Multi-fleet cooperative path planning method for large-scale road network

Abstract

The embodiment of the invention provides a multi-fleet cooperative path planning method for a large-scale road network, and belongs to the technical field of data processing, and the method specifically comprises the steps: designing a target function of multi-fleet cooperative path planning; constructing constraint conditions of multi-motorcade collaborative path planning; designing a motorcade path planning algorithm, and performing global path planning on the plurality of motorcades; comparing and analyzing the path planning scheme of each motorcade, detecting whether space-time conflicts exist among different motorcades by using a space-time conflict detection algorithm, and analyzing the types, space data and time windows of the space-time conflicts among multiple motorcades; setting a motorcade priority rule, and analyzing the comprehensive priority of a plurality of motorcades according to the space-time conflict condition among the motorcades; and selecting a space-time conflict resolution strategy, and comparing the priority of the motorcade to perform space-time conflict resolution on path intersection space-time conflicts, homodromous intersection path space-time conflicts and reverse intersection path space-time conflicts. Through the scheme of the invention, the planning efficiency and adaptability are improved.

Description

Technical Field

[0001] The disclosed embodiments relate to the field of data processing technology, and in particular to a multi-vehicle collaborative path planning method for large-scale road networks. Background Art

[0002] In areas such as autonomous driving and logistics, platooning is a promising approach to reducing uncertainty and danger in road traffic. By platooning vehicles with similar origins and destinations and then implementing unified route planning for the platoon, energy consumption can be reduced, while also minimizing the risk of traffic accidents, ultimately achieving efficient, energy-efficient, and safe travel.

[0003] Currently, there is no research on conflict detection and conflict resolution in multi-vehicle collaborative path planning. Existing research mainly focuses on path planning for single vehicles.

[0004] It can be seen that there is an urgent need for a multi-vehicle collaborative path planning method for large-scale road networks that can realize multi-vehicle collaborative path planning and improve the overall traffic capacity of the road traffic network. Summary of the Invention

[0005] In view of this, the embodiments of the present disclosure provide a multi-vehicle collaborative path planning method for large-scale road networks, which at least partially solves the problems of poor planning efficiency and adaptability in the existing technology.

[0006] The present disclosure provides a multi-vehicle collaborative path planning method for a large-scale road network, including:

[0007] Step 1: Design the objective function of the multi-vehicle collaborative path planning mathematical model;

[0008] Step 2: Construct the constraints of the multi-vehicle collaborative path planning mathematical model;

[0009] Step 3: Design a fleet path planning algorithm, perform global path planning for multiple fleets, and obtain a path planning solution;

[0010] Step 4: Compare and analyze the path planning solutions of each fleet, use the spatiotemporal conflict detection algorithm to detect whether there are spatiotemporal conflicts between different fleets, and analyze the type, spatial data, and time window of spatiotemporal conflicts between multiple fleets;

[0011] Step 5: Set the fleet priority rules and analyze the comprehensive priorities of multiple fleets based on the temporal and spatial conflicts between fleets;

[0012] Step 6: Select a spatiotemporal conflict resolution strategy and resolve spatiotemporal conflicts at path intersections, same-direction intersection paths, and opposite-direction intersection paths by comparing the priorities of the fleets.

[0013] According to a specific implementation manner of an embodiment of the present disclosure, step 1 specifically includes:

[0014] Taking the minimum sum of the path planning scheme distances of multiple fleets as the target requirement, the shortest distance objective functions of all individual fleets are weighted and summed to construct the objective function of the multi-fleet collaborative path planning mathematical model

[0015]

[0016] where p k is the priority of fleet k, that is, the weight of fleet k in the objective function, f k is the shortest distance objective function of an individual fleet, d ij is the length of section (i, j), PV is the fleet set, x kij ∈ {0, 1}, is a decision variable. When fleet k chooses to pass through path (i, j), x kij = 1, otherwise x ij = 0, where i ∈ V, j ∈ V, i ≠ j, k ∈ PV.

[0017] According to a specific implementation manner of an embodiment of the present disclosure, the constraint conditions include single-fleet path constraints, multi-fleet spatio-temporal conflict constraints, and fleet time window calculation constraints.

[0018] According to a specific implementation manner of an embodiment of the present disclosure, the expression of the multi-fleet spatio-temporal conflict constraint is

[0019]

[0020] where ττ ki is the time when fleet k arrives at node i, d ij is the length of section (i, j), v k is the driving speed of fleet k, l k is the queue length of fleet k, y klij ∈ {0, 1}, is an auxiliary variable. When fleet k passes through path (i, j) before fleet l, y klij = 1, otherwise y klij = 0, where i, j ∈ V, i ≠ j, k, l ∈ PV, z klij ∈ {0, 1}, is an auxiliary variable. When both fleet k and fleet l choose to pass through path (i, j), z klij = 1, otherwise z klij = 0, where i, j ∈ V, i ≠ j, k, l ∈ PV;

[0021] Constraints 1 and 2 mean that for any two fleets k, l ∈ PV and any path (i, j) ∈ A, if both fleets choose to pass through this path (x kij = xlij =1), then the following conditions need to be met: the departure time of team k is less than the arrival time of team l or the departure time of team l is less than the arrival time of team k. Constraints 3, 4, and 5 are used to constrain the auxiliary variable z klij , which means that only when both teams choose to go through the path (i, j) klij =1, otherwise z klij =0,z klij Indicates that constraints 1 and 2 are considered only when both teams choose to go through this path. Constraint 6 is used to constrain the auxiliary variable y. klij , indicating z klij =1 when y klij It can be freely taken, otherwise y klij =0,y klij It means that only one of constraints 1 and 2 needs to be satisfied;

[0022] The expression of the fleet time window calculation constraint is:

[0023]

[0024] Among them, M is a sufficiently large constant, τ k is the departure time of fleet k. Constraint 1 defines the departure time of any fleet k∈PV, which is the initial condition for the fleet time window calculation. Constraint 2 means that for any fleet k∈PV, if it chooses to pass through the path (i, j), the time passing through the node is obtained by speed and distance. Otherwise, this constraint does not need to be considered.

