CN114253265B - On-time arrival probability maximum path planning algorithm and system based on fourth-order moment - Google Patents
On-time arrival probability maximum path planning algorithm and system based on fourth-order moment Download PDFInfo
- Publication number
- CN114253265B CN114253265B CN202111553773.9A CN202111553773A CN114253265B CN 114253265 B CN114253265 B CN 114253265B CN 202111553773 A CN202111553773 A CN 202111553773A CN 114253265 B CN114253265 B CN 114253265B
- Authority
- CN
- China
- Prior art keywords
- time
- strategy
- moment
- node
- upper bound
- 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
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 44
- 238000004364 calculation method Methods 0.000 claims abstract description 13
- 238000006243 chemical reaction Methods 0.000 claims abstract description 11
- 239000007788 liquid Substances 0.000 claims description 4
- 238000000034 method Methods 0.000 claims description 4
- 238000004590 computer program Methods 0.000 claims description 3
- 238000007476 Maximum Likelihood Methods 0.000 claims 1
- 230000000694 effects Effects 0.000 abstract description 5
- 238000009826 distribution Methods 0.000 description 4
- 230000001788 irregular Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
-
- 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
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Landscapes
- Engineering & Computer Science (AREA)
- Aviation & Aerospace Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Navigation (AREA)
Abstract
The invention provides a time arrival probability maximum path planning algorithm and a system based on fourth-order moment, wherein the algorithm comprises the following steps: obtaining fourth-order moment of each path node in the strategy through a Belman equation; converting the obtained fourth-order moment to meet the calculation requirement of the probability upper bound of the node arrival in time; calculating the upper bound of the inequality obtained by conversion from the fourth moment; and selecting a strategy with the minimum untimely arrival probability upper bound as an optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies. As the road network becomes larger gradually, the time consumption of the algorithm increases linearly, while the time consumption of other algorithms increases exponentially; compared with the performance of other algorithms, the performance of the algorithm is better than that of other algorithms in terms of effect and time consumption.
Description
Technical Field
The invention relates to the technical field of intelligent traffic, in particular to a time arrival probability maximum path planning algorithm and system based on fourth-order moment.
Background
In the related application of the current intelligent traffic system, uncertainty caused by various weather conditions, vehicle faults, even natural disasters and the like is quite common, and finding the shortest path under the uncertainty has become a common research direction. However, finding the shortest path algorithm does not meet the needs of all users, such as users who catch up with the aircraft, want to take a most reliable path with the highest probability of on-time arrival.
The simplest goal to solve this problem is to find a shortest time path, which has been applied in large-scale road networks by many efficient algorithms, such as a dynamic planning algorithm that recursively updates the value of the time each node reaches the end point based on previously obtained estimates, until convergence, which requires as input raw road network data, which typically contains travel time, variance of each road segment and assumptions that satisfy various distributions, but which involves convolution calculations, is computationally intensive, and requires complete travel time distribution as input, with poor practical performance on the road network.
Disclosure of Invention
The invention aims to provide a fourth-order moment-based on-time arrival probability maximum path planning algorithm and a system, and aims to solve the problems pointed out in the background art, wherein the algorithm is more excellent in performance than other algorithms in terms of effect and time consumption.
The embodiment of the invention is realized by the following technical scheme: the on-time arrival probability maximum path planning algorithm based on the fourth moment comprises the following steps:
s1, obtaining fourth-order moment of each path node in a strategy through a Belman equation;
s2, converting the obtained fourth-order moment to meet the calculation requirement that the node does not arrive at the upper bound of the probability on time;
s3, calculating the upper bound of the inequality obtained by conversion by fourth-order moment;
s4, selecting a strategy with the minimum untimely arrival probability upper bound as an optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies.
