CN113625771A

CN113625771A - Shadow following single unmanned aerial vehicle area coverage path planning method

Info

Publication number: CN113625771A
Application number: CN202111059806.4A
Authority: CN
Inventors: 杨文婧; 王欢; 史殿习; 杨绍武; 李宁; 徐嘉迟; 郭敏
Original assignee: National University of Defense Technology
Current assignee: National University of Defense Technology
Priority date: 2021-09-10
Filing date: 2021-09-10
Publication date: 2021-11-09
Anticipated expiration: 2041-09-10
Also published as: CN113625771B

Abstract

The invention discloses a shadow following single unmanned aerial vehicle area coverage path planning method, and aims to solve the problem of low coverage efficiency caused by not executing a coverage task to ensure the integrity of a residual uncovered target area when a single unmanned aerial vehicle returns to a charging station. The technical scheme is as follows: preprocessing a known target area; calculating surrounding grids of the internal obstacle set, connection relations of all grids in the grid unit set G to be covered and the shortest distance from all grids in the G to the starting point; calculating a flight path set P of the unmanned aerial vehicle by adopting a shadow following method, and synchronously updating a shadow path when calculating the advancing position of the unmanned aerial vehicle; unmanned aerial vehicle follows the path in P from P₁To p_NThe order of execution of the overlay tasks. The invention enables the unmanned aerial vehicle to return to the starting point along the shadow path and execute the coverage task when the energy is insufficient to continue to advance, fully utilizes the airborne energy of the unmanned aerial vehicle, improves the completion efficiency of the coverage task, and completes the coverage task with fewer times of reciprocating the starting point.

Description

Shadow following single unmanned aerial vehicle area coverage path planning method

Technical Field

The invention relates to the field of unmanned aerial vehicle area coverage based on path planning, in particular to a path planning method for a single unmanned aerial vehicle to go and return to the same starting point by considering limited airborne energy constraint.

Background

Unmanned aerial vehicle is one of the representatives of intelligent unmanned system, because of advantages such as its high mobility, high-utility, is used in each field, solves various problems by the wide application. Area coverage is a class of classical path planning problem that solves for a planned path that traverses all points in the target area from a starting point and avoids obstacles. With the continuous development of unmanned aerial vehicle technology and the continuously reduced cost, the practical application of the unmanned aerial vehicle in solving the problem of area coverage is very wide, for example, the unmanned aerial vehicle is used for spraying pesticides in agricultural plant protection, so that crops in a cultivated land are fully covered by the pesticides; use unmanned aerial vehicle to replace manpower to accomplish high and cold or high altitude regional panorama survey and drawing work etc. in the geographical survey and drawing.

When the target area range is large, if the constraint condition that the airborne energy of the unmanned aerial vehicle is limited in the actual flight process is not considered, the coverage task cannot be completed due to insufficient flight capability of the unmanned aerial vehicle, and an unknown disaster is caused. A common approach to consider the limited energy of drones is to deploy a charging station at the origin. When the flight energy is insufficient, the unmanned aerial vehicle returns to the charging station to supplement the energy and continues to perform the covering task, and multiple charging operations enable the unmanned aerial vehicle to have the capability of completely covering the target area.

According to the strategy that the unmanned aerial vehicle returns to the charging station, the returning mode is divided into a straight line returning mode and a curve returning mode. The straight line returning means that the unmanned aerial vehicle returns to the position of the charging station from the current position according to the shortest straight line distance. Limited airborne energy is mapped to a limited flight distance in an article on line Coverage of Battery Powered Autonomous Mobile Robot on-line Coverage plane environment, published in the article on line Coverage of Mobile robots, on board Environments by a Battery Powered Autonomous Mobile Robot, volume 2, volume 13, IEEE Transactions on Automation Science and Engineering, 2016. When the remaining flying distance of the unmanned aerial vehicle is insufficient, the unmanned aerial vehicle marks the current position as a breakpoint, returns to the charging station for supplementing energy from the current position according to the shortest straight-line distance while avoiding the obstacle, and then returns to the breakpoint to continue to execute the covering task, as shown in fig. 1 (a). The grid cell where S is located in FIG. 1(a) is the grid cell where the charging station is located; the solid line arrow represents the flight direction of the unmanned aerial vehicle and the unmanned aerial vehicle executes the coverage task in the flight process, the dotted line arrow represents the flight direction of the unmanned aerial vehicle and the unmanned aerial vehicle does not execute the coverage task in the flight process; the grid cells filled by the solid points represent the grid cells passed by the unmanned aerial vehicle in the process of executing the coverage task, and the grid cells are in a covered state; the grid cells without filler elements represent grid cells in an uncovered state. In fig. 1(a), the drone returns the supplementary energy to the grid cell where the charging station is located along the dotted arrow, and no coverage task is performed during the return process, i.e. the grid cell through which the dotted line passes is still in an uncovered state. The curve returning means that the unmanned aerial vehicle returns to the starting point in a non-linear mode. An article, "Coverage Path Planning and Coverage Under Energy Constraint," published by Minghan Wei and Volkan Isler at the international society for robotics and automation (ICRA 2018) divides the target area into square grid cells of the same size and shape, along with the assumption that limited flight distances represent limited airborne Energy. Two grid cells whose center distance is equal to the side length of the grid cell are called adjacent grid cells. When the remaining flight capacity of the drone is insufficient, the drone returns to the starting point along the adjacent grid cell to supplement the energy, which is a typical curved return, as shown in fig. 1 (b). The grid cell where S is located in fig. 1(b) is a starting grid cell; the solid line arrow represents the flight direction of the unmanned aerial vehicle and the unmanned aerial vehicle executes the coverage task in the flight process, the dotted line arrow represents the flight direction of the unmanned aerial vehicle and the unmanned aerial vehicle does not execute the coverage task in the flight process; the grid cells filled with the solid points represent the grid cells through which the unmanned aerial vehicle executes the coverage task process, and the grid cells are in a covered state; the grid cells without filler elements represent grid cells in an uncovered state. In fig. 1(b), the drone follows the dotted arrow to replenish energy from the currently located grid cell to the adjacent grid cell until returning to the starting point grid cell, and no coverage task is performed during the returning process, that is, the grid cell passed by the dotted line is still in an uncovered state.