[0025] According to a specific implementation of the embodiment of the present disclosure, step 3 specifically includes:

[0026] Step 3.1: pre-process the intermediate nodes and end nodes of the road segments in the original road network G to obtain a new road network G';

[0027] Step 3.2, calculate the importance of all nodes in the new road network G', select important nodes and expand nodes to form the regional road network Z i ;

[0028] Step 3.3, record all regional road networks Z i The shortest paths between the main nodes of adjacent areas are found and stored in advance through the path search algorithm to establish a new contraction road network G";

[0029] Step 3.4: Find the path planning starting point s of team k based on the node correspondence of the road network G→G'→G" k and the end point t k The corresponding node s k ” and t k", based on the contracted road network graph G", use the Dijkstra algorithm to perform path search to obtain the initial shortest path path in the contracted road network G" k ″;

[0030] Step 3.5, based on the correspondence relationship of the road network G" → G' → G, perform path unpacking, and restore the initial shortest path path k ″ to the shortest path path in the original road network G k ;

[0031] Step 3.6, re-perform the shortest path search within each regional road network Z i and check and adjust path k to obtain the path planning scheme for fleet k

[0032] where u k1 = s k , u ki is the i-th node in Path k , and m k is the total number of nodes passed by the path planning scheme;

[0033] Step 3.7, calculate the time window of the path planning scheme of the fleet according to the fleet length, fleet speed, and departure time. Let the time for fleet k to reach node u ki be ττ ki , the fleet length be l k , the fleet speed be v k , calculate the time for fleet k to pass through and leave node u ki , and establish a time window set for the path planning scheme of fleet k accordingly. Among them, the time for fleet k to leave node u ki is:

[0034]

[0035] The time window for fleet k to pass through node u ki is:

[0036]

[0037] The time window set for the path planning scheme of fleet k is:

[0038]

[0039] According to a specific implementation manner of the embodiment of the present disclosure, the step 4 specifically includes:

[0040] Step 4.1, according to the spatial topological relationship and movement direction of the conflict, set the spatio-temporal conflict type Conflict_type of the multi-fleet pathki Including path intersection time and space conflict NC, same-direction cross-path time and space conflict SEC and reverse cross-path time and space conflict REC, namely Conflict_type ki ={NC,SEC,REC};

[0041] Step 4.2: Get the path planning solution Path for all fleets k k , compare the path planning solutions of different fleets k Whether there is a point or path overlap in space and its spatial data of spatiotemporal conflict, when the path planning scheme of the fleet x and y is Path x and Path y If there is an intersection, it is determined that there is a spatial conflict between the two fleets, and the conflict node set NCN of the two fleets is recorded. xy If the size of the conflict node set is 1 or there are no adjacent nodes in the set, the conflict type is determined to be NC. If there are adjacent nodes in the conflict node set, the continuous node paths of the two convoys are extracted. If the two convoys pass through the path in opposite directions, the conflict type is REC. If the two convoys pass through the path in the same direction, the conflict type is SEC.

[0042] Step 4.3, obtain the driving speed v of all fleet k k , queue length l k , path planning time window T k , detect the time window T of the convoy passing through the spatial conflict intersection or path k Overlap and analyze the time window data recording spatiotemporal conflicts. For spatial conflict intersections, compare the intersection u of the paths of convoys x and y. xi If there is overlap in the time window, it means that there is indeed a spatiotemporal conflict NC at the path intersection, and the time window conflict data NCT is recorded. xyi :

[0043] NCT xyi =[max(ττ xi ,ττ yi ),min(ττ xi ',ττ yi ')]

[0044] For the reverse cross-path time-space conflict, compare the paths REC of convoys x and y. xy If there is overlap in the time window, it means that there is indeed a reverse cross-path time-space conflict REC, and the reverse path time window conflict data RECT is recorded xyi :

[0045] RECT xyi =[max(ττ xi ,ττ yi),min(ττ xj ',ττ yj ')]

[0046] For the spatiotemporal conflict of the same-direction cross-path, compare the paths SEC of convoys x and y. xy If there is overlap, it means that there is indeed a same-direction cross-path time-space conflict SEC. The time-space conflict time window is determined according to the speed of the convoy. When the speed of the rear convoy is slower than that of the front convoy, the convoy follows the vehicle and records the same-direction path time window conflict data SECT. xyi :

[0047] SECT xyi =[max(ττ xi ,ττ yi ),min(ττ xi ',ττ yi ')]

[0048] When the rear convoy is faster than the front convoy, it is necessary to wait until the front convoy completely leaves the path before driving again. At this time, the same-direction path time window conflict data SECT is recorded. xyi :

[0049] SECT xyi =[max(ττ xi ,ττ yi ),min(ττ xj ',ττ yj '].

[0050] According to a specific implementation of the embodiment of the present disclosure, step 5 specifically includes:

[0051] Step 5.1: Calculate the static priority sp based on the fleet's own attributes k , wherein the attributes of the fleet itself include the urgency of the fleet's driving mission, the importance of the fleet and special attributes;

[0052] Step 5.2: Dynamically update the dynamic priority dp based on the actual driving situation of the fleet ki ;

[0053] Step 5.3, combined with static priority sp k and dynamic priority dp ki Calculate the overall priority p of the fleet ki

[0054] p ki =sp k +dp ki .

[0055] Step 5.4, when there is a time-space conflict between the fleets, let the comprehensive priority p kiThe highest fleet follows the original path planning scheme Path k Drive and let other teams change their path planning k or time window T k .

[0056] According to a specific implementation of the embodiment of the present disclosure, step 6 specifically includes:

[0057] Step 6.1: When the path planning solutions of two or more fleets have a time-space conflict, first perform a time-space conflict detection, and then let the comprehensive priority p ki The convoy with relatively low k stops and waits at the time-space conflict path or intersection until the conflict is resolved before continuing;

[0058] Step 6.2: When the path planning schemes of two or more fleets are about to have a spatiotemporal conflict, perform spatiotemporal conflict detection and let the comprehensive priority p ki The relatively low-speed convoy re-plans a new path planning scheme that bypasses the time-space conflict intersection or path and continues to drive according to the new path planning scheme.

[0059] The multi-vehicle collaborative path planning scheme for large-scale road networks in the disclosed embodiment includes: step 1, designing an objective function of a multi-vehicle collaborative path planning mathematical model; step 2, constructing constraint conditions for the multi-vehicle collaborative path planning mathematical model; step 3, designing a fleet path planning algorithm, performing global path planning for multiple fleets separately, and obtaining a path planning scheme; step 4, comparing and analyzing the path planning scheme of each fleet, using a spatiotemporal conflict detection algorithm to detect whether there is spatiotemporal conflict between different fleets, and analyzing the type, spatial data, and time window of spatiotemporal conflicts between multiple fleets; step 5, setting fleet priority rules, and analyzing the comprehensive priority of multiple fleets based on the spatiotemporal conflict situations between fleets; step 6, selecting a spatiotemporal conflict resolution strategy, and comparing the priorities of the fleets to resolve spatiotemporal conflicts at path intersections, spatiotemporal conflicts on same-direction intersection paths, and spatiotemporal conflicts on opposite-direction intersection paths.

[0060] The beneficial effects of the embodiments of the present disclosure are as follows: Through the solution of the present disclosure, an in-depth discussion is carried out on the research of the multi-fleet collaborative path planning method. The spatio-temporal conflict problems that may occur between multi-fleets are analyzed emphatically, and the effectiveness of relevant algorithms is verified through theoretical analysis and simulation experiments. In the context of multi-fleet collaborative path planning and dynamic adjustment, this study first detects the spatial conflicts and time conflicts between multi-fleets according to the path planning scheme, and then analyzes the types of spatio-temporal conflicts, spatial data and time window data. In addition, by setting the fleet priority rules and selecting appropriate spatio-temporal conflict resolution strategies, different types of spatio-temporal conflicts are effectively resolved and avoided, so as to ensure the safe driving of the fleets. The simulation experiments show that the proposed algorithm can successfully detect the spatio-temporal conflicts at intersections and the spatio-temporal conflicts of intersecting paths, and realizes the resolution of multi-fleet spatio-temporal conflicts through the waiting strategy and the replanning strategy. This achievement not only provides theoretical support for the collaborative operation of fleets, but also provides a new solution for the path planning problem in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present disclosure. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0062] Figure 1 It is a schematic flow chart of a multi-fleet collaborative path planning method for large-scale road networks provided by the embodiments of the present disclosure;

[0063] Figure 2 It is an algorithm framework diagram of a multi-fleet collaborative path planning method for large-scale road networks provided by the embodiments of the present disclosure;

[0064] Figure 3 It is a schematic diagram of a spatio-temporal conflict detection algorithm provided by the embodiments of the present disclosure;

[0065] Figure 4 It is a schematic diagram of a spatio-temporal conflict resolution method provided by the embodiments of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] The embodiments of the present disclosure will be described in detail below with reference to the drawings.

[0067] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand the other advantages and effects of the present disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present disclosure without creative efforts belong to the scope of protection of the present disclosure.

[0068] It should be noted that the following describes various aspects of the embodiments within the scope of the appended claims. It should be obvious that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present disclosure, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionality in addition to one or more of the aspects described herein.

[0069] It should also be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present disclosure in a schematic manner. The diagrams only show the components related to the present disclosure and are not drawn according to the number, shape, and size of the components in actual implementation. The type, quantity, and ratio of each component in its actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0070] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0071] The embodiments of the present disclosure provide a multi-fleet collaborative path planning method for large-scale road networks, and the method can be applied to the fleet path planning process in scenarios such as autonomous driving and logistics transportation.

[0072] See Figure 1 , which is a schematic flowchart of a multi-fleet collaborative path planning method for large-scale road networks provided by the embodiments of the present disclosure. As Figure 1 shown, the method mainly includes the following steps:

[0073] Step 1, design the objective function of the multi-fleet collaborative path planning mathematical model;

[0074] In specific implementation, a large-scale road network includes a large number of intersection nodes and directed line segments. For the convenience of description and research, the large-scale road network is represented as a directed graph G=(V, A), where V is the set of nodes in the road network, and A ={(i, j)|i, j ∈ V, i ≠ j} is the set of edges in the road network.

[0075] The study of multi-fleet collaborative path planning problem can be summarized as: in the road network graph G=(V, A), for multiple fleets with different lengths, different driving speeds, different departure times, and different priorities, plan the shortest-distance path planning schemes starting from s and ending at t respectively, while avoiding spatio-temporal conflicts between different fleets.

[0076] The multi-fleet collaborative path planning algorithm consists of three parts: First, based on the global road traffic network and fleet attributes (length, speed, priority, etc.), use the single-fleet path planning algorithm to generate the initial path planning schemes for each fleet, including information such as path node coordinates and node occupancy time windows; then, through the initial path planning schemes and time windows of all fleets, analyze the spatio-temporal trajectories, identify the path space overlap and time window conflicts between multiple fleets, and detect the spatio-temporal conflicts between multiple fleets; finally, combine the static and dynamic priorities of the fleets to formulate fleet scheduling and path spatio-temporal adjustment strategies to eliminate the spatio-temporal conflicts of multi-fleet collaboration and optimize the total system cost.

[0077] This study takes the fleet as the basic unit, and its attributes include the queue length l of the fleet k , driving speed v k , departure time τ k , priority weight p k etc. It is necessary to calculate the time window for each node passed by the fleet and adjust the path or time window of the fleet to avoid spatio-temporal conflicts between fleets. Compared with the single-vehicle path planning algorithm, the difference in multi-fleet collaborative path planning lies in the addition of spatio-temporal coupling constraints and conflict resolution mechanisms. The algorithm framework is as Figure 2 shown.

[0078] The objective function of the multi-fleet collaborative path planning mathematical model is as follows:

[0079] Construct the objective function for the requirement of the shortest distance of a single fleet:

[0080]

[0081] where k ∈ PV, this formula is for the shortest-distance objective of a single fleet k; d ij is the length of section (i, j); PV is the fleet set.

[0082] The problem of multi-fleet collaborative path planning aims to minimize the sum of the distances of the path planning schemes of multiple fleets. It is necessary to weighted sum the objective functions of all single fleets to construct the objective function of the multi-fleet collaborative path planning mathematical model:

[0083]

[0084] Among them, p k is the priority of fleet k and also the weight of fleet k in the objective function.

[0085] x kij ∈{0,1} is a decision variable. When fleet k chooses to pass through path (i,j), x kij =1; otherwise, x ij =0. Where i∈V, j∈V, i≠j, k∈PV.

[0086] Step 2, construct the constraint conditions of the multi-fleet collaborative path planning mathematical model;

[0087] In specific implementation, the constraint conditions of the multi-fleet collaborative path planning mathematical model include the following three parts: single-fleet path constraint, multi-fleet spatio-temporal conflict constraint, and fleet time window calculation constraint.

[0088] ① Single-fleet path constraint

[0089] For the path planning of single fleet k with the starting point s k and the ending point t k , there are the following constraints:

[0090]

[0091] Constraint 1 means that fleet k departs from the starting point s k only once, and constraint 2 means that fleet k does not return to the starting point s k ; constraint 3 means that fleet k does not leave from the ending point t k , and constraint 4 means that fleet k only arrives at the ending point t k once; constraints 5 and 6 mean that the number of times fleet k passes through any node in the road network graph does not exceed 1; constraint 7 means that for any node in the road network graph except the starting point and the ending point, the arrival times of fleet k are equal to the departure times.

[0092] ② Multi-fleet spatio-temporal conflict constraint

[0093] For the path planning of different single fleets k in PV, it is required that the path planning schemes of different fleets do not have simultaneous overlap in time and space in all paths in the road network graph. That is, for any path in the road network, the time windows for all fleets to pass through this path cannot overlap. Therefore, there are the following spatio-temporal conflict time window constraints:

[0094]

[0095] where ττ ki is the time when vehicle fleet k arrives at node i; d ij is the length of road section (i, j); v k is the driving speed of vehicle fleet k; l k is the queue length of vehicle fleet k. y klij ∈ {0, 1}, is an auxiliary variable. When vehicle fleet k passes through path (i, j) before vehicle fleet l, y klij = 1, otherwise y klij = 0. Where i, j ∈ V, i ≠ j, k, l ∈ PV. z klij ∈ {0, 1}, is an auxiliary variable. When both vehicle fleets k and l choose to pass through path (i, j), z klij = 1, otherwise z klij = 0. Where i, j ∈ V, i ≠ j, k, l ∈ PV.

[0096] Constraints 1 and 2 mean that for any two vehicle fleets k, l ∈ PV and any path (i, j) ∈ A, if both vehicle fleets choose to pass through this path (x kij = x lij = 1), then the condition needs to be satisfied: the departure time of vehicle fleet k is less than the arrival time of vehicle fleet l or the departure time of vehicle fleet l is less than the arrival time of vehicle fleet k. Constraints 3, 4, and 5 are to constrain the auxiliary variable z klij , indicating that z klij = 1 only when both vehicle fleets choose to pass through path (i, j), otherwise z klij = 0. Using z klij means that constraints 1 and 2 are only considered when both vehicle fleets choose to pass through this path. Constraint 6 is to constrain the auxiliary variable y klij , indicating that y klij can take free values only when z klij = 1, otherwise y klij = 0. Using y klij means that only one of constraints 1 and 2 needs to be satisfied.

[0097] ③ Vehicle fleet time window calculation constraints

[0098] For the path planning of any single vehicle fleet k in PV, it is necessary to calculate the time to reach all passing nodes based on the departure time. Therefore, there are the following vehicle fleet time window calculation constraints:

[0099]

[0100] where M is a sufficiently large constant; τ k is the departure time of vehicle fleet k.

[0101] Constraint 1 defines the departure time of any vehicle fleet k ∈ PV, which is the initial condition for calculating the time window of the vehicle fleet. Constraint 2 means that for any vehicle fleet k ∈ PV, if the selected path passes through (i, j), the time of the passing node is obtained from the speed and distance, otherwise this constraint does not need to be considered.

[0102] Step 3: Design a vehicle fleet path planning algorithm to perform global path planning for multiple vehicle fleets respectively to obtain a path planning scheme.

[0103] In specific implementation, global path planning is performed for multiple vehicle fleets respectively. The goal of the single-vehicle fleet path planning algorithm is to generate a globally optimal path for a single vehicle fleet, and calculate the time window of the path planning scheme of the vehicle fleet based on the vehicle fleet length, vehicle fleet speed, and departure time. The scenario discussed in this algorithm is an undirected graph, that is, all road sections are two-way roads. There are three different levels of road networks involved in the algorithm. G = (V, A) represents the original road network, G' = (V', A') represents the preprocessed road network, G'' = (V'', A'') represents the final contracted road network, and Z i represents the small regional road network after division. The basic steps of the single-vehicle fleet path planning algorithm include the following steps:

[0104] A1: Road network preprocessing: Process the intermediate nodes and road end nodes of the road sections in the original road network G. After preprocessing, a new road network G' is generated, which greatly reduces the scale of the road network.

[0105] A2: Road network zoning: Calculate the importance of all nodes in the road network G', select important nodes and expand the nodes to form an independent regional road network Z i .

[0106] A3: Key path pre-storage: Record all the main nodes of the regional road network Z i , and pre-find and store the shortest paths between the main nodes of adjacent regions through the path search algorithm to establish a new contracted road network G''.

[0107] A4: Path search: Find the path planning starting point s k and end point t k of the vehicle fleet k according to the node correspondence relationship of G → G' → G'', and use the dijkstra algorithm to perform path search based on the contracted road network graph G'' to obtain the initial shortest path path k ″ in the road network G''. k ″. k ″.

[0108] A5: Path unpacking: Based on the correspondence relationship of the road network graph G'' → G' → G, perform path unpacking to restore path k ″ to the shortest path path k in the original road network graph G.

[0109] A6: Route adjustment: In each area road network Z i Re-search the shortest path within the k Check and adjust to get the path planning solution for fleet k where u k1 =s k , u ki Path k The i-th node in m k The total number of nodes along the path planning scheme.

[0110] A7: Time window calculation: In addition to generating the global optimal path, the single-vehicle routing algorithm also needs to calculate the time window of the vehicle’s routing plan based on the vehicle’s length, vehicle speed, and departure time. ki The time is ττ ki , the length of the fleet is l k , the convoy speed is v k , calculate the leaving node u ki The time is:

[0111]

[0112] Car team k passes through node u ki The time window is:

[0113]

[0114] Establish a set of time windows for the routing plan of fleet k:

[0115]

[0116] Step 4: Compare and analyze the path planning solutions of each fleet, use the spatiotemporal conflict detection algorithm to detect whether there are spatiotemporal conflicts between different fleets, and analyze the type, spatial data, and time window of spatiotemporal conflicts between multiple fleets;

[0117] When implementing it specifically, Figure 3 As shown in the figure, we compare and analyze the path planning schemes of multiple fleets, use the spatiotemporal conflict detection algorithm to detect whether there are spatiotemporal conflicts between different fleets, and analyze the types, spatial data, and time window data of spatiotemporal conflicts between multiple fleets. The steps are as follows:

[0118] B1: Spatiotemporal conflict type analysis: Based on the spatial topological relationship and movement direction of the conflict, the spatiotemporal conflict type of multiple fleet paths is Confilct_type ki There are three types: Path intersection time-space conflict (NC), same-direction cross-path time-space conflict (SEC), and reverse cross-path time-space conflict (REC).ki = {NC, SEC, REC}。

[0119] Spatial-temporal conflict at path intersection means that multiple vehicle fleets have overlapping trajectories at the intersection node. The spatial feature is reflected in the path planning schemes Path k of different vehicle fleets coinciding at a certain node u ki in the road network, and the adjacent path points before the path intersection do not coincide; the temporal feature is reflected in the time windows TN ki of different vehicle fleets passing through the path intersection u ki having an overlap, that is, u ki will be occupied by multiple vehicle fleets simultaneously during a certain time period.

[0120] Reverse path conflict means the spatio-temporal conflict caused by multiple vehicle fleets occupying the path simultaneously when driving in opposite directions on the same road section. The spatial feature is reflected in the path planning schemes Path x and Path y coinciding at a certain path REC xy in the road network, and the two vehicle fleets are driving towards each other. The intersecting path can also be represented as multiple consecutive adjacent path nodes:

[0121] REC xy = {u xi ,…u xi …,u xj} x ∈ PV

[0122] The temporal feature is reflected in the time windows TE xy of different vehicle fleets passing through REC xi and TE yi having an overlap, that is, REC xy will be occupied by multiple vehicle fleets simultaneously during a certain time period.

[0123] Same-direction path conflict means the spatio-temporal conflict caused by multiple vehicle fleets occupying the path simultaneously when driving in the same direction on the same road section. The spatial feature is reflected in the path planning schemes Path x and Path y coinciding at a certain path SEC xy in the road network, and the two vehicle fleets are driving in the same direction. The intersecting path can also be represented as multiple consecutive adjacent path nodes.

[0124] SEC xy = {u xi ,…u xi …,u xj} x ∈ PV

[0125] The temporal feature is reflected in the time windows TE xy of different vehicle fleets passing through SEC xi and TEyi There is an overlap, i.e., SEC xy will be occupied by multiple vehicle fleets simultaneously during a certain time period.

[0126] B2: Spatial conflict detection: Obtain the path planning scheme Path of all vehicle fleets k k , and compare the Path of different vehicle fleets k to check if there are any coincidences of points or paths in space, and analyze and record the spatial data of spatio-temporal conflicts.

[0127] When the path planning schemes Path x and Path y of vehicle fleets x and y have an intersection, it indicates that there is a spatial conflict between the two vehicle fleets, and record the set of conflict nodes NCN xy . If the size of the set of conflict nodes is 1 or there are no adjacent nodes in the set, the conflict type is NC. If there are adjacent nodes in the set of conflict nodes, extract the continuous node paths of the two vehicle fleets; if the directions of the two vehicle fleets passing through this path are opposite, the conflict type is REC; if the directions of the two vehicle fleets passing through this path are the same, the conflict type is SEC.

[0128] B3: Temporal conflict detection: Obtain the driving speed v k , queue length l k , and path planning scheme time window T k of all vehicle fleets k, and detect whether the time windows T k when the vehicle fleets pass through the spatio-temporal conflict intersection or path overlap, and analyze and record the time window data of spatio-temporal conflicts.

[0129] For intersection spatial conflicts, compare the time windows when vehicle fleets x and y pass through the path intersection u xi . If there is an overlap, it indicates that there is indeed a spatio-temporal conflict NC. Record the time window conflict data NCT xyi :

[0130] NCT xyi = [max(ττ xi , ττ yi ), min(ττ xi ', ττ yi )]

[0131] For reverse path spatial conflicts, compare the time windows when vehicle fleets x and y pass through the path REC xy . If there is an overlap, it indicates that there is indeed a path spatio-temporal conflict REC. Record the time window conflict data RECT xyi :

[0132] RECT xyi = [max(ττ xi , ττ yi), min(ττ xj ', ττ yj )]

[0133] For the spatial and temporal conflicts of the same - direction paths, compare the time windows of the vehicle platoons x and y passing through the path SEC xy . If there is an overlap, it indicates that there is indeed a spatio - temporal conflict SEC in the path. Determine the spatio - temporal conflict time window based on the speed of the vehicle platoons. When the speed of the rear vehicle platoon is slower than that of the front vehicle platoon, the vehicle platoon can follow the vehicle in front. At this time, the same - direction path conflict is similar to the intersection conflict, and record the data of the same - direction path time - window conflict SEC Txyi :

[0134] SECT xyi = [max(ττ xi , ττ yi ), min(ττ xi ', ττ yi )]

[0135] When the speed of the rear vehicle platoon is faster than that of the front vehicle platoon, it needs to wait for the front vehicle platoon to completely leave the path before driving. At this time, it is similar to the analysis of the reverse - path conflict, and record the data of the same - direction path time - window conflict SECT xyi :

[0136] SECT xyi = [max(ττ xi , ττ yi ), min(ττ xj ', ττ yj [[ID=42'])].

[0137] Step 5, set the vehicle - platoon priority rules, and analyze the comprehensive priority of multiple vehicle platoons according to the spatio - temporal conflict situation among the vehicle platoons;

[0138] Specifically, when implementing, set the vehicle - platoon priority rules and analyze the comprehensive priority of each vehicle platoon when spatio - temporal conflicts occur. One of the good ways to resolve the spatio - temporal conflicts of multiple vehicle platoons is to set the comprehensive priority p of the vehicle platoon ki . When spatio - temporal conflicts occur between vehicle platoons, let the vehicle platoon with a higher comprehensive priority p ki travel according to the original path - planning scheme Path k , and let the vehicle platoon with a lower p ki change the path - planning scheme Path k or the time window T k . This is an easy - to - implement and easy - to - operate spatio - temporal conflict resolution idea. The key to this method lies in how to reasonably set the comprehensive priority p of the vehicle platoon ki . Design two priority indicators based on the actual traffic situation: static priority sp k and dynamic priority dp ki , and sum the two priority indicators to obtain the comprehensive priority p of the vehicle platoonki .

[0139] p ki = sp k + dp ki

[0140] Static priority sp k is the priority determined by the attributes of the vehicle fleet itself, and is determined according to the urgency of the driving tasks of the vehicle fleet, the importance of the vehicle fleet, and other special attributes. The static priority sp k is generated when the vehicle fleet is established and changes with the change of the vehicle fleet. The static priority is an absolute priority and is not affected by the spatio-temporal conflict situation, that is, the static priority sp of the same vehicle fleet at different spatio-temporal conflict intersection points and intersection paths k is the same. In actual situations, if the vehicle fleet has no urgent tasks, important vehicles, or other special attributes, the static priority of the vehicle fleet is assigned a value of 0 (sp k = 0); if the vehicle fleet has urgent tasks or special attributes, the static priority of the vehicle fleet is assigned a positive integer between 0 and 10 according to the urgency of the tasks (sp k = {1, 2,..., 10}).

[0141] Dynamic priority dp ki is a relative priority that is dynamically updated according to the actual driving situation of the vehicle fleet and changes with the change of spatio-temporal conflict points or edges. The vehicle fleet may have different dynamic priorities dp at each of its spatio-temporal conflict points u ki . ki . There are two dynamic priority measurement criteria. Choose one measurement criterion according to the actual situation to determine the dynamic priority of the vehicle fleet. In special cases, the two measurement criteria can also be used together.

[0142] The first measurement criterion (d_standard = 1) is the order in which the vehicle fleet arrives at the spatio-temporal conflict node or path. Compare the time windows TN ki of different vehicle fleets arriving at the spatio-temporal conflict intersection point or intersection path, and assign a high priority to the vehicle fleet that arrives at the conflict point first and a low priority to the vehicle fleet that arrives at the conflict point later.

[0143] The second measurement criterion (d_standard = 2) is the length of the time window for the vehicle fleet to pass through the spatio-temporal conflict node or path. Compare the time windows TN ki or TE ki of different vehicle fleets passing through the spatio-temporal conflict intersection point or intersection path, and assign a low priority to the vehicle fleet with a longer time window for passing through the conflict path and a high priority to the vehicle fleet with a shorter time window.

[0144] In actual situations, the static priority sp of the vehicle fleet k will be higher than the dynamic priority dp kiMore important. If a convoy has an important task, even if it has a lower dynamic priority in the time-space conflict evaluation, it should be allowed to go first to ensure that it follows the original planned path. Therefore, the dynamic priority of the convoy is assigned a decimal between 0 and 1 (dp ki ={0,0.1,0.2,…,0.9}). Different dynamic priorities are assigned in turn according to the relative dynamic priorities between conflicting convoys at the time-space conflict point or path: dp ki =0,0.1,0.2,0.3….

[0145] Step 6: Select a spatiotemporal conflict resolution strategy and resolve spatiotemporal conflicts at path intersections, same-direction intersection paths, and opposite-direction intersection paths by comparing the priorities of the fleets.

[0146] When implementing it specifically, Figure 4 As shown in the figure, a spatiotemporal conflict resolution strategy is selected to resolve the spatiotemporal conflicts at path intersections, the spatiotemporal conflicts of same-direction intersection paths, and the spatiotemporal conflicts of opposite-direction intersection paths. By adjusting the fleet's driving path or driving time window, possible spatiotemporal conflicts can be avoided.

[0147] There are many different conflict resolution strategies for path planning, each with its own unique advantages and disadvantages. In practical applications, the appropriate conflict resolution strategy must be selected based on factors such as the specific system requirements, the characteristics of the mobile entities, and environmental conditions, ultimately resulting in a rational and efficient multi-vehicle conflict resolution solution. The conflict resolution strategies used here are the waiting strategy and the local path replanning strategy.

[0148] The waiting strategy is a simple and effective conflict resolution method. When the path planning schemes of two or more fleets have a time-space conflict, the time-space conflict detection is performed first, and then the comprehensive priority p is used to determine the conflict. ki The convoy with low k stops and waits at the spatiotemporal conflict path or intersection until the conflict is resolved before continuing to drive. The advantage of the waiting strategy is that it is simple to implement and does not require complex calculation processes. It can ensure that convoys will not collide with each other when a conflict occurs, ensuring the safety of road traffic. The waiting strategy is suitable for road traffic network environments with a small number of convoys and low vehicle density. This will not cause more spatiotemporal conflicts and waiting time for the overall road traffic, and will not cause road traffic congestion. Due to the small number of convoys and low vehicle density, the trafficability of spatiotemporal conflict intersections and cross paths is better. At this time, it is only necessary to calculate the convoy waiting time window under different conflict types to enable the convoy to successfully and safely avoid spatiotemporal conflicts. The convoy waiting time window WT of the waiting strategy ki This discussion needs to be categorized by conflict type and fleet priority, calculated from the travel time window for each fleet at the spatiotemporal conflict intersection and path. The pseudocode for the spatiotemporal conflict resolution waiting strategy process is as follows.

[0149]

[0150]

[0151] The path replanning strategy is another effective conflict resolution method. When the path planning schemes of two or more vehicle fleets will have spatio-temporal conflicts, spatio-temporal conflict detection is carried out, and the comprehensive priority p ki The vehicle fleet with a low value re-plans a path planning scheme Path that bypasses the spatio-temporal conflict intersection or path k and continues to drive according to the new Path k . The advantage of the path replanning strategy is that it can bypass the conflict path, does not need to wait in place, and at the same time ensures the safety of road traffic. It is applicable to road traffic situations where there are few overlapping intersections in the path planning schemes between different vehicle fleets. Since there are few intersections in the path planning schemes between different vehicle fleets, at this time, only the vehicle fleet with a low comprehensive priority needs to be planned a new path scheme to enable the vehicle fleet to successfully and safely avoid spatio-temporal conflicts. Analyze all spatio-temporal conflicts in the original path scheme Path of the vehicle fleet in turn k record the conflict paths and conflict points that need to be avoided, update the temporary road network, and use the dijkstra algorithm to plan the new path scheme Path of the vehicle fleet under the path replanning strategy k . The pseudo-code of the spatio-temporal conflict resolution path replanning strategy process is as follows:

[0152]

[0153]

[0154] The multi-vehicle-fleet collaborative path planning method for large-scale road networks provided in this embodiment, in the context of multi-vehicle-fleet collaborative path planning, first detects the spatial conflicts and time conflicts between multiple vehicle fleets according to the path planning scheme, and then analyzes the types, spatial data, and time window data of the spatio-temporal conflicts. In addition, by setting vehicle fleet priority rules and selecting appropriate spatio-temporal conflict resolution strategies, different types of spatio-temporal conflicts are effectively resolved and avoided, thereby ensuring the safe driving of the vehicle fleet. The simulation experiment shows that the proposed algorithm can successfully detect the spatio-temporal conflicts at intersections and the spatio-temporal conflicts of intersecting paths, and realizes the resolution of multi-vehicle-fleet spatio-temporal conflicts through the waiting strategy and the replanning strategy. This achievement not only provides theoretical support for the collaborative operation of vehicle fleets, but also provides a new solution for the path planning problem in practical applications.

[0155] It should be understood that each part of the present disclosure can be implemented by hardware, software, firmware, or a combination thereof.

[0156] As described above, it is only the specific implementation manner of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present disclosure should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be subject to the protection scope of the claims.

Claims

1. A multi-fleet collaborative path planning method for large-scale road networks, characterized in that, include: Step 1: Design the objective function of the multi-vehicle collaborative path planning mathematical model; Step 2: Construct the constraints of the multi-vehicle collaborative path planning mathematical model; Step 3: Design a fleet path planning algorithm, perform global path planning for multiple fleets, and obtain a path planning solution; Step 4: Compare and analyze the path planning solutions of each fleet, use the spatiotemporal conflict detection algorithm to detect whether there are spatiotemporal conflicts between different fleets, and analyze the type, spatial data, and time window of spatiotemporal conflicts between multiple fleets; Step 5: Set the fleet priority rules and analyze the comprehensive priorities of multiple fleets based on the temporal and spatial conflicts between fleets; Step 6: Select a spatiotemporal conflict resolution strategy and resolve spatiotemporal conflicts at path intersections, same-direction intersection paths, and opposite-direction intersection paths by comparing the priorities of the fleets.

2. The method according to claim 1, characterized in that, The step 1 specifically includes: Taking the minimum sum of the path planning scheme distances of multiple fleets as the target requirement, the weighted sum of the shortest distance objective functions of all individual fleets is used to construct the objective function of the multi-fleet collaborative path planning mathematical model. Among them, p k is the priority of fleet k, that is, the weight of fleet k in the objective function, f k is the objective function of the shortest distance for a single fleet, d ij is the length of section (i, j), PV is the set of fleets, x kij ∈{0,1}, is a decision variable. When fleet k chooses to pass through path (i, j), x kij = 1, otherwise x ij = 0, where i ∈ V, j ∈ V, i ≠ j, k ∈ PV.

3. The method according to claim 2, wherein The constraints include single-vehicle path constraints, multi-vehicle spatiotemporal conflict constraints, and vehicle fleet time window calculation constraints.

4. The method according to claim 3, wherein The expression of the multi-vehicle spatiotemporal conflict constraint is: Among them, ττ ki is the time when fleet k arrives at node i, d ij is the length of section (i, j), v k is the driving speed of fleet k, l k is the queue length of fleet k, y klij ∈ {0, 1} is an auxiliary variable. When fleet k passes through path (i, j) before fleet l, y klij = 1, otherwise y klij = 0, where i, j ∈ V, i ≠ j, k, l ∈ PV, z klij ∈ {0, 1} is an auxiliary variable. When both fleet k and fleet l choose to pass through path (i, j), z klij = 1, otherwise z klij = 0, where i, j ∈ V, i ≠ j, k, l ∈ PV; Constraints 1 and 2 mean that for any two vehicle fleets k, l ∈ PV and any path (i, j) ∈ A, if both vehicle fleets choose to pass through this path (x kij = x lij = 1), then the condition needs to be satisfied: the departure time of vehicle fleet k is less than the arrival time of vehicle fleet l or the departure time of vehicle fleet l is less than the arrival time of vehicle fleet k. Constraints 3, 4, and 5 are used to constrain the auxiliary variable z klij , indicating that z klij = 1 only when both vehicle fleets choose to pass through the path (i, j), otherwise z klij = 0. z klij means that Constraints 1 and 2 are considered only when both vehicle fleets choose to pass through this path. Constraint 6 is used to constrain the auxiliary variable y klij , indicating that y klij can take free values only when z klij = 1, otherwise y klij = 0. y klij means that only one of Constraints 1 and 2 needs to be satisfied; The expression of the fleet time window calculation constraint is: where M is a sufficiently large constant, and τ k is the departure time of fleet k. Constraint 1 defines the departure time of any fleet k ∈ PV, which is the initial condition for calculating the time window of the fleet. Constraint 2 means that for any fleet k ∈ PV, if the selected path is (i, j), the time of the passing node is obtained from the speed and distance; otherwise, this constraint does not need to be considered.

5. The method according to claim 4, characterized in that The step 3 specifically includes: Step 3.1: pre-process the intermediate nodes and end nodes of the road segments in the original road network G to obtain a new road network G'; Step 3.2, calculate the importance degrees of all nodes in the new road network G', and select important nodes accordingly and expand the nodes to form the regional road network Z i ; Step 3.3, record all the main nodes of the regional road network Z i , and pre-find and store the shortest paths between the main nodes of adjacent regions through a path search algorithm to establish a new contracted road network G". Step 3.4, find the starting point s of the path planning of fleet k according to the node correspondence of the road network G → G' → G'' k and the end point t k corresponding nodes s k ” and t k ”, use the dijkstra algorithm to perform path search based on the contracted road network graph G'', and obtain the initial shortest path path in the contracted road network G'' k ”; Step 3.5, perform path unpacking based on the corresponding relationship of the road network G” → G' → G, and restore the initial shortest path path k ” to the shortest path path k ; Step 3.6, perform a new shortest path search within each regional road network Z i and check and adjust path k to obtain the path planning scheme for fleet k where u k1 = s k , u ki is the i-th node in Path k , and m k is the total number of nodes passed by the path planning scheme; Step 3.7, calculate the time window of the path planning scheme of the vehicle fleet according to the fleet length, fleet speed, and departure time. Assume that the time when vehicle fleet k arrives at node u ki is ττ ki , the fleet length is l k , the fleet speed is v k , calculate the time when vehicle fleet k passes through and leaves node u ki , and establish a set of time windows for the path planning scheme of vehicle fleet k accordingly. Among them, the time when vehicle fleet k leaves node u ki is: The time window for vehicle fleet k to pass through node u ki is as follows: The time window set of the path planning solution for fleet k is:

6. The method according to claim 5, characterized in that, The step 4 specifically includes: Step 4.1: Set the spatiotemporal conflict type of the multi-vehicle path according to the spatial topological relationship and movement direction of the conflict. ki Including path intersection time and space conflict NC, same-direction cross-path time and space conflict SEC and reverse cross-path time and space conflict REC, namely Conflict_type ki ={NC,SEC,REC}; Step 4.2, obtain the path planning scheme Path of all fleets k k , compare the path planning schemes Path of different fleets k to check if there are overlapping points or paths in space and record the spatial data of their spatio-temporal conflicts. When the path planning schemes Path x and Path y of fleets x and y have an intersection, it is determined that there is a spatial conflict between the two fleets, and the conflict node set NCN of the two fleets is recorded xy . If the size of the conflict node set is 1 or there are no adjacent nodes in the set, the conflict type is determined to be NC. If there are adjacent nodes in the conflict node set, extract the continuous node paths of the two fleets. If the directions of the two fleets through this path are opposite, the conflict type is REC. If the directions of the two fleets through this path are the same, the conflict type is SEC; Step 4.3, obtain the driving speed v of all vehicle fleets k k , the queue length l k , the time window T of the path planning scheme k , detect the time window T when the vehicle fleet passes through the spatial conflict intersection or path k whether there is an overlap, and analyze and record the time window data of the spatio-temporal conflict. For the spatial conflict intersection, compare the time windows when vehicle fleets x and y pass through the path intersection u xi If there is an overlap, it indicates that there is indeed a spatio-temporal conflict NC at the path intersection, and record the time window conflict data NCT xyi : NCT xyi = [max(ττ xi , ττ yi ), min(ττ xi ', ττ yi ')] For the spatio-temporal conflict of reverse intersection paths, compare the time windows of vehicle platoons x and y passing through path REC xy If there is an overlap, it indicates that there is indeed a spatio-temporal conflict REC of reverse intersection paths. Record the reverse path time window conflict data RECT xyi : RECT xyi = [max(ττ xi , ττ yi ), min(ττ xj ', ττ yj ')] For the spatio-temporal conflict of the same-direction crossing paths, compare the time windows when the vehicle platoons x and y pass through the path SEC xy If there is an overlap, it indicates that there is indeed a spatio-temporal conflict SEC of the same-direction crossing paths. Determine the spatio-temporal conflict time window based on the speeds of the vehicle platoons. When the speed of the following vehicle platoon is slower than that of the leading vehicle platoon, the vehicle platoons follow each other. At this time, record the spatio-temporal conflict data SECT of the same-direction path time window xyi : SECT xyi = [max(ττ xi , ττ yi ), min(ττ xi ', ττ yi ')] When the speed of the rear vehicle fleet is faster than that of the front vehicle fleet, it is necessary to wait until the front vehicle fleet has completely left the path before proceeding. At this time, record the data of the time window conflict of the same-direction path SECT xyi : SECT xyi = [max(ττ xi , ττ yi ), min(ττ xj ', ττ yj ']。 7. The method according to claim 6, characterized in that, The step 5 specifically includes: Step 5.1, calculate the static priority sp according to the attributes of the vehicle fleet itself k , where the attributes of the vehicle fleet itself include the urgency of the driving task of the vehicle fleet, the importance of the vehicle fleet, and special attributes; Step 5.2, dynamically update the dynamic priority dp according to the actual driving conditions of the vehicle fleet ki ; Step 5.3, combine the static priority sp k and the dynamic priority dp ki to calculate the comprehensive priority p of the vehicle fleet ki p ki = sp k + dp ki ; Step 5.4, when there is a spatio-temporal conflict between convoys, let the convoy with the highest comprehensive priority p ki travel according to the original path planning scheme Path k and let the other convoys change their path planning schemes Path k or time window T k .

8. The method according to claim 7, wherein The step 6 specifically includes: Step 6.1, when spatio-temporal conflicts occur in the path planning schemes of two or more vehicle fleets, first perform spatio-temporal conflict detection, and then let the vehicle fleet k with a relatively low comprehensive priority p ki stop and wait at the spatio-temporal conflict path or intersection until the conflict is resolved and then continue to drive; Step 6.2, when there will be spatio-temporal conflicts in the path planning schemes of two or more vehicle fleets, perform spatio-temporal conflict detection, and let the vehicle fleet with a relatively low comprehensive priority p ki re-plan a new path planning scheme to bypass the spatio-temporal conflict intersection or path, and continue to drive according to the new path planning scheme.

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