Further, step S1 includes:
deducing a recursion relation of a node i and a node j in the extended Belman equation, wherein the node j is the next node of the node i in the strategy, and obtaining the following expression:
in the above, c ij Lines representing paths ijTravel time, G π (j) Representing the travel time from node j to the end point in policy pi according toTo->And recursively updating the time of each node reaching the end point until the fourth moment converges.
Further, step S2 includes:
according to inequalityConverting the obtained fourth-order moment to obtain the following expression:
in the above formula, o represents a starting point, and x is an upper bound. .
Further, step S4 includes:
changing the path of the initial strategy pi to obtain a strategy pi ', comparing the initial strategy pi with the non-time arrival probability upper bound of the strategy pi', and selecting the strategy with small non-time arrival probability upper bound to change the path to obtain a new strategy pi * And selecting a strategy with the minimum probability upper bound of arrival in time as an optimal strategy until all paths are traversed.
The invention also provides a time arrival probability maximum path planning system based on fourth-order moment, which is applied to the algorithm, and comprises the following steps:
the extended Belman equation module is used for obtaining the fourth-order moment of each path node in the strategy through the Belman equation;
the conversion module is used for converting the obtained fourth-order moment so as to meet the calculation requirement of the probability upper bound of the node arrival in time;
the fourth-order moment calculation module is used for calculating the upper bound of the inequality obtained by conversion;
and the strategy updating module is used for selecting the strategy with the minimum untimely arrival probability upper bound as the optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies.
The invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor implements an algorithm as described above.
The technical scheme of the embodiment of the invention has at least the following advantages and beneficial effects: as the road network becomes larger gradually, the time consumption of the algorithm increases linearly, while the time consumption of other algorithms increases exponentially; compared with the performance of other algorithms, the performance of the algorithm is better than that of other algorithms in terms of effect and time consumption.
Drawings
Fig. 1 is a flow chart of a path planning algorithm provided in embodiment 1 of the present invention;
fig. 2 is a logic block diagram of a path planning system according to embodiment 1 of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Example 1
The applicant has found that the dynamic programming algorithm is currently applied in large-scale road networks by a number of efficient algorithms, which recursively update the value of the time for each node to reach the end point according to the previously obtained estimated value until convergence to find a shortest time path, the algorithm needs to take as input the original road network data, which generally contains the travel time, variance of each road segment and assumptions satisfying various distributions, but the dynamic programming method involves convolution calculation, is very computationally intensive, requires complete travel time distribution as input, and has poor practical performance on the road network. Based on the above, the embodiment of the invention provides a time arrival probability maximum path planning algorithm based on fourth-order moment, and the algorithm has better performance compared with other algorithms in terms of effect and time consumption. The method specifically comprises the following steps:
s1, obtaining fourth-order moment of each path node in a strategy through a Belman equation; in the step, a recursion relation of a node i and a node j in an extended bellman equation is deduced, wherein the node j is the next node of the node i in the strategy, and the following expression is obtained:
in the above, c ij Represents the travel time of the route ij, G π (j) Lines representing nodes j to end point in policy piTravel time according toTo->And recursively updating the time of each node reaching the end point until the fourth moment converges.
After the fourth-order moment is obtained, further executing the step S2, and converting the obtained fourth-order moment; in the present embodiment, the inequality required to be used in step S3 is in the form ofIn order to meet the requirement of inequality requirement, the obtained fourth-order moment is converted to obtain the following expression:
in the above formula, o represents a starting point,respectively representing the first moment, the second moment, the third moment and the fourth moment of the starting point o.
After the fourth moment is converted into the inequality required by calculation, further executing step S3, and calculating the upper bound of the inequality obtained by conversion from the fourth moment; the embodiment shows five upper bound calculation methods of the arrival probability without time under different conditions, which are specifically as follows:
case 1: when M 1 (Z) =0 andin the time-course of which the first and second contact surfaces,
case 2: when M 1 (Z) =0 andin the time-course of which the first and second contact surfaces,
case 3: at the position ofOn the premise of (1) when M 1 (Z)<At the time of 0, the temperature of the liquid,
when M 1 (Z)>At the time of 0, the temperature of the liquid,
case 4: when (when)And->In the time-course of which the first and second contact surfaces,
in the above-mentioned method, the step of,
v satisfies: -M 1 (Z)V 3 +3M 2 (Z)V 2 -2M 4 (Z)＝0
Case 5: when (when)And->In the time-course of which the first and second contact surfaces,
after the upper bound of the irregular arrival probability is calculated, step S4 is further executed, and the policy with the smallest irregular arrival probability upper bound is selected as the optimal policy by comparing irregular arrival probability upper bounds of different path planning policies. In this embodiment, step S4 specifically includes: modifying the path of the initial strategy pi to obtain a strategy pi ', and enabling the non-time arrival probability of the initial strategy pi and the strategy pi' to reach the upper limit g of the probability π ,g π′ Comparing, selecting a strategy with small upper bound of non-on-time arrival probability to change the path to obtain a new strategy pi * And selecting a strategy with the minimum probability upper bound of arrival in time as an optimal strategy until all paths are traversed.
Referring to fig. 2, the embodiment of the present invention further provides a fourth-order moment-based maximum probability of arrival on time path planning system, which is applied to the algorithm described above, and includes:
the extended Belman equation module is used for obtaining the fourth-order moment of each path node in the strategy through the Belman equation;
the conversion module is used for converting the obtained fourth-order moment so as to meet the calculation requirement of the probability upper bound of the node arrival in time;
the fourth-order moment calculation module is used for calculating the upper bound of the inequality obtained by conversion;
and the strategy updating module is used for selecting the strategy with the minimum untimely arrival probability upper bound as the optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies.
Embodiments of the present invention also provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements an algorithm as described above.
In summary, the technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects: as the road network becomes larger gradually, the time consumption of the algorithm increases linearly, while the time consumption of other algorithms increases exponentially; compared with the performance of other algorithms, the performance of the algorithm is better than that of other algorithms in terms of effect and time consumption.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The on-time arrival probability maximum path planning algorithm based on the fourth moment is characterized by comprising the following steps of:
s1, obtaining a fourth-order moment of each path node in a strategy through a Belman equation, wherein the fourth-order moment is a fourth-order center distance of a random variable, and the random variable is the driving time from each path node to an end point in the strategy;
s2, based on inequalityConverting the obtained fourth moment toThe calculation requirement of the probability upper bound of the node arrival time is met;
s3, calculating the upper bound of the inequality obtained by conversion by using fourth-order moment, wherein the upper bound comprises the following conditions:
case 1: when M 1 (Z) =0 andin the time-course of which the first and second contact surfaces,
case 2: when M 1 (Z) =0 andin the time-course of which the first and second contact surfaces,
case 3: at the position ofOn the premise of (1) when M 1 (Z)<At the time of 0, the temperature of the liquid,
when M 1 (Z)>At the time of 0, the temperature of the liquid,
case 4: when (when)And->In the time-course of which the first and second contact surfaces,
in the above-mentioned method, the step of,
v satisfies: -M 1 (Z)V 3 +3M 2 (Z)V 2 -2M 4 (Z)＝0
Case 5: when (when)And->In the time-course of which the first and second contact surfaces,
in the above, M 1 (Z) represents a first moment-transformed form, M 2 (Z) represents a second moment-transformed form, M 4 (Z) represents a fourth-order moment conversion form, o represents a starting point, x is an upper bound, G π (o) represents the travel time from the start point o to the end point in the strategy pi, T represents a specific time threshold as a random variable of the inequality;
s4, selecting a strategy with the minimum untimely arrival probability upper bound as an optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies.