Whether the mode is a straight line return mode or a curve return mode, the unmanned aerial vehicle returns to the starting point along the shortest path. Since the position relationship between the position passed by the return process and the covered area, the position relationship between the position passed by the return process and the boundary area of the obstacle area or the target area may not be adjacent, if the mesh unit passed by the return path is considered to be in the covered state, the remaining uncovered target area may be divided into two or more sub-areas without connection relationship. If the remaining uncovered target area is divided into a plurality of sub-areas without connection relationship, covered grid cells need to be passed when covering different sub-areas. The unmanned aerial vehicle can cause repeated coverage through the covered grid unit, and energy utilization rate and coverage efficiency are reduced. Assuming that the grid cells passed by the drone returning process are considered to be in the covered state, the description is given by taking fig. 1(b) as an example, namely the grid cells passed by the dotted arrows in fig. 1(b) are to be set to be the grid cells filled with solid dots and the covered state; at this time, the remaining set of mesh cells in the uncovered state is composed of white mesh cells that are not passed by the dotted line in fig. 1(b), i.e., the remaining set of mesh cells in the uncovered state is { g }_1，4，g_1，5，g_2，2，g_3，2，g_3，3，g_3，4}; the remaining uncovered grid cell set is divided into two sub-regions without connection, such as the grid cell set in the uncovered state shown in FIG. 1(b) divided into two subsets g_1，4，g_1，5And { g }_2，2，g_3，2，g_3，3，g_3，4The grids in the two subsets have no connection, i.e. the set g_1，4，g_1，5And set g_2，2，g_3，2，g_3，3，g_3，4Denotes two sub-areas with no connection; when the unmanned aerial vehicle starts from the starting point grid unit S again to cover the rest grid unit in the uncovered stateThe elements need to pass through the grid cells passing by one or more dotted arrows, e.g. in fig. 1(b), the unmanned plane passes through the grid cells g from S_2，2、g_3，2、g_3，3、g_3，4Then through the grid cell g via the dashed arrow₂，4、g_2，3、g_1，3、g_1，2Reach grid cell g_1，4Then continue to cover the grid cell g_1，5That is, when the drone covers two sub-areas without connection relation in fig. 1(b), the drone needs to pass through the grid unit passed by the dotted arrow one or more times, i.e. g_2，4、g_2，3、g_1，3、g_1，2(ii) a Since the mesh unit through which the dotted arrow passes is assumed to be in a covered state in the foregoing, the energy utilization rate and the coverage efficiency of the unmanned aerial vehicle are reduced by repeatedly passing through the covered mesh unit. Therefore, no matter whether the existing single unmanned aerial vehicle area coverage path planning algorithm is a straight line return or a curve return, the algorithm assumes that the unmanned aerial vehicle does not execute the coverage task in the return process, namely, the mesh unit passed by the unmanned aerial vehicle in the return process is not set to be in a covered state, so that the integrity of the residual uncovered target area is maintained. The unmanned aerial vehicle does not generate gain to the coverage task in the return process, but the energy consumption and the execution time of the task are increased. Therefore, the farther the drone is returned to the charging station, the more frequent the charging, and the greater the impact on coverage efficiency.

Therefore, how to solve the problem that when a single unmanned aerial vehicle returns to a charging station, coverage efficiency is reduced because a coverage task is not executed to ensure the integrity of a residual uncovered target area is a technical problem which needs to be solved urgently by the person in the art.

Disclosure of Invention

The invention provides a shadow following method for planning an area coverage path of a single unmanned aerial vehicle, aiming at the problem that when a single unmanned aerial vehicle returns to a charging station, coverage efficiency is reduced due to the fact that the integrity of a residual uncovered target area is ensured and a coverage task is not executed. For a single unmanned aerial vehicle with limited airborne energy, the shadow path is updated when the forward position is calculated. The shadow path refers to a set of uncovered grid cells adjacent to covered grid cells, obstacle grid cells or target area boundary grid cells in the set of grid cells to be covered, and ensures the integrity of the remaining uncovered area. According to the invention, when the residual flight capacity of the unmanned aerial vehicle is not enough to fly to the target grid cell, the unmanned aerial vehicle returns to the charging station to supplement energy along the shadow path, the passing grid cell can be covered while the integrity of the residual uncovered area is not damaged in the returning process, and the unmanned aerial vehicle continues to cover the residual uncovered area after returning to the starting point to supplement energy until the target area is completely covered. As shown in fig. 2, the grid cell where S is located represents a starting grid cell, the solid arrow represents that the unmanned aerial vehicle flies from the grid cell where the current position is located to a target grid cell, and the passing grid cell is filled with solid dots; the grid unit set passed by the dotted arrow is a shadow path and filled with hollow points; when the residual flight capacity of the unmanned aerial vehicle is not enough to fly to the target grid, the unmanned aerial vehicle returns to the starting point grid unit along the shadow path according to the direction of the dotted arrow to supplement energy; because the grid cells in the shadow path are adjacent to the boundary of the target area or the grid cells in the covered state, when the unmanned aerial vehicle flies along the shadow path, the passed grid cells are set to be in the covered state, that is, the grid cells passed by the shadow path are filled with hollow points, and the integrity of the residual uncovered target area cannot be damaged. The invention can improve the energy utilization rate and the coverage efficiency of the unmanned aerial vehicle while satisfying the integrity constraint of the limited energy and the uncovered area of the unmanned aerial vehicle. By the shadow following method, the invention improves the completion efficiency of the coverage task and the energy utilization rate of the unmanned aerial vehicle, so that a single unmanned aerial vehicle can efficiently complete the coverage task of the target area, namely, compared with the coverage effect of not adopting the shadow following method in the figure 1, the number of covered grids adopting the shadow following method in the figure 2 is more than that of the covered grids in the figures 1(a) and 1 (b). Wherein the covered grid cells in fig. 2 include solid dot filled grid cells and empty dot filled grid cells, and the number of covered grid cells in fig. 2 is equal to 14; the covered grid cells of fig. 1(a) and 1(b) comprise grid cells filled with solid dots, the number of covered grid cells in fig. 1(a) being equal to 10 and the number of covered grid cells in fig. 1(b) being equal to 10. Therefore, the number of covered meshes in fig. 2 is 4 more than that of fig. 1(a) and 1 (b).

The invention comprises the following steps:

in the first step, a known target region is preprocessed. The target area includes a boundary of the area to be covered, a position of an obstacle within the area to be covered, and a start position at which the charging station is disposed. The target area T is divided into square grid cells with the same shape and size in a decomposition mode. The side length of the grid cell is denoted as R, which is determined according to the capacity of the airborne sensor and the task requirements.

h is the flying height of the unmanned aerial vehicle, and alpha is the visual field range of the airborne camera on the unmanned aerial vehicle. The target area T includes two types of grid cells: grid cells g to be covered and obstacle grid cells m. The set formed by the grid cells G to be covered is referred to as a grid cell set G to be covered, and the set formed by the barrier grid cells M is referred to as a barrier grid cell set M. Wherein, there is a grid cell in G as the starting point, denoted as S. And the unmanned aerial vehicle executes the coverage task from S, and returns to S when the energy is insufficient or the task is finished. The grid cells in M are divided into two categories: set of boundary obstacles M_aAnd internal set of obstacles M_e。M_aIncluding grid cells having a connection relationship with the target area boundary and grid cells having a connection relationship with other boundary barrier grid cells, denoted m_d. Except that M_dThe rest grid cells in M are internal obstacle grid cells M_eForm an internal obstacle set M_e. The connection relationship here includes a direct adjacent relationship and an oblique adjacent relationship. Directly adjacent means that the center distance of two grid cells is equal to R; diagonally adjacent means that the center distance of two grid cells is equal to

Second, calculate the internal obstacle set M_eThe surrounding grid, the connection relation of all grids in the grid unit set G to be covered and the shortest distance from all grids in the G to the starting point are as follows:

2.1 Collection of M from internal obstacles_eThe pair of connection relations M between the grid cells in (1)_eThe grid cells in the cluster are grouped, the surrounding grids of each group of internal obstacle grid cells are respectively calculated and are sorted in the clockwise direction, and the sorted surrounding grids are all put into a surrounding grid set Sur. The surrounding grid is M_eHas a connected relation of the grid cells to be covered.

The method comprises the following specific steps:

2.1.1 mixing M_eThe grid cells with connection relations in the grid structure are divided into one group, and the grid cells between different groups do not have any connection relations. Let M_eIs divided into K groups, and K is a positive integer.

2.1.2 the initialization index value k is 1.

2.1.3 according to the connection relation of the grid units, finding out the directly adjacent and obliquely adjacent grid units of each grid unit in the k group of internal obstacle grid units, and storing the directly adjacent and obliquely adjacent grid units to the k group of surrounding grid set Sur_kAnd from the set Sur_kAnd delete the obstacle grid cells. Set Sur at this time_kThe grid cells in (e) are the surrounding grids of the kth group of internal obstacle grids.

2.1.4 according to Sur_kThe positions of the middle grid cells are from bottom to top and from left to right to Sun_kThe grid cells in (1) are sorted and numbered. The grid cell number value located in the lower left corner is the smallest. Rearranging Sur in ascending order according to numbering value_kThe grid cell of (1).

2.1.5 initializing ordered set order { }, initializing grid unit record stack { }, and setting current grid unit position g ═ Sur { }_k[1]I.e. with Sur_kAnd the grid cell with the minimum middle number value is used as a traversal starting point.

2.1.6 finding all grid cells directly adjacent to G from the set G of grid cells to be covered, the grid cells to be found being directly adjacent to GAdjacent grid cell and located at Sun_kThe grid cell in (a) is saved to a set ad of grid cells directly adjacent to (g)_g。

2.1.7 if ad_gThe grid cells are found in the grid cell, and the step 2.1.8 is carried out; otherwise, G is not directly adjacent to G and is located at Sur_kGo to step 2.1.13.

2.1.8 if ad_gWith only one grid cell, put g to the end of order, from Sur_kDeleting g, when g equals ad_gThe only grid unit in the step (2) is turned to the step (2.1.6); if ad_gWhere there are multiple grid cells, go to step 2.1.9.

2.1.9 if g is at the traversal start, put g to the end of order, from Sur_kDeleting g, when g equals ad_gThe grid unit with the minimum number value in the middle number is turned to the step 2.1.6; if g is not at the traversal starting point, go to step 2.1.10.

2.1.10 Slave ad_gIn which a grid cell having the same immediate adjacent obstacle grid cell as the last grid cell in the order is selected, denoted g_next。

2.1.11 if g_nextPressing g into the stack top of the stack, and turning to step 2.1.12, wherein the number of barrier grid cells in the directly adjacent grid cells is more than or equal to 2; if g is_nextIs less than 2, go directly to step 2.1.12.

2.1.12 put g at the end of order from Sur_kDeleting g, making g equal to g_nextTurning to the step 2.1.6;

2.1.13 view stack information. If the grid cells are not stored in the stack, it indicates that the traversal of the surrounding grid cells of the current group of internal obstacles is finished, and go to step 2.1.14; if the stack has grid cells, making g equal to the grid cells at the top of the stack, deleting the grid cells at the top of the stack, and going to the step 2.1.6.

2.1.14 order Sur_kGet sure ═ order, get sure_kAnd saving the data to the surrounding grid set Sur, and updating the index value k to k + 1. If K is larger than K, the traversal and the sorting of all the surrounding grid units are completed, and S is performed at the momentur＝{Sur₁，...，Sur_k，...，Sur_KK is more than or equal to 1 and less than or equal to K, and the step 2.2 is carried out; otherwise, go to step 2.1.3 and continue to traverse the surrounding grid cells of the internal obstacle.

2.2 statistics of each grid cell G in the set G of grid cells to be covered₁，...，g_j，...g_num(G)Respectively storing the directly adjacent grid cells to g₁，...，g_j，...g_num(G)Of directly adjacent grid cells

In (1), obtaining a grid cell g to be covered₁，...，g_j，...g_num(G)Of directly adjacent grid cells

Where num (G) represents the number of grid cells in G,

denotes the jth grid cell G in G_jJ is 1. ltoreq. num (G).

2.3 statistics of each grid cell G in the set G of grid cells to be covered₁，...，g_j，...g_num(G)Storing the oblique adjacent grid cell to g₁，...，g_j，...g_num(G)Set of diagonally adjacent grid cells

In the method, an oblique adjacent grid unit set of the grid unit to be covered is obtained

Wherein the content of the first and second substances,

denotes the jth grid cell G in G_jIs selected.

2.4 in the area Coverage algorithm research field, when the target area is divided by square grids, the default unmanned aerial vehicle movement rule is to move from the grid cell where the current position is located to the directly adjacent grid cell, and cannot directly reach the diagonally adjacent grid cell of the grid cell where the current position is located, see the Coverage Path Planning Under the Energy Constraint and the Coverage published by Minghan Wei and Volkan Isler on international robot and automation society (ICRA 2018). According to the rule that the unmanned aerial vehicle moves from the grid cell where the current position is located to the directly adjacent grid cell, the shortest distance from each grid cell to be covered to the starting point S in the G is calculated, namely G₁，...，g_j，...g_num(G) The minimum number of grid cells that need to be passed to S is recorded as

Obtaining the shortest distance collecting platform from the grid unit to be covered to the starting point

Wherein the content of the first and second substances,

denotes the jth grid cell G in G_jThe shortest distance to S.

And thirdly, calculating a flight path set P of the unmanned aerial vehicle by adopting a shadow following method. The flight path set P is composed of paths from the starting point of each round trip of the unmanned aerial vehicle, i.e. P ═ P₁，...，p_i，...p_N}. Wherein p is_iAnd the path from the starting point to the starting point after the unmanned aerial vehicle starts from the starting point for the ith time and executes the covering task is shown, N shows the total times of reciprocating the starting point when the unmanned aerial vehicle completely covers the target area, and i is more than or equal to 1 and less than or equal to N. p is a radical of_iConsisting of grid cells traversed by the unmanned aerial vehicle during flight, i.e.

Wherein, g_imRepresents p_iM-th grid cell of (1), num (p)_i) Represents p_iTotal number of middle grid cells. The unmanned plane completely covers the target area after N times of starting points, namely p₁∪...∪p_i∪...∪p_NG. The method updates the shadow path while calculating the target grid unit, so that the unmanned aerial vehicle can return to the starting point along the shadow path when the energy is insufficient, and executes the covering task while not damaging the continuity of the uncovered target area, thereby improving the covering efficiency of a single unmanned aerial vehicle and reducing the times of the unmanned aerial vehicle for returning to and fro the starting point. The finite airborne Energy of the unmanned aerial vehicle is represented by a finite flight distance D, which is an assumption in the Coverage Planning and Coverage Under Energy Constraint of the information Constraint of the application published by Minghan Wei and Volkan Isler in the International society of robotics and Automation (ICRA 2018). The limited flying distance D is converted into the maximum flying grid unit number B of the unmanned aerial vehicle through the side length R of the grid unit, so that the requirement of the maximum flying grid unit number B of the unmanned aerial vehicle is met

In order to ensure that the unmanned aerial vehicle has the capability of completing the coverage task of the target area, the distance from all grid units to be covered to S is required to be not more than 2B, otherwise, the unmanned aerial vehicle with better flight capability is required to execute the coverage task.

The specific steps of calculating P by adopting a shadow following method are as follows:

3.1 starting the unmanned aerial vehicle from a starting point, namely initializing the position of a current grid unit g of the unmanned aerial vehicle to be S; initializing a flight path set P { } of the unmanned aerial vehicle; the number i of times of starting and returning the unmanned aerial vehicle is initialized is 1. Let path p traverse the starting point the ith time_iThe unmanned plane starts from the starting point grid unit; let shadow path p_wAnd (S) indicating that the unmanned aerial vehicle returns to the starting grid unit along the shadow path. Initializing all grid cells in the mesh cell set G to be covered to be in an uncovered state, and setting the state (G) of the current grid cell G to be in a covered state, that is, making the state (G) be covered. Initializing remaining flight capabilities B of the drone_restB, the number of grid cells that the drone may fly remainingEqual to the maximum number of flyable mesh cells of the drone at the initial state.

3.2 if grid cells in an uncovered state exist in the G, turning to the step 3.3; otherwise, the target area is completely covered, and go to step 3.6.

3.3 according to the position of the current grid cell g of the unmanned aerial vehicle, the coverage state of the target area and the information of the obstacles, calculating the grid cell g of the unmanned aerial vehicle going to next step_nextThe position of (a).

The method comprises the following specific steps:

3.3.1 find all grid cells in G that are directly adjacent to G and in an uncovered state, and save to the set of directly adjacent grid cells ad_g。

3.3.2 if ad_gIf the grid cell is an empty set, all grid cells in G with the shortest distance to G and in an uncovered state are found and stored to ad_gThe method comprises the following steps:

3.3.2.1, calculating the distance from the grid cell in G to G by: the distance from the grid unit where g is located to the grid unit is equal to 0, and the mark g is 0; the distance from the grid cell directly adjacent to g and not an obstacle to g is equal to 1, and the grid cell marked directly adjacent to g and not an obstacle is 1; traversing the directly adjacent grid cells of the grid cell marked 1, and adding one to the mark value of the grid cell which is not an obstacle and is not marked, namely the distance from the grid cell to g is equal to 2; and marking all grid cells in G according to the breadth-first idea to obtain the distance from all grid cells in G to G.

3.3.2.2 when ad_gWhen the grid cell is an empty set, it is indicated that all grid cells in G directly adjacent to G are in a covered state, i.e., all grid cells in G having a distance to G equal to 1 are in a covered state. Therefore, starting from the grid cells with the distance to G equal to 2 in G, the grid cells in the uncovered state in G are searched according to the sequence of the distances to G from small to large. When the first uncovered grid cell in G is found, the distance dis from the found first uncovered grid cell to G is recorded.

3.3.2.3 finding all grid cells in G with distance to G equal to dis and in uncovered state, saving to ad_g。

3.3.3 if ad_gOnly one grid cell in the network, the grid cell is used as a target grid cell g of the unmanned aerial vehicle_nextTurning to the step 3.4; if ad_gWith a plurality of grid cells, go to step 3.3.4.

3.3.4 finding ad_gThe distance of the middle grid cell to the starting point S. The shorter the distance, the higher the priority of the grid cell; the distances are equal and the priorities of the grid cells are the same. Will ad_gAnd deleting the grid cells with the medium and low priority, and only keeping the grid cells with the highest priority. If ad_gIf there is only one grid cell, the grid cell is used as the target grid cell g of the unmanned plane_nextTurning to the step 3.4; if ad_gThere are multiple grid cells with the highest priority, go to step 3.3.5.

3.3.5 calculating ad_gOf the immediately adjacent grid cells of each grid cell, is located in G and is the sum of the number of grid cells in the covered state and the number of obstacle grid cells. If the number of covered grid cells and obstacle grid cells around a grid cell is larger, it means that the number of uncovered grid cells directly adjacent to the grid cell is smaller. If the grid cell is not covered preferentially, it may happen that there is no directly adjacent uncovered grid cell around the grid cell, resulting in that other covered grid cells need to be passed when covering the grid cell, causing repeated coverage and wasting the limited energy of the drone. Thus, ad_gThe greater the number of covered grid cells and obstacle grid cells around the middle grid cell, the more ads_gThe higher the priority of the middle grid cell; equal number, ad_gThe priority of the middle grid cells is the same. Ad (cell-bone growth promoting)_gOnly the grid cell with the highest priority is reserved. If ad_gIn which there is only one grid cell, set that grid cell to g_nextTurning to the step 3.4; if ad_gThere are still a plurality of grid cells with the highest priority, go to step 3.3.6.

3.3.6 according to path p_iThe last grid cell in (b) gets the last covered grid cell p_i(end) connecting g and p_i(end) constituting and following a line segmentAnd (3) making an extension line outwards from the g (namely in the direction opposite to the line segment), wherein the extension line is a ray with the g as a starting point. And rotating the extension line clockwise by taking the g as a center and the direction of the extension line as an initial direction. According to the extension line and ad_gGiven ad in the order of grid cell intersection in_gThe grid cell ordering in (1). Extension line and ad_gThe earlier the grid cells in (A) intersect, then ad_gThe higher the priority of the grid cell in (b). Due to ad_gThe grid cells in (1) are all the grid cells directly adjacent to g or the grid cells with equal distances to g, so that the situation that two or more grid cells are positioned on a scanning line at the same time does not occur in the scanning process. Fetching ad_gThe grid cell with the highest medium priority is used as g_next。

3.4 according to g_nextFinding an updated value for a shadow path

Is to update the value without regard to the shadow path surrounding the grid cell,

the method is to consider the updating value of the shadow path of the surrounding grid unit and comprises the following steps:

3.4.1 initialization regardless of the shadow path update values surrounding the grid cell

3.4.2 if

In which g is contained_nextDescription of shadow Path sum g_nextOverlap, delete

The last grid unit of (3) goes to the step 3.4.3; otherwise, go to step 3.4.4.

3.4.3 if

Does not contain g_nextIndicate deleted

Turning to the 3.4.4 step by the redundant grid in the step (3); otherwise, go to step 3.4.2 to continue the delete operation.

3.4.4 if

Last grid cell of

And g_nextDirectly adjacent, say that unmanned aerial vehicle is located g_nextFrom g, can be_nextGo to

Then along

Returning to the starting grid unit, and turning to step 3.4.8; if it is

And g_nextNot directly adjacent, it needs to calculate if the drone is from g_nextGo to

If the other uncovered grid cells pass, the step 3.4.5 is carried out.

3.4.5 neutralizing G with G_nextMesh cells that are directly adjacent and in a non-overlapping state are saved to a set of adjacent mesh cells of a target mesh cell

If it is

Middle-sized boatWith grid cells, go to step 3.4.9; if it is

And only one grid cell, will

Put the grid cells in

In the last grid cell

Then go to step 3.4.9; if it is

If there are more grid cells satisfying the condition, go to step 3.4.6.

3.4.6 calculation

Grid cells of (1) to

Last grid cell of

The distance of (c). The shorter the distance is,

the higher the grid cell priority in (1); the distances are equal to each other and the distance between the two adjacent plates is equal,

the grid cell priorities in (1) are the same. Deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority. If it is

Only one grid cell in the grid array, then put the grid cell into

Then go to step 3.4.9; if not, then,

there are multiple grid cells with the highest priority, go to step 3.4.7.

3.4.7 calculation

To S. The further away the distance is from the ground,

the higher the grid cell priority in (c). Deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority. If it is

Has only one grid cell, and places the grid cell into

Then go to step 3.4.9; otherwise, go to step 3.4.8.

3.4.8 connection 9 and g_nextComposing a line segment and following the line segment from g_nextExtending outwards (i.e. in the direction opposite to the line segment) by g_nextIs the ray of origin. In g_nextAs a center, the direction of the extension line is the starting directionThe extension line is rotated in a clockwise direction. According to an extension line and

the order of grid cell intersection in (1)

The grid cell ordering in (1). Extension line and

the earlier the grid cells in (A) intersect, then

The higher the priority of the grid cell in (b). Due to the fact that

The grid cells in (1) are all g_nextThe situation that two or more grid cells are positioned on the scanning line at the same time does not occur in the scanning process of the directly adjacent grid cells. Get

Put the grid cell with the highest medium priority to

And a rear face.

3.4.9 initialization considers the shadow path update values of the surrounding grid cells

To preserve

The original value of (a).

3.4.10 if

Last grid cell of

And g_nextSurrounding grid cells of obstacles within the same set of Sur (let Sur be_k) In, then from Sur_kIn (1)

Begin to put the ordered surrounding grid cells in order

Later, until Sur is encountered_kG in (1)_nextStopping placing the surrounding grid into

And a rear face. Note that g here_nextIs not put into

Rear, to avoid repeated coverage g_next。

3.5 remaining flight capability B according to unmanned aerial vehicle_restUpdating the position of the current grid cell g of the drone and the shadow path p_w。

The method comprises the following steps:

3.5.1 remaining flight Capacity B of the unmanned aerial vehicle_restCan support unmanned aerial vehicle to fly to g from g_nextAnd along

Go back to the starting point, i.e. satisfy

Wherein, len (g, g)_next) Indicating the grid cell g from which the current position is located to the target grid cell g_nextThe shortest distance of (d);

representing the slave target grid cell g_nextTo

Last mesh of (2)Unit cell

The shortest distance of (d);

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (c). Updating the remaining flight capacity of the drone, i.e. order B_rest＝B_rest-len(g，g_next) (ii) a Updating the unmanned aerial vehicle to move from the grid unit where the current position is located to the target grid unit, namely, making g equal to g_next(ii) a Updating the grid unit where the current position of the unmanned aerial vehicle is located to be in a coverage state, namely, commanding state (g) to be covered; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell; update the shadow path to

Go to step 3.5.4; if the remaining flight capability B of the unmanned aerial vehicle_restCan not support the unmanned plane to fly from g to g_nextAnd along

Returning to the starting point, the step 3.5.2 is carried out.

3.5.2 if unmanned aerial vehicle's remaining flight ability can support unmanned aerial vehicleFly from g to g_nextAnd along

Go back to the starting point, i.e. satisfy

Wherein the content of the first and second substances,

indicating the grid cell g from the current position_nextTo

Last grid cell of

The shortest distance of (d);

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (c). Updating the remaining flight capacity of the drone, i.e. order B_rest＝B_rest-len(g，g_next) (ii) a The unmanned aerial vehicle moves from the grid unit where the current position is located to the target grid unit, namely, g is set as g_next(ii) a Updating the grid cell where the current position of the drone is located to be in the covered state, i.e. making state (g) covReed; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell of (a); update the shadow path to

Returning to the starting point, go to step 3.5.3.

3.5.3 at this time, the remaining flight energy of the drone is not enough to support the drone to proceed to perform the coverage task, and the drone must follow the shadow path p_wReturning to the starting point to supplement energy, the method comprises the following steps: p is to be_wThe grid cells in (1) are added to the path p of the ith round-trip starting point from back to front in sequence_iAnd setting each added grid cell to a covered state; after the unmanned aerial vehicle returns to the starting point, the path index value i is updated to i +1, and the ith path and the shadow path are initialized to p_i＝{g}，p_w-g; the remaining flight capacity of the unmanned plane at the starting point is equal to the maximum flying grid cell number B_restGo to step 3.5.4.

3.5.4 if the surrounding grid cell with some group of obstacles in the surrounding grid cell set Sur is in a covering state, deleting the group of surrounding grid cells from Sur to avoid repeated covering, and going to step 3.2.

3.6 the target area is completely covered, the number of times N of the starting point of the single unmanned aerial vehicle is obtained, the number is i, and the covering path is stored as P, P₁，...，p_i，...，p_N}，1≤i≤N。

And fourthly, outputting the times N of the unmanned aerial vehicle to return to and fro the starting point and the flight path P for executing the covering task. The unmanned aerial vehicle follows the path in the flight path P, and follows the slave P₁To p_NThe sequential execution of the covering tasks enables complete coverage of the target area.

The invention can achieve the following technical effects:

on the premise of balancing the constraint of the finite airborne energy of the unmanned aerial vehicle and the continuity of the uncovered target area, the shadow path is synchronously updated when the advancing position of the unmanned aerial vehicle is calculated in the third step, so that the unmanned aerial vehicle can return to the starting point along the shadow path and execute the covering task when the energy is insufficient, the airborne energy of the unmanned aerial vehicle is fully utilized, the completion efficiency of the covering task is improved, and the covering task is completed by using fewer times of returning the starting point.

Drawings

Fig. 1 is a schematic diagram illustrating that when the remaining distance available for flying of the drone is insufficient, the drone returns to the starting point to supplement energy in the prior art; FIG. 1(a) is a schematic view of a straight-line return manner, and FIG. 1(b) is a schematic view of a curved-line return manner;

fig. 2 is a schematic diagram of the unmanned aerial vehicle shown in fig. 1, in which the unmanned aerial vehicle returns along the shadow path by using the third step of calculation of the present invention when the unmanned aerial vehicle needs to return to the starting point for supplementing energy;

FIG. 3 is an overall flow chart of the present invention;

FIG. 4 is a schematic view of a scene representation of a target area of a first step in accordance with an embodiment of the present invention;

FIG. 5 is a diagram illustrating a second step of the bounding grid cell traversal order according to an embodiment of the present invention;

FIG. 6 is a diagram illustrating a shortest distance from a grid to be covered to a starting point in a target area in a second step according to an embodiment of the present invention;

FIG. 7 is a flowchart of a third step of calculating a flight path of the UAV using a shadow following method according to the present invention;

FIG. 8 is a diagram illustrating a shadow path when the UAV encounters an obstacle in the third step of the present invention; FIG. 8(a) is a schematic diagram of not adding a bounding grid to a shadow path; FIG. 8(b) is a schematic diagram of adding bounding grid elements to a shadow path;

FIG. 9 is a schematic diagram showing a comparison of path planning results of the present invention and other single-machine area coverage path planning algorithms of the background art;

Detailed Description

In order to make the technical solutions of the present invention better understood, the present invention is further described in detail below with reference to the accompanying drawings.

FIG. 3 is an overall flow chart of the present invention; as shown in fig. 3, the present invention comprises the steps of:

h is the flying height of the unmanned aerial vehicle, and alpha is the visual field range of the airborne camera on the unmanned aerial vehicle. The target area T includes two types of grid cells: grid cells g to be covered and obstacle grid cells m, as shown in fig. 4. The grid cells filled with shading in fig. 4 represent the obstacle grid cells, and the other grids are the grid cells to be covered. The set formed by the grid cells G to be covered is referred to as a grid cell set G to be covered, and the set formed by the barrier grid cells M is referred to as a barrier grid cell set M. Wherein, there is a grid cell in G as the starting point, denoted as S. G in FIG. 4₃₇Is S. And the unmanned aerial vehicle executes the coverage task from S, and returns to S when the energy is insufficient or the task is finished. The grid cells in M are divided into two categories: set of boundary obstacles M_dAnd internal set of obstacles M_e。M_dIncluding grid cells having a connection relationship with the target area boundary and grid cells having a connection relationship with other boundary barrier grid cells, denoted m_d. For the boundary obstacle grid cells in FIG. 4

Where r and c represent the number of rows and columns, respectively, in which the boundary barrier grid cells are located. In FIG. 4

Is related to the targetGrid cells with region boundaries having a connected relationship;

and

are diagonally adjacent, thus

Is also a boundary barrier grid cell;

and

are directly adjacent, thus

Also a boundary obstacle grid cell. Except that M_dThe rest grid cells in M are internal obstacle grid cells M_eForm an internal obstacle set M_e. For internal obstacle grid cells in fig. 4

Where r and c represent the number of rows and columns, respectively, in which the internal obstacle grid cells are located. The connection relationship here includes a direct adjacent relationship and an oblique adjacent relationship. Directly adjacent means that the center distance of two grid cells is equal to R; diagonally adjacent means that the center distance of two grid cells is equal to

For example, in FIG. 4

And

is in a direct adjacent relationship with each other,

and

are in a diagonal adjacent relationship.

The method comprises the following specific steps:

2.1.1 mixing M_eThe grