distances;
the calculation unit is further configured to calculate a heuristic value set of sub-circles corresponding to the plurality of circle centers according to the sub-distance set and the geometric distance set; the radius of the sub-circle is the difference of the distance between the circle center and the nearest barrier minus the safety distance of the vehicle;
the determining unit is further configured to determine a child circle corresponding to a minimum heuristic value in the heuristic value set as a second parent circle;
a generating unit, configured to generate a first list and a second list when a coincidence degree of the mth parent circle and the first end circle is greater than a preset first threshold; the first list comprises circle center positions and radiuses of the first father circle to the mth father circle; the second list includes positions and radii from a sub-circle centered on the circumference of the first parent circle to a center of a sub-circle centered on the circumference of the mth parent circle; m is an integer greater than 2;
the obtaining unit is further used for obtaining a first parameter of the vehicle at the current moment;
the calculation unit is further used for calculating a second parameter of the vehicle at the next moment according to the first parameter at the current moment and the dynamic model of the vehicle;
the calculation unit is further used for calculating a first track set of the vehicle from the current moment to the next moment according to the first parameter and the second parameter;
the processing unit is used for processing the first track set according to the first list and the second list to generate a processed first track set;
the evaluation unit is used for evaluating the tracks in the processed first track set through a heuristic value function;
the determining unit is further used for determining a first target track from the processed first track set according to the evaluation result;
the processing unit is further configured to process the first target track to the nth target track to generate a target path when a difference between a terminal point of the nth target track and a distance between the terminal point is smaller than a preset second threshold; n is an integer greater than 2.
In a third aspect, the invention provides an apparatus comprising a memory for storing a program and a processor for performing the method of any of the first aspects.
In a fourth aspect, the present invention provides a computer program product comprising instructions which, when run on a computer, cause the computer to perform the method according to any one of the first aspect.
In a fifth aspect, the invention provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the method of any one of the first aspects.
By applying the path planning method and the path planning device provided by the invention, the following technical effects are achieved:
1. a series of search circles are generated, which correspond to a fast space search that fills the available space. The heuristic track searching direction is guided by utilizing the exploration circles, so that the barrier and the end point are considered in the heuristic searching process, the space utilization rate is also considered, and the reasonability of the unmanned vehicle planning path is greatly enhanced.
2. The process of generating the path samples the acceleration of the vehicle and the rotating speed of the steering wheel, and the generated path contains information such as coordinates, orientation, speed, steering wheel rotation angle and the like of the vehicle, so that the generated path is continuous in coordinates and orientation and continuous in speed and steering wheel rotation angle, the generated path is more reasonable, the control difficulty of the unmanned vehicle control module is reduced, and the real-time performance is improved.
Drawings
Fig. 1 is a schematic flow chart of a path planning method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a spatial search according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of heuristic track search according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a path planning apparatus according to a second embodiment of the present invention.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be further noted that, for the convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Fig. 1 is a schematic flow chart of a path planning method according to an embodiment of the present invention. The method is applied to the field of automatic driving, the execution subject of the method is a calculation processing unit of a vehicle, the calculation processing unit can be a vehicle control unit, and as shown in fig. 1, the method comprises the following steps:
The reference path refers to a global path planned in an off-line or real-time manner by the vehicle, and the path does not consider the temporary obstacles on the road. The reference path is used for guiding a planning target of a path planning algorithm, and the vehicle can return to the set road while avoiding obstacles.
The reference path can be acquired by a method that firstly, a starting point of a journey and an end point of the journey sent by a server are received; then, calling an environment map file according to the starting point and the end point of the journey; and finally, generating a reference path according to the starting point of the travel, the end point of the travel and the environment map file.
The server may receive a start point or an end point of a trip transmitted by the user terminal, and the environment map file may be stored in the server, for example, the vehicle may transmit a request message including a current location of the vehicle to the server, and the server may transmit the environment map file including the current location, the start point, and the end point of the vehicle to the vehicle according to the current location of the vehicle. The vehicle may have an environment map file stored therein.
And the vehicle acquires a starting point and an end point of the journey from the server, and then carries out path planning according to the environment map file to generate a reference path.
Wherein, before step 101, obstacle information and a vehicle dynamics model need to be obtained.
The obstacle information is mainly obtained by obtaining the position and speed information of the obstacle from an upstream node (such as perception, prediction and the like), and the information is uniformly stored and sorted according to the relative distance from the vehicle.
The vehicle dynamics model mainly includes intrinsic parameters of the length and width of the vehicle, the vehicle wheel base, the minimum turning radius, the acceleration limit value, the safe distance and the like, which are generally defined in a configuration file.
Specifically, since the length of the reference path is generally long, in order to increase the processing speed, the reference path may be divided, for example, a point is taken on the reference path and is referred to as a first end point, and for example, a circle is made with the starting point of the reference path as a point and the diameter D as a diameter, and an intersection of the circle and the reference path may be referred to as a first end point. D is a preset length.
Specifically, since the obstacle information has been acquired before step 101 and the positions of the obstacles have also been sorted, it is possible to determine whether or not an obstacle exists in a circle having a start point and a first end point as two points on the circle, based on the result of sorting the obstacles.
And when no obstacle exists, continuously judging whether the obstacle exists in a circle with the first end point as one point on the circle and the second end point as the other point on the circle.
The second endpoint may be determined according to the above-mentioned method for determining the first endpoint.
104, when a first obstacle exists, determining a first distance between a starting point and the first obstacle; the first barrier is the barrier closest to the starting point in the barriers; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle.
Specifically, the safety distance of the vehicle is already included in the vehicle dynamics model. When a plurality of obstacles are searched in a circle with a starting point and a first end point as two points on the circle, the obstacle closest to the starting point is used as a first obstacle, and the distance between the starting point and the first obstacle is calculated according to the position of the first obstacle and the position of the starting point.
Subsequently, a first distance may be calculated based on the distance of the origin from the first obstacle.
Wherein, the formula R = L can be passed obs -d safety L obs Calculating a first distance, wherein R is the first distance, L obs Is the distance from the starting point to the first obstacle, d safety Is the safe distance of the vehicle.
And 105, setting a first father circle by taking the starting point as a circle center and the first distance as a radius.
And 106, setting a first endpoint circle by taking the first endpoint as a circle center and the first distance as a radius.
Specifically, referring to fig. 2, a first parent circle is generated by taking the starting point as the center of a circle and the first distance as the radius, referring to the leftmost dark circle of fig. 2, and an end point circle is generated by taking the first end point as the center of a circle and the first distance as the radius, referring to the rightmost dark circle of fig. 2.
And step 107, taking a point on the circumference of the first parent circle as a circle center, determining the distance between each of a plurality of circles on the circumference and the nearest obstacle, and generating a sub-distance set.
Specifically, on the circumference of the first parent circle, the obstacle is searched by taking a point on the circumference as a center of circle, for example, on the circumference of the first parent circle, the positions of the centers of circle are respectively R1, R2 and R3, the obstacle is searched, the positions are respectively A1, A2 and A3, the distances between R1 and A1, between R2 and A2, and between R3 and A3 are calculated, and the generated sub-distance set is { | R1-A1|, | R2-A2|, | R3-A3| }.
Of course, the location information here may be latitude and longitude information, and for ease of understanding, only the sub-distance set is illustrated here simply. The specific calculation process is not detailed.
And step 108, calculating the geometric distance between each of the circles on the circumference and the first end point, and generating a geometric distance set.
Where geometric distances include, but are not limited to, euler distances, manhattan distances, and durbin distances.
The calculation of each specific geometric distance belongs to the prior art, and is not described in the present application.
Specifically, by the formula f = d end -R calculating heuristic values of a plurality of sub-circles corresponding to the center of the circle;
wherein d is end The geometric distance from the center of the circle to the first end point is shown, and R is the radius of the sub-circle.
And step 110, determining the child circle corresponding to the minimum heuristic value in the heuristic value set as a second parent circle.
Specifically, through the above calculation, assuming that the heuristic value of R2 is the smallest among the sub-circles corresponding to R1, R2, and R3, R2 can be regarded as the second parent circle.
Subsequently, steps 107 to 110 may be repeated until the mth parent circle is searched. Wherein m is an integer greater than 2.
Specifically, the overlapping ratio here may be an overlapping area of two circles. When the overlapping area of the mth parent circle and the first end circle is greater than a preset first threshold, it may be determined that the search from the start point to the first end point ends.
Subsequently, steps 102 to 111 may be continued until the reference path is searched. This process may be referred to as spatial exploration.
At the current time, a first parameter of the vehicle is obtained, step 112.
Specifically, the steering wheel angle and the acceleration under the current state are sampled within the current maximum steering wheel angle and the current maximum driving acceleration of the vehicle. I.e. vehicle speed (calculated from acceleration) and steering wheel angle, in the following first parameters.
The first parameters comprise an x coordinate, a y coordinate, a direction, a vehicle speed and a steering wheel angle of the vehicle at the current moment. The second parameters include the vehicle's x-coordinate, y-coordinate, heading, vehicle speed, steering wheel angle at the next time.
And 113, calculating a second parameter of the vehicle at the next moment according to the first parameter at the current moment and the dynamic model of the vehicle.
Wherein, step 113 specifically includes: calculating a second parameter of the vehicle at the next time by the following formula:
x t+Δt ＝x t +vcosθcosβΔt
y t+Δt ＝y t +vsinθcosβΔt
θ t+Δt ＝θ t +vsinβΔt/l
v t+Δt ＝v t +aΔt
β t+Δt ＝β t +ωΔt
wherein x is t The x coordinate and y coordinate of the vehicle at the current moment t Is the y-coordinate, theta, of the vehicle at the current time t Is the orientation of the vehicle at the present moment, v t Speed of the vehicle at the present moment, beta t The steering wheel angle of the vehicle at the current moment; x is the number of t+Δt For the x-coordinate, y, of the vehicle at the next instant t+Δt Is the y-coordinate, θ, of the vehicle at the next instant t+Δt Is the orientation of the vehicle at the next moment, v t+Δt Is the speed of the vehicle at the next momentDegree, beta t+Δt Is the steering wheel angle of the vehicle at the next moment, and l is the vehicle wheelbase. The vehicle wheel base belongs to one of the parameters in the vehicle dynamic model, so when the parameter of the next moment is calculated, the dynamic model parameter of the vehicle is considered, and the vehicle dynamic constraint is met.
And step 114, calculating a first track set of the vehicle from the current time to the next time according to the first parameter and the second parameter.
Specifically, the trajectory of the vehicle from the current time to the next time may be calculated through a model to obtain a first trajectory set, see fig. 3, where a first circle from the left in fig. 3 is a first parent circle, a second circle is a child circle of the first parent circle (where the first parent circle is called the second parent circle when the heuristic value of the child circle of the first parent circle is minimum), a third circle is a child circle of the second parent circle (where the second parent circle is called the third parent circle when the heuristic value of the child circle of the second parent circle is minimum), and the first trajectory set from the current time to the next time includes a dashed line 11, a dashed line 12, a dashed line 13, a solid line 14, and a dashed line 15.
When the vehicle travels to the next time, the second set of trajectories between the next time and the next time includes a broken line 21, a broken line 22, a solid line 23, a broken line 24, and a broken line 25. The method for determining the second track set from the next time to the next time is the same as the method for calculating the first track set from the current time to the next time, and is not repeated here.
And step 115, processing the first track set according to the first list and the second list to generate a processed first track set.
Specifically, the tracks of the first track set outside the sub-circle are deleted according to the positions and the radii of the first parent circle to the mth parent circle, and the positions and the radii of the centers of the sub-circle taking the circumference of the first parent circle as the center of a circle to the sub-circle taking the circumference of the mth parent circle as the center of a circle.
With continued reference to fig. 3, in fig. 3, from the left, of the broken lines and the solid lines between the first circle and the second circle, the broken lines 11 and 15 are beyond the range of the first circle and the second circle, and therefore, the broken lines 11 and 15 in the first trajectory set are deleted, and the processed first trajectory set includes the broken line 12, the broken line 13, and the solid line 14.
In the second set of tracks, the dashed lines 24 and 25 are beyond the second and third circles, and therefore, the dashed lines 24 and 25 in the second set of tracks are deleted and the processed second set of tracks includes 21, 22 and 23.
And step 116, evaluating the tracks in the processed first track set through a heuristic value function.
And step 117, determining a first target track from the processed first track set according to the evaluation result.
Specifically, calculating a heuristic value of each track in the processed first track set through f = g + h;
and when the heuristic value of the track is minimum, determining the track as a first target track.
Wherein f is a heuristic value of each trajectory, and g is a distance from the starting point to a position at which the vehicle is located at the next moment; h comprises a circle center guide item and an end point guide item;
by the formula h = l next +l 1 +l 2 ...l dist H is calculated;
wherein l next A circle center guide item which represents the distance from the position of the vehicle at the next moment to the nearest circle center, l 1 +l 2 ...l dist The vehicle navigation system is an end point guide item and represents the distance from the circle center closest to the position of the vehicle at the next moment to the next circle center, the distance from the next circle center to the next circle center, \ 823030, and the sum of the distances from the last circle center to the end point.
After the first target trajectory is calculated, the next time is taken as a start time and the next time is taken as an end time, and the steps 112 to 117 are repeated to determine a second target trajectory. This process may be referred to as heuristic track searching.
For example, in fig. 3, it is calculated that the heuristic value of 14 is the smallest in the first trajectory set, and the heuristic value of 23 is the smallest in the second trajectory set, so that 14 can be determined as the first target trajectory and 23 can be determined as the second target trajectory.
And step 118, when the difference between the distances between the end point and the end point of the nth target track is smaller than a preset second threshold, processing the first target track to the nth target track to generate a target path.
Continuing to take fig. 3 as an example, in fig. 3, after calculation, the first target track is determined to be 14, the second target track is determined to be 23, 14 and 23 are spliced, and if other nth target tracks exist subsequently, the splicing is continued to obtain the target track. Wherein n is an integer greater than 2.
Specifically, step 118 includes: splicing the first target track to the nth target track to generate an original target path;
and when the original target path does not meet the vehicle kinematic constraint, performing smoothing processing to generate a target path.
For example, the vehicle dynamics model includes a minimum turning radius, when a plurality of target tracks are spliced, the curvature of the spliced part is calculated, the curvature is compared with the reciprocal of the minimum turning radius of the vehicle, when the curvature is not more than the reciprocal of the minimum turning radius, the curvature is in accordance with the requirement, and when the curvature is more than the reciprocal of the minimum turning radius, the smoothing process is performed. By way of example and not limitation, the smoothing process may be performed according to a mean filtering manner.
Further, before step 111, the method further includes:
and when the heuristic values of all the sub-circles of a certain parent circle are equal, returning to the parent circle at the upper level of the parent circle, and deleting the position and the radius of the center of the parent circle from the first list.
It is understood that the spatial exploration in the present application uses circular measurements, but may also take the form of rectangular, elliptical, etc. measurements.
Therefore, the path planning method provided by the invention has the following advantages:
1. a series of exploration circles are generated, which correspond to a fast space exploration that fills the available space. The heuristic track searching direction is guided by utilizing the exploration circles, so that the barrier and the end point are considered in the heuristic searching process, the space utilization rate is also considered, and the reasonability of the unmanned vehicle planning path is greatly enhanced.
2. The process of generating the path samples the acceleration of the vehicle and the rotating speed of the steering wheel, and the generated path contains information such as coordinates, orientation, speed, steering wheel rotation angle and the like of the vehicle, so that the generated path is continuous in coordinates and orientation and continuous in speed and steering wheel rotation angle, the generated path is more reasonable, the control difficulty of the unmanned vehicle control module is reduced, and the real-time performance is improved.
The embodiment of the invention provides a path planning device. Fig. 4 is a schematic structural diagram of a path planning apparatus according to a second embodiment of the present invention. As shown in fig. 4, the path planning apparatus includes: an acquisition unit 401, a setting unit 402, a judgment unit 403, a determination unit 404, a calculation unit 405, a generation unit 406, a processing unit 407, and an evaluation unit 408.
The acquiring unit 401 is configured to acquire a reference path of the vehicle, where the reference path includes a start point and an end point;
the setting unit 402 is configured to take a first end point on the reference path; the first end point is positioned between the starting point and the end point;
the judgment unit 403 is used for judging whether an obstacle exists in a circle with the diameter of the distance between the starting point and the first end point;
the determining unit 404 is configured to determine, when a first obstacle exists, a first distance between the starting point and the first obstacle; the first barrier is the barrier closest to the starting point in the barriers; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle;
the setting unit 402 is further configured to set a first parent circle by taking the starting point as a circle center and taking the first distance as a radius;
the setting unit 402 is further configured to set a first endpoint circle by taking the first endpoint as a circle center and the first distance as a radius;
the determining unit 404 is further configured to determine, with a point on the circumference of the first parent circle as a center, a distance between each of a plurality of circles on the circumference and the nearest obstacle, and generate a child distance set;
the calculating unit 405 is configured to calculate a geometric distance between each of a plurality of circles on the circumference and the first end point, and generate a set of geometric distances;
the calculating unit 405 is further configured to calculate a set of heuristic values of sub-circles corresponding to the plurality of circle centers according to the set of sub-distances and the set of geometric distances; the radius of the sub-circle is the difference of the distance between the circle center and the nearest barrier minus the safety distance of the vehicle;
the determining unit 404 is further configured to determine a child circle corresponding to the minimum heuristic value in the heuristic value set as a second parent circle;
the generating unit 406 is configured to generate a first list and a second list when the overlap ratio of the mth parent circle and the first end circle is greater than a preset first threshold; the first list comprises circle center positions and radiuses of the first father circle to the mth father circle; the second list includes positions and radii of centers of a sub-circle having the circumference of the first parent circle as a center of a circle to a sub-circle having the circumference of the mth parent circle as a center of a circle; m is an integer greater than 2;
the obtaining unit 401 is further configured to obtain, at the current time, a first parameter of the vehicle at the starting point;
the calculating unit 405 is further configured to calculate a second parameter of the vehicle at a next time according to the first parameter at the current time and the dynamic model of the vehicle;
the calculating unit 405 is further configured to calculate a first trajectory set of the vehicle from the current time to the next time according to the first parameter and the second parameter;
the processing unit 407 is configured to process the first track set according to the first list and the second list, and generate a processed first track set;
the evaluation unit 408 is configured to evaluate the tracks in the processed first track set through a heuristic value function;
the determining unit 404 is further configured to determine, according to the evaluation result, a first target trajectory from the processed first trajectory set;
the processing unit 407 is further configured to, when a difference between distances of an end point and an end point of the nth target track is smaller than a preset second threshold, process the first target track to the nth target track to generate a target path; n is an integer greater than 2.
The specific functions of each module in fig. 4 are the same as those described in the first embodiment, and are not described again here. It can be understood that the technical effect of the second embodiment is also the same as that of the first embodiment, and the description thereof is omitted.
The third embodiment of the invention provides equipment, which comprises a memory and a processor, wherein the memory is used for storing programs, and the memory can be connected with the processor through a bus. The memory may be a non-volatile memory such as a hard disk drive and a flash memory, in which a software program and a device driver are stored. The software program is capable of performing various functions of the above-described methods provided by embodiments of the present invention; the device drivers may be network and interface drivers. The processor is used for executing a software program, and the software program can realize the method provided by the first embodiment of the invention when being executed.
A fourth embodiment of the present invention provides a computer program product including instructions, which, when the computer program product runs on a computer, causes the computer to execute the method provided in the first embodiment of the present invention.
Fifth embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the method provided in the first embodiment of the present invention.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the technical solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method of path planning, the method comprising:
acquiring a reference path of a vehicle, wherein the reference path comprises a starting point and an end point;
taking a first end point on the reference path; the first end point is located between the start point and the end point;
judging whether an obstacle exists in a circle with the diameter of the distance between the starting point and the first end point;
when a first obstacle exists, determining a first distance between the starting point and the first obstacle; the first obstacle is the obstacle closest to the starting point in the obstacles; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle;
setting a first father circle by taking the starting point as a circle center and the first distance as a radius;
setting a first end point circle by taking the first end point as a circle center and the first distance as a radius;
determining the distance between each of a plurality of circles on the circumference and the nearest barrier to the circle by taking the point on the circumference of the first father circle as the center of the circle, and generating a child distance set;
calculating the geometric distance between each of a plurality of centers of circles on the circumference and the first end point, and generating a geometric distance set;
calculating a set of heuristic values of the sub-circles corresponding to the circle centers according to the sub-distance set and the geometric distance set; the radius of the sub-circle is the difference of the distance between the circle center and the nearest barrier minus the safety distance of the vehicle;
determining a child circle corresponding to the minimum heuristic value in the heuristic value set as a second parent circle;
when the coincidence degree of the mth father circle and the first end circle is larger than a preset first threshold value, generating a first list and a second list; the first list comprises circle center positions and radii of the first father circle to the mth father circle; the second list includes positions and radii from a sub-circle centered on the circumference of the first parent circle to a center of a sub-circle centered on the circumference of the mth parent circle; m is an integer greater than 2;
at the current moment, acquiring a first parameter of the vehicle;
calculating a second parameter of the vehicle at the next moment according to the first parameter at the current moment and the dynamic model of the vehicle;
calculating a first track set of the vehicle from the current moment to the next moment according to the first parameter and the second parameter;
processing the first track set according to the first list and the second list to generate a processed first track set;
evaluating the tracks in the first track set after processing through a heuristic value function;
determining a first target track from the processed first track set according to the evaluation result;
when the distance difference between the end point of the nth target track and the end point is smaller than a preset second threshold value, processing the first target track to the nth target track to generate a target path; n is an integer greater than 2.
2. The method according to claim 1, wherein the obtaining a reference path of a vehicle comprises:
receiving a starting point of a journey and an end point of the journey sent by a server;
calling an environment map file according to the starting point of the travel and the end point of the travel;
and generating a reference path according to the starting point of the travel, the end point of the travel and the environment map file.
3. The method according to claim 1, wherein the calculating a set of heuristic values of sub-circles corresponding to a plurality of circle centers according to the set of sub-distances and the set of geometric distances comprises:
by the formula f = d end -R calculating heuristic values of a plurality of sub-circles corresponding to the center of the circle;
wherein d is end The geometric distance from the center of the circle to the first end point is shown, and R is the radius of the sub-circle.
4. The method of claim 3, wherein the geometric distance comprises one of an Euler distance, a Manhattan distance, and a Dubin distance.
5. The method according to claim 1, wherein the first parameters comprise an x-coordinate, a y-coordinate, an orientation, a vehicle speed, and a steering wheel angle of the vehicle at a current time, and the calculating a second parameter of the vehicle at a next time based on the first parameter at the current time and a dynamic model of the vehicle comprises:
calculating a second parameter of the vehicle at the next time by the following formula:
x t+Δt ＝x t +v t ·cosθ t ·cosβ t ·Δt
y t+Δt ＝y t +v t ·sinθ t ·cosβ t ·Δt
θ t+Δt ＝θ t +v t ·sinβ t ·Δt/l
v t+Δt ＝v t +a·Δt
β t+Δt ＝β t +ω·Δt
wherein x is t The x coordinate and y coordinate of the vehicle at the current moment t Is the y-coordinate, theta, of the vehicle at the current time t Is the orientation of the vehicle at the present moment, v t Speed of the vehicle at the present moment, beta t The steering wheel angle of the vehicle at the current moment; x is the number of t+Δt Is the x coordinate, y of the vehicle at the next moment t+Δt Is the y-coordinate, theta, of the vehicle at the next instant t+Δt Is the orientation of the vehicle at the next moment, v t+Δt Is the speed of the vehicle at the next moment, beta t+Δt The steering wheel angle for the vehicle at the next moment; and l is the vehicle wheel base.
6. The method according to claim 1, wherein the processing the first track set according to the second list to generate a processed first track set specifically includes:
and deleting the tracks of the first track outside the sub-circle in a centralized manner according to the position and the radius from the sub-circle taking the circumference of the first father circle as the center of the circle to the center of the sub-circle taking the circumference of the mth father circle as the center of the circle.
7. The method according to claim 1, wherein the evaluating the processed trajectories in the first trajectory set by a heuristic function specifically comprises:
calculating a heuristic value of each track in the processed first track set through f = g + h;
when the heuristic value of the track is minimum, determining the track as a first target track;
wherein f is a heuristic value of each trajectory, and g is a distance from the starting point to a position where the vehicle is located at the next moment; h comprises a circle center guide item and an end point guide item.
8. Method according to claim 7, characterized in that by the formula h = l next +l 1 +l 2 ...l dist H is calculated;
wherein l next A circle center guide item which represents the distance from the position of the vehicle at the next moment to the nearest circle center, l 1 +l 2 ...l dist In order to be the end point guide item,and (3) representing the distance from the nearest circle center to the next circle center, the distance from the next circle center to the next lower circle center, and the sum of the distances from the last circle center to the terminal point.
9. The method according to claim 1, wherein before generating the first list and the second list when the coincidence degree of the mth parent circle and the end circle is greater than a preset first threshold, the method further comprises:
and when the heuristic values of all the sub-circles of a certain parent circle are equal, returning to the parent circle at the upper level of the parent circle, and deleting the position and the radius of the center of the parent circle from the first list.
10. A path planning apparatus, characterized in that the path planning apparatus comprises:
an acquisition unit configured to acquire a reference path of a vehicle, the reference path including a start point and an end point;
the setting unit is used for taking a first end point on the reference path; the first end point is located between the start point and the end point;
a determination unit configured to determine whether or not an obstacle exists in a circle having a diameter equal to a distance between the start point and the first end point;
a determining unit configured to determine, when a first obstacle exists, a first distance between the starting point and the first obstacle; the first obstacle is the obstacle closest to the starting point in the obstacles; the first distance is the difference of the distance between the starting point and the first obstacle minus the safety distance of the vehicle;
the setting unit is further configured to set a first father circle by taking the starting point as a circle center and the first distance as a radius;
the setting unit is further used for setting a first end point circle by taking the first end point as a circle center and the first distance as a radius;
the determining unit is further configured to determine, with a point on the circumference of the first parent circle as a center, a distance between each of a plurality of circles on the circumference and an obstacle closest thereto, and generate a sub-distance set;
a calculation unit, configured to calculate a geometric distance between each of a plurality of centers of circles on the circumference and the first end point, and generate a geometric distance set;
the calculation unit is further configured to calculate a heuristic value set of sub-circles corresponding to the plurality of circle centers according to the sub-distance set and the geometric distance set; the radius of the sub-circle is the difference of the distance between the circle center and the nearest barrier minus the safety distance of the vehicle;
the determining unit is further configured to determine a child circle corresponding to a minimum heuristic value in the heuristic value set as a second parent circle;
the generating unit is used for generating a first list and a second list when the coincidence degree of the mth father circle and the first end circle is larger than a preset first threshold; the first list comprises circle center positions and radiuses of the first father circle to the mth father circle; the second list includes positions and radii from a sub-circle centered on the circumference of the first parent circle to a center of a sub-circle centered on the circumference of the mth parent circle; m is an integer greater than 2;
the obtaining unit is further used for obtaining a first parameter of the vehicle at the current moment;
the calculation unit is further used for calculating a second parameter of the vehicle at the next moment according to the first parameter at the current moment and the dynamic model of the vehicle;
the calculation unit is further used for calculating a first track set of the vehicle from the current moment to the next moment according to the first parameter and the second parameter;
the processing unit is used for processing the first track set according to the first list and the second list to generate a processed first track set;
the evaluation unit is used for evaluating the tracks in the processed first track set through a heuristic value function;
the determining unit is further used for determining a first target track from the processed first track set according to the evaluation result;
the processing unit is further used for processing the first target track to the nth target track to generate a target path when the difference between the distance between the end point of the nth target track and the end point is smaller than a preset second threshold; n is an integer greater than 2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910201609.8A CN109916421B (en) | 2019-03-18 | 2019-03-18 | Path planning method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910201609.8A CN109916421B (en) | 2019-03-18 | 2019-03-18 | Path planning method and device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109916421A CN109916421A (en) | 2019-06-21 |
| CN109916421B true CN109916421B (en) | 2023-02-10 |
Family
ID=66965397
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910201609.8A Active CN109916421B (en) | 2019-03-18 | 2019-03-18 | Path planning method and device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109916421B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111795699B (en) * | 2019-11-26 | 2021-12-14 | 北京京东乾石科技有限公司 | Unmanned vehicle path planning method and device and computer readable storage medium |
| CN111055274B (en) * | 2019-11-28 | 2021-12-17 | 深圳优地科技有限公司 | Robot path smoothing method and robot |
| CN112985373B (en) * | 2019-12-18 | 2023-08-01 | 中国移动通信集团四川有限公司 | Path planning method and device and electronic equipment |
| CN111121795B (en) * | 2020-03-26 | 2020-07-07 | 腾讯科技（深圳）有限公司 | Road network generation method, navigation device, equipment and storage medium |
| CN112880700B (en) * | 2021-02-26 | 2024-04-16 | 北京智行者科技股份有限公司 | Local path planning method and device for in-situ steering vehicle |
| CN113119995B (en) * | 2021-03-11 | 2023-01-31 | 京东鲲鹏(江苏)科技有限公司 | Path searching method and device, equipment and storage medium |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101358855A (en) * | 2008-09-23 | 2009-02-04 | 光庭导航数据（武汉）有限公司 | Navigation head based on layering bidirectional heuristic route planning method |
| CN105717929A (en) * | 2016-04-29 | 2016-06-29 | 中国人民解放军国防科学技术大学 | Planning method for mixed path of mobile robot under multi-resolution barrier environment |
| CN106275066A (en) * | 2016-08-30 | 2017-01-04 | 北京智行者科技有限公司 | The rotating direction control method of a kind of intelligent vehicle and device |
| CN106970648A (en) * | 2017-04-19 | 2017-07-21 | 北京航空航天大学 | Unmanned plane multi-goal path plans combined method for searching under the environment of city low latitude |
| WO2018227387A1 (en) * | 2017-06-13 | 2018-12-20 | Beijing Didi Infinity Technology And Development Co., Ltd. | Methods and systems for route planning |
| CN109269518A (en) * | 2018-08-31 | 2019-01-25 | 北京航空航天大学 | A kind of movable fixture confined space path generating method based on intelligent body |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106740868B (en) * | 2016-12-30 | 2019-03-29 | 东软集团股份有限公司 | A kind of method, apparatus and equipment of speed planning |
-
2019
- 2019-03-18 CN CN201910201609.8A patent/CN109916421B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101358855A (en) * | 2008-09-23 | 2009-02-04 | 光庭导航数据（武汉）有限公司 | Navigation head based on layering bidirectional heuristic route planning method |
| CN105717929A (en) * | 2016-04-29 | 2016-06-29 | 中国人民解放军国防科学技术大学 | Planning method for mixed path of mobile robot under multi-resolution barrier environment |
| CN106275066A (en) * | 2016-08-30 | 2017-01-04 | 北京智行者科技有限公司 | The rotating direction control method of a kind of intelligent vehicle and device |
| CN106970648A (en) * | 2017-04-19 | 2017-07-21 | 北京航空航天大学 | Unmanned plane multi-goal path plans combined method for searching under the environment of city low latitude |
| WO2018227387A1 (en) * | 2017-06-13 | 2018-12-20 | Beijing Didi Infinity Technology And Development Co., Ltd. | Methods and systems for route planning |
| CN109269518A (en) * | 2018-08-31 | 2019-01-25 | 北京航空航天大学 | A kind of movable fixture confined space path generating method based on intelligent body |
Non-Patent Citations (1)
| Title |
|---|
| 局部网格生成中初始探索圆半径的搜索算法;樊祥阔等;《计算力学学报》;20080430;第25卷(第2期);第188-193页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109916421A (en) | 2019-06-21 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109916421B (en) | Path planning method and device | |
| CN109900289B (en) | Path planning method and device based on closed-loop control | |
| CN108151751B (en) | Path planning method and device based on combination of high-precision map and traditional map | |
| EP3109842B1 (en) | Map-centric map matching method and apparatus | |
| EP1733287B1 (en) | System and method for adaptive path planning | |
| US20220107647A1 (en) | Speed planning method and apparatus, electronic device and storage medium | |
| WO2017162036A1 (en) | Yawing recognition method, terminal and storage medium | |
| CN109785667A (en) | Deviation recognition methods, device, equipment and storage medium | |
| CN109491377A (en) | The decision and planning based on DP and QP for automatic driving vehicle | |
| CN111750886A (en) | Local path planning method and device | |
| CN112444263B (en) | Global path planning method and device | |
| CN111830979A (en) | Trajectory optimization method and device | |
| CN114005280A (en) | Vehicle track prediction method based on uncertainty estimation | |
| JP7330142B2 (en) | Method, Apparatus, Device and Medium for Determining Vehicle U-Turn Path | |
| CN113286985A (en) | Path planning method and path planning device | |
| CN107917716B (en) | Fixed line navigation method, device, terminal and computer readable storage medium | |
| CN113587944B (en) | Quasi-real-time vehicle driving route generation method, system and equipment | |
| JP2023523350A (en) | Vehicle-based data processing method, data processing apparatus, computer apparatus, and computer program | |
| CN111707258B (en) | External vehicle monitoring method, device, equipment and storage medium | |
| CN112327826A (en) | Path planning method, device, equipment and medium | |
| JP6507841B2 (en) | Preceding vehicle estimation device and program | |
| CN115560771A (en) | Sampling-based path planning method and device and automatic driving equipment | |
| CN113867336B (en) | Mobile robot path navigation and planning method suitable for complex scene | |
| CN113515111B (en) | Vehicle obstacle avoidance path planning method and device | |
| Karimi et al. | A methodology for predicting performances of map-matching algorithms |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| CB02 | Change of applicant information | ||
| CB02 | Change of applicant information |
Address after: B4-006, maker Plaza, 338 East Street, Huilongguan town, Changping District, Beijing 100096 Applicant after: Beijing Idriverplus Technology Co.,Ltd. Address before: B4-006, maker Plaza, 338 East Street, Huilongguan town, Changping District, Beijing 100096 Applicant before: Beijing Idriverplus Technology Co.,Ltd. |
|
| GR01 | Patent grant | ||
| GR01 | Patent grant |