2. The fourth order moment based on-time arrival probability maximum path planning algorithm according to claim 1, wherein step S1 comprises:
deducing a recursion relation of a node i and a node j in the extended Belman equation, wherein the node j is the next node of the node i in the strategy, and obtaining the following expression:
in the above, c ij Represents the travel time of the route ij, G π (j) Represents the travel time of node j to the endpoint in policy pi,and +.>Respectively representing the first moment, the second moment, the third moment and the fourth moment of the node i in the strategy pi, ++>And +.>Respectively representing the first, second, third and fourth moments of the path ij according to +.>To->And recursively updating the time of each node reaching the end point until the fourth moment converges.
3. The fourth order moment based on-time arrival probability maximum path planning algorithm according to claim 2, wherein step S2 comprises:
according to inequalityConverting the obtained fourth-order moment to obtain the following expression:
in the above, M 3 (Z) represents a converted form of third-order moment.
4. The fourth order moment based on-time arrival probability maximum path planning algorithm as set forth in claim 3, wherein step S4 comprises:
changing the path of the initial strategy pi to obtain a strategy pi', and obtaining the non-time arrival probability of the initial strategy pi and the strategy piComparing the bounds, selecting a strategy with small non-on-time arrival probability upper bound to change the path to obtain a new strategy pi * And selecting a strategy with the minimum probability upper bound of arrival in time as an optimal strategy until all paths are traversed.
5. A fourth order moment based maximum likelihood arrival on time path planning system, applied to an algorithm as claimed in any one of claims 1 to 4, comprising:
the extended Belman equation module is used for obtaining the fourth-order moment of each path node in the strategy through the Belman equation;
the conversion module is used for converting the obtained fourth-order moment so as to meet the calculation requirement of the probability upper bound of the node arrival in time;
the fourth-order moment calculation module is used for calculating the upper bound of the inequality obtained by conversion;
and the strategy updating module is used for selecting the strategy with the minimum untimely arrival probability upper bound as the optimal strategy by comparing untimely arrival probability upper bound of different path planning strategies.
6. A computer readable storage medium having stored thereon a computer program, which when executed by a processor implements an algorithm according to any of claims 1 to 4.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111553773.9A CN114253265B (en) | 2021-12-17 | 2021-12-17 | On-time arrival probability maximum path planning algorithm and system based on fourth-order moment |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111553773.9A CN114253265B (en) | 2021-12-17 | 2021-12-17 | On-time arrival probability maximum path planning algorithm and system based on fourth-order moment |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114253265A CN114253265A (en) | 2022-03-29 |
| CN114253265B true CN114253265B (en) | 2023-10-20 |
Family
ID=80792834
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111553773.9A Active CN114253265B (en) | 2021-12-17 | 2021-12-17 | On-time arrival probability maximum path planning algorithm and system based on fourth-order moment |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114253265B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115494844B (en) * | 2022-09-26 | 2024-06-28 | 成都朴为科技有限公司 | Multi-robot searching method and system |
| CN115290098B (en) * | 2022-09-30 | 2022-12-23 | 成都朴为科技有限公司 | Robot positioning method and system based on variable step length |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101420304B1 (en) * | 2013-09-26 | 2014-07-17 | 주식회사 피도텍 | Method for reliability analysis |
| CN108562301A (en) * | 2018-05-21 | 2018-09-21 | 北京石油化工学院 | A kind of method and device for planning of driving path |
| WO2019148645A1 (en) * | 2018-02-01 | 2019-08-08 | 苏州大学张家港工业技术研究院 | Partially observable markov decision process-based optimal robot path planning method |
| CN110633850A (en) * | 2019-09-11 | 2019-12-31 | 中电科新型智慧城市研究院有限公司 | Optimal path planning algorithm for trip time reliability |
| CN111026784A (en) * | 2019-11-13 | 2020-04-17 | 浙江大学 | Uncertain data stream probability summation threshold query method |
| CN113515127A (en) * | 2021-07-23 | 2021-10-19 | 华北电力大学（保定） | Mobile robot path planning method and system |
| CN113537628A (en) * | 2021-08-04 | 2021-10-22 | 郭宏亮 | General reliable shortest path algorithm based on distributed reinforcement learning |
| CN113741484A (en) * | 2021-09-30 | 2021-12-03 | 暨南大学 | Path planning method, system and medium based on probability model |
-
2021
- 2021-12-17 CN CN202111553773.9A patent/CN114253265B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101420304B1 (en) * | 2013-09-26 | 2014-07-17 | 주식회사 피도텍 | Method for reliability analysis |
| WO2019148645A1 (en) * | 2018-02-01 | 2019-08-08 | 苏州大学张家港工业技术研究院 | Partially observable markov decision process-based optimal robot path planning method |
| CN108562301A (en) * | 2018-05-21 | 2018-09-21 | 北京石油化工学院 | A kind of method and device for planning of driving path |
| CN110633850A (en) * | 2019-09-11 | 2019-12-31 | 中电科新型智慧城市研究院有限公司 | Optimal path planning algorithm for trip time reliability |
| CN111026784A (en) * | 2019-11-13 | 2020-04-17 | 浙江大学 | Uncertain data stream probability summation threshold query method |
| CN113515127A (en) * | 2021-07-23 | 2021-10-19 | 华北电力大学（保定） | Mobile robot path planning method and system |
| CN113537628A (en) * | 2021-08-04 | 2021-10-22 | 郭宏亮 | General reliable shortest path algorithm based on distributed reinforcement learning |
| CN113741484A (en) * | 2021-09-30 | 2021-12-03 | 暨南大学 | Path planning method, system and medium based on probability model |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114253265A (en) | 2022-03-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN114253265B (en) | On-time arrival probability maximum path planning algorithm and system based on fourth-order moment | |
| CN112180734B (en) | Multi-agent consistency method based on distributed adaptive event triggering | |
| CN111770019B (en) | Q-learning optical network-on-chip self-adaptive route planning method based on Dijkstra algorithm | |
| CN110601748B (en) | Multi-state space information network topology generation optimization algorithm | |
| CN110601973B (en) | Route planning method, system, server and storage medium | |
| CN113110039B (en) | Finite time distributed aggregation optimization method of multi-agent system | |
| CN113268083B (en) | Multi-unmanned aerial vehicle system formation tracking control method based on dynamic event triggering | |
| CN116192760B (en) | Traffic shaping method and device for space terahertz communication network | |
| CN114371617A (en) | Pulse control-based grouping consistency control method of multi-agent system with switching topological structure | |
| CN112484733B (en) | Reinforced learning indoor navigation method based on topological graph | |
| CN111523669A (en) | Knowledge graph meta-information-based least-order relation model training method | |
| CN114186410A (en) | Traffic shortest reliable path method driven by random GIS network | |
| CN101662489A (en) | Method, device and system for discovering semantic Web service | |
| Wang et al. | Dynamic Routing Algorithm with Q-learning for Internet of things with Delayed Estimator | |
| CN113537628B (en) | Universal reliable shortest path method based on distributed reinforcement learning | |
| CN115759370A (en) | Mapping operation method based on MADDPG algorithm | |
| CN111369052B (en) | Simplified road network KSP optimization algorithm | |
| CN114697221B (en) | Reliability mapping algorithm based on snapshot tree model in space-earth integrated network | |
| CN111262739B (en) | Distributed self-adaptive local diffusion control method under event-triggered communication | |
| CN114244854B (en) | Data center data backup method and system based on reinforcement learning | |
| CN116149175A (en) | Design method of dynamic event driven consistency protocol under switching topology | |
| CN113918319A (en) | Topology segmentation graph neural network training mechanism based on breadth-first segmentation | |
| CN112819048A (en) | Distributed community detection method for inter-satellite dynamic network | |
| CN117857429A (en) | Routing path selection method based on approximate estimation | |
| CN116647455A (en) | Virtual network mapping method based on deep reinforcement learning |
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 | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |