CN113029174A - Path identification method and device under engineering transportation environment - Google Patents

Path identification method and device under engineering transportation environment Download PDF

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Publication number
CN113029174A
CN113029174A CN202110259583.XA CN202110259583A CN113029174A CN 113029174 A CN113029174 A CN 113029174A CN 202110259583 A CN202110259583 A CN 202110259583A CN 113029174 A CN113029174 A CN 113029174A
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path
historical
route
current
point
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CN113029174B (en
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李昭
赵荣
庞亚娜
何湘
胥帆
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Xi'an Main Function Intelligent Technology Co ltd
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Xi'an Main Function Intelligent Technology Co ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34Route searching; Route guidance
    • G01C21/3453Special cost functions, i.e. other than distance or default speed limit of road segments
    • G01C21/3492Special cost functions, i.e. other than distance or default speed limit of road segments employing speed data or traffic data, e.g. real-time or historical

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  • Automation & Control Theory (AREA)
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  • General Physics & Mathematics (AREA)
  • Feedback Control In General (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a path identification method in an engineering transportation environment, which comprises the following steps: s02, acquiring a current path point, a current path and a historical path; s04, judging whether the current path point is on the historical path, if so, entering S06, otherwise, returning and judging again; and S06, judging whether a plurality of path points which are continuous from the current path point on the current path are on the historical path, if the plurality of path points are continuous on the historical path, determining that the current path and the historical path are the same path, otherwise, determining that the current path and the historical path are different paths. According to the invention, the driving path of the vehicle is stored and identified, so that the whole vehicle control system realizes the function of 'road condition prediction', the whole vehicle state is adjusted in advance before the road condition changes, the discontinuous running condition of the vehicle caused by the hysteresis of the system when the road condition changes is avoided, and the whole transportation process is more smooth and efficient.

Description

Path identification method and device under engineering transportation environment
Technical Field
The invention relates to the field of an intelligent control system of an engineering transport vehicle. More specifically, the invention relates to a method and a device for identifying a path in an engineering transportation environment.
Background
The working condition under the engineering transportation environment changes violently, and a skilled driver can predict and continuously correct operation instructions such as gear up and gear down, speed up and speed down, a manual control switch and the like according to the road condition ahead, so that the whole transportation process is smooth and efficient.
Along with the higher degree of automation of the existing engineering transport vehicle, many original instructions operated by a driver gradually realize automatic control, but the existing whole vehicle control system basically belongs to a real-time control system, namely, the control instructions are output in real time through different control algorithms according to the real-time state of the whole vehicle, and the continuity of the driving process is poor due to the fact that no driver is used for predicting road conditions.
Disclosure of Invention
The invention aims to provide a path identification method in an engineering transportation environment so as to identify a driving path of a vehicle.
The invention further aims to provide a path identification method in the engineering transportation environment, which is used for intelligent control of vehicles, so that a vehicle control system can predict road conditions and output control instructions in a prejudgment mode, and further the consistency of the vehicle running process is improved.
To achieve the objects and other advantages in accordance with the present invention, there is provided a method for path identification in an engineering transportation environment, comprising:
s02, acquiring a current path point, a current path and a historical path;
s04, judging whether the current path point is on the historical path, if so, entering S06, otherwise, returning and judging again;
s06, judging whether a plurality of path points which are continuous from the current path point on the current path are on the historical path, if the plurality of path points are on the historical path, determining that the current path and the historical path are the same path, otherwise, determining that the current path and the historical path are different paths.
Preferably, in the method for identifying a route in a construction transportation environment, in S02, before the current route and the historical route are acquiredAnd also includes when the vehicle is running at speed V>=V1And the distance D between the current path point and the last storage path point0>=L1Then, storing the current path point, wherein the current path point storage set forms the current path; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance.
Preferably, in the method for identifying a route in an engineering transportation environment, the step S04 of determining whether the current route point is on the historical route includes the step S41 of determining whether a time route at the current route point is the same as the historical route, and if so, calculating Index values [ Index-a, Index + b ] of the current route point and the historical route one by one]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1; s42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting an Index value Index of the current path point on the historical path, otherwise, determining that the current path point is not on the historical path.
Preferably, in the method for identifying a route in an engineering transportation environment, in S41, the step of determining whether a previous route at the current route point is the same as the historical route includes determining whether a plurality of consecutive route points on the current route from the previous route point at the current route point are on the historical route, and if the plurality of consecutive route points are on the historical route, determining that the previous route at the current route point is the same as the historical route, otherwise, determining that the previous route at the current route point is different from the historical route.
The invention also provides a path identification method and a device under the engineering transportation environment, which comprises,
the acquisition module is used for acquiring a current path point, a current path and a historical path;
the first judging module is connected with the acquiring module and used for judging whether the current path point is on the historical path or not;
and the second judging module is connected with the first judging module and used for judging whether a plurality of continuous path points on the current path from the current path point are on the historical path or not after the first judging module judges that the current path point is on the historical path, if the plurality of continuous path points are on the historical path, the current path and the historical path are judged to be the same path, and if not, the current path and the historical path are judged to be different paths.
Preferably, the route recognition device under the engineering transportation environment further comprises a storage module, connected with the acquisition module, and used for determining the vehicle running speed V>=V1And the distance D between the current path point and the last storage path point0>=L1Then, storing the current path point, wherein the current path point storage set forms the current path; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance.
Preferably, the determining, by the path identifying device in the engineering transportation environment, whether the current waypoint is on the historical path in the first determining module specifically includes S41, determining whether a path at a time on the current waypoint and the historical path are the same path, and if so, calculating Index values [ Index-a, Index + b ] of the current waypoint and the historical path one by one]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1; s42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting the Index value Index of the current path point on the historical path, otherwise, determining that the current path point is on the historical pathThe waypoint is not on the historical path.
Preferably, the determining, by the route identifying device in the engineering transportation environment, in S41, whether the route at the previous time of the current route point is the same as the historical route or not specifically includes determining whether a plurality of consecutive route points on the current route from the previous route point of the current route point are on the historical route or not, if the plurality of consecutive route points are on the historical route, determining that the route at the previous time of the current route point is the same as the historical route, and otherwise, determining that the route at the previous time of the current route point is different from the historical route.
The present invention also provides an electronic device, comprising: the system comprises at least one processor and a memory communicatively coupled to the at least one processor, wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the above method.
The invention also provides a storage medium having stored thereon a computer program which, when executed by a processor, carries out the above-mentioned method.
The invention at least comprises the following beneficial effects:
firstly, under the engineering transportation environment, the driving path of the vehicle has the characteristics of short transportation distance, strong repeatability, violent road condition change and the like. The invention enables the whole vehicle control system to predict road conditions and output control instructions in a prejudgment mode, such as prejudgment type gear shifting, prejudgment type acceleration and deceleration and the like, by storing and identifying the vehicle running path, thereby improving the consistency of the vehicle running process.
Secondly, the invention can also realize that the whole vehicle control system analyzes the whole vehicle state data set under the historical path, continuously optimizes the control output instruction and achieves the self-learning function of the control instruction set.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a flow chart of a method for identifying a route in a construction transportation environment according to an embodiment of the invention;
fig. 2 is a schematic diagram of a path recognition device in a project transportation environment according to an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples and the accompanying drawings so that those skilled in the art can practice the invention with reference to the description.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
It is to be noted that the experimental methods described in the following embodiments are all conventional methods unless otherwise specified, and the reagents and materials, if not otherwise specified, are commercially available; in the description of the present invention, the terms "lateral", "longitudinal", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention.
As shown in fig. 1, the present invention provides a method for identifying a route in an engineering transportation environment, including:
s02, acquiring a current path point, a current path and a historical path;
s04, judging whether the current path point is on the historical path, if so, entering S06, otherwise, returning and judging again;
s06, judging whether a plurality of path points which are continuous from the current path point on the current path are on the historical path, if the plurality of path points are on the historical path, determining that the current path and the historical path are the same path, otherwise, determining that the current path and the historical path are different paths.
In the above technical solution, the waypoints are longitude and latitude data provided by the global positioning navigation device, the current route is a set of all waypoints on the current driving route, and is specifically represented as an array including longitude and latitude data of all waypoints on the current driving route, the historical route is a set of all waypoints on the historical driving route, and is specifically represented as an array including longitude and latitude data of all waypoints on the historical driving route, and further, the historical route is obtained by assigning the current route to the historical route when the vehicle satisfies a certain driving condition. Specifically, when identifying a path in an engineering transportation environment, first acquiring a current path point, a current path and a historical path, then judging whether the current path point is on the historical path, if the current path point is on the historical path, then judging whether a plurality of path points on the current path from the current path point are on the historical path, if the plurality of path points are on the historical path, then the current path and the historical path are determined to be the same path, otherwise, the current path and the historical path are determined to be different paths, further, if a plurality of path points on the current path from the current path point are on the historical path, then the current path and the historical path are determined to be the same path, if a plurality of path points on the current path from the current path point are not on the historical path, then the current path and the historical path are determined to be different paths, the values of m and n are finally determined according to the actual calibration process, wherein the initial value can be m-3, and n-4.
The invention stores and identifies the driving path of the vehicle, so that the whole vehicle control system can determine the change trend of the subsequent path according to the stored historical path and the current position of the vehicle in the historical path, and realize the function of 'road condition foreknowing', so as to adjust the state of the whole vehicle in advance before the road condition changes, avoid the occurrence of the discontinuous running condition of the vehicle caused by the hysteresis of the system when the road condition changes, finally ensure that the whole transportation process is smoother and more efficient, and simultaneously, the whole vehicle control system can also realize the analysis of the data set of the state of the whole vehicle in the historical path, continuously optimize the control output instruction, and achieve the function of 'self-learning' of the control instruction set.
In another technical solution, in the method for identifying a route in a construction transportation environment, in S02, before the obtaining of the current route and the historical route, the method further includes when the vehicle driving speed V is>=V1And the distance D between the current path point and the last storage path point0>=L1Then, storing the current path point, wherein the current path point storage set forms the current path; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance. Here, a way of storing the route point and the route is enumerated, and specifically, the vehicle running speed V will be satisfied>=V1And the distance D between the last storage path point0>=L1The current route points are stored, the current route is formed by gathering, and when the vehicle is positioned at the starting point of the driving route, the current route is converted into a historical route, and further V1The value is finally determined according to the actual calibration process, and the initial value can be 5 km/h; the distance between the current path point and the last stored path point can be calculated according to longitude and latitude data of the current path point and the last stored path point, and can also be calculated according to the vehicle speed, L1The value is finally determined in the actual calibration process, and the initial value can be 10 m; the starting point of the vehicle running path is comprehensively judged by a whole vehicle control system, for example, in an engineering transport vehicle, the starting point is judged by a container lifting signal.
In another technical solution, the method for identifying a route under a construction transportation environment, in S04, determining whether the current waypoint is on the historical route specifically includes, in S41, determining a route at a time on the current waypoint and the historical routeWhether the paths are the same or not is judged, if yes, the current path point and the Index values in the historical path are calculated one by one to be [ Index-a, Index + b ]]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1(ii) a S42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting an Index value Index of the current path point on the historical path, otherwise, determining that the current path point is not on the historical path. Specifically, it is determined whether a time path at the current path point is the same as the historical path, and if yes, the Index values of the current path point and the historical path are calculated one by one as [ Index-a, Index + b ] respectively]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1According to D1Whether or not less than or equal to second preset distance L2Judging whether the current path point is on the historical path; further, L2The value is finally determined according to the actual calibration process, and the initial value can be 15 m; index is a variable, the Index value Index of the current path point output at the current time on the historical path is applied to the next time, whether the path point at that time is on the historical path at that time (the current path at that time) is calculated in a recursion manner, and the Index value Index of the path point at that time on the historical path at that time is output; a. b is a constant, the values of a and b are finally determined according to the actual calibration process, and the initial value can be 1 or 2.
In another technical solution, in the method for identifying a route under an engineering transportation environment, in S41, determining whether a time path at the current route point is the same as the historical path, specifically, determining whether a plurality of consecutive route points on the current route from the last route point of the current route point are on the historical path, if the plurality of consecutive route points are on the historical path, determining that the time path at the current route point is the same as the historical path, otherwise, determining that the time path at the current route point is different from the historical path. Specifically, the method determines whether a plurality of consecutive route points on the current route point from a previous route point of the current route point are on the historical route, further determines that the route at the previous time point of the current route point is the same as the historical route if m consecutive route points on the current route point from the previous route point of the current route point are on the historical route, determines that the route at the previous time point of the current route point is different from the historical route if n consecutive route points on the current route point from the previous route point of the current route point are not on the historical route, and determines that the values of m and n are finally determined according to an actual calibration process, wherein the initial value of m is 3 and n is 4.
As shown in fig. 2, the present invention further provides a method and an apparatus for identifying a route in an engineering transportation environment, including,
the acquisition module is used for acquiring a current path point, a current path and a historical path;
the first judging module is connected with the acquiring module and used for judging whether the current path point is on the historical path or not;
and the second judging module is connected with the first judging module and used for judging whether a plurality of continuous path points on the current path from the current path point are on the historical path or not after the first judging module judges that the current path point is on the historical path, if the plurality of continuous path points are on the historical path, the current path and the historical path are judged to be the same path, and if not, the current path and the historical path are judged to be different paths.
In another technical solution, the path recognition device under the engineering transportation environment further includes a storage module, connected to the obtaining module, for when the vehicle runs at a speed V>=V1And the distance D between the current path point and the last storage path point0>=L1When in use, willThe current path point is stored, and the current path is formed by the stored collection of the current path point; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance.
In another technical solution, the determining, by the path identifying device in the engineering transportation environment, whether the current waypoint is on the historical path in the first determining module specifically includes, S41, determining whether a path at a time on the current waypoint and the historical path are the same path, and if so, calculating Index values [ Index-a, Index + b ] in the current waypoint and the historical path one by one]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1; s42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting an Index value Index of the current path point on the historical path, otherwise, determining that the current path point is not on the historical path.
In another technical solution, the determining, in S41, whether the path at the previous time of the current path point and the historical path are the same path specifically includes determining whether a plurality of consecutive path points on the current path from the previous path point of the current path point are on the historical path, if the plurality of consecutive path points are on the historical path, determining that the path at the previous time of the current path point and the historical path are the same path, otherwise, determining that the path at the previous time of the current path point and the historical path are different paths.
The present invention also provides an electronic device, comprising: the system comprises at least one processor and a memory communicatively coupled to the at least one processor, wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the above method.
The invention also provides a storage medium having stored thereon a computer program which, when executed by a processor, carries out the above-mentioned method.
The above device, electronic equipment, and storage medium are obtained based on the same inventive concept as the path feature extraction method in the engineering transportation environment, and reference may be made to the description of the method section.
Example 1:
as shown in fig. 1, the present invention provides a path identification method in an engineering transportation environment, which mainly includes a path point storage method and a path identification method.
1. The path points refer to longitude and latitude data provided by global positioning navigation equipment;
2. the storage method of the path point is that when the condition 1 and the condition 2 are simultaneously satisfied, the current path point is stored into the current path (array);
3. the condition 1 is a vehicle running speed V>=V1,V1The value is finally determined according to the actual calibration process, and the initial value can be 5 km/h;
4. the condition 2 is the distance D between the current path point and the last stored path point0>=L1,L1The value is finally determined according to the actual calibration process, and the initial value can be 10 m;
5. the current path (array) refers to a collection stored by the current path point;
6. the path identification method comprises the steps of firstly judging whether a current path point is on a historical path (array), then judging whether the current path (array) and the historical path (array) are the same path, and outputting a position Index of the current path point on the historical path (array);
7. the historical path (array) is that when the condition 3 is met, the current path (array) is assigned to the historical path (array);
8. the condition 3 refers to a condition that the whole vehicle control system can comprehensively judge the starting point of the transportation path, for example, in an engineering transport vehicle, a container lifting signal can be used as one of the judging conditions of the starting point;
9. the method for judging whether the current path point is on the historical path (array) is that firstly judging whether the path at the moment on the current path point is the same as the historical path, if the path is different, calculating the distance D between the current path point and all the points in the historical path array one by one1(ii) a If the path is the same, calculating the current path point and the Index as [ Index-a, Index + b ] one by one]Has a distance D from the historical path point1;D1When the condition 4 is met, the current path point is shown on the historical path (array), and the Index value Index of the current path point on the historical path (array) is output at the same time; otherwise, the current path point is not on the historical path (array), wherein Index is a variable, the Index value Index of the current path point output at the current time on the historical path is applied to the next time, whether the path point at the time is on the historical path at the time (the current path at the time) is calculated in a recursion manner, the Index value Index of the path point at the time on the historical path at the time is output, the values of a and b are finally determined according to the actual calibration process, and the initial value can be a-1 and b-2;
10. the condition 4 is to calculate the distance D1<=L2,L2The value is finally determined according to the actual calibration process, and the initial value can be 15 m;
11. the method for judging whether the previous time is the same path is to judge whether the current path is the same path as the historical path at the previous time, and the method is to judge that m path points are continuously on the historical path array, and then the current path and the historical path are determined to be the same path; if the continuous n path points are not on the historical path array, the current path and the historical path are determined to be different paths; the values of m and n are finally determined according to the actual calibration process, wherein the initial value can be m-3, and n-4.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (10)

1. The path identification method under the engineering transportation environment is characterized by comprising the following steps:
s02, acquiring a current path point, a current path and a historical path;
s04, judging whether the current path point is on the historical path, if so, entering S06, otherwise, returning and judging again;
s06, judging whether a plurality of path points which are continuous from the current path point on the current path are on the historical path, if the plurality of path points are on the historical path, determining that the current path and the historical path are the same path, otherwise, determining that the current path and the historical path are different paths.
2. The method for identifying a route under a construction transportation environment as claimed in claim 1, wherein, in step S02, before obtaining the current route and the historical route, the method further comprises when the vehicle driving speed V is>=V1And the distance D between the current path point and the last storage path point0>=L1Then, storing the current path point, wherein the current path point storage set forms the current path; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance.
3. The method according to claim 1, wherein the step of determining whether the current waypoint is on the historical path in S04 includes the step of determining whether a path at a time on the current waypoint and the historical path are the same path in S41, and if so, calculating Index values [ Index-a, Index + b ] in the current waypoint and the historical path one by one]Distance D of the historical path points1Whether or notCalculating the distances between the current path point and all historical path points in the historical path one by one to be D1; s42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting an Index value Index of the current path point on the historical path, otherwise, determining that the current path point is not on the historical path.
4. The method according to claim 3, wherein in step S41, determining whether the current route point last time route and the historical route are the same route, specifically comprises determining whether a plurality of consecutive route points on the current route from the current route point last time route point are on the historical route, if the plurality of consecutive route points are on the historical route, determining that the current route point last time route and the historical route are the same route, otherwise, determining that the current route point last time route and the historical route are different routes.
5. The path identification method device under the engineering transportation environment is characterized by comprising the following steps of,
the acquisition module is used for acquiring a current path point, a current path and a historical path;
the first judging module is connected with the acquiring module and used for judging whether the current path point is on the historical path or not;
and the second judging module is connected with the first judging module and used for judging whether a plurality of continuous path points on the current path from the current path point are on the historical path or not after the first judging module judges that the current path point is on the historical path, if the plurality of continuous path points are on the historical path, the current path and the historical path are judged to be the same path, and if not, the current path and the historical path are judged to be different paths.
6. Such as rightThe apparatus for recognizing a route under an engineering transportation environment as claimed in claim 1, further comprising a storage module connected to the acquiring module for storing the vehicle running speed V>=V1And the distance D between the current path point and the last storage path point0>=L1Then, storing the current path point, wherein the current path point storage set forms the current path; when the vehicle is positioned at the starting point of the driving path, assigning the current path to the historical path, wherein the current path is V1Preset running speed, L1Is a first predetermined distance.
7. The apparatus for identifying a route under an engineering transportation environment according to claim 1, wherein the determining, in the first determining module, whether the current waypoint is on the historical route specifically includes, S41, determining whether a route at a time on the current waypoint and the historical route are the same route, and if so, calculating Index values [ Index-a, Index + b ] of the current waypoint and the historical route one by one]Distance D of the historical path points1Otherwise, calculating the distances between the current path point and all historical path points in the historical path one by one to be D1; s42, judgment D1Whether or not less than or equal to second preset distance L2If so, determining that the current path point is on the historical path, and simultaneously outputting an Index value Index of the current path point on the historical path, otherwise, determining that the current path point is not on the historical path.
8. The apparatus for identifying a route under a construction transportation environment as claimed in claim 7, wherein in S41, the determining whether the route at the previous time of the current route point is the same as the historical route includes determining whether a plurality of consecutive route points on the current route from the previous route point of the current route point are on the historical route, and if the plurality of consecutive route points are on the historical route, determining that the route at the previous time of the current route point is the same as the historical route, otherwise, determining that the route at the previous time of the current route point is different from the historical route.
9. An electronic device, comprising: at least one processor, and a memory communicatively coupled to the at least one processor, wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the method of any of claims 1-4.
10. Storage medium on which a computer program is stored which, when being executed by a processor, carries out the method of any one of claims 1 to 4.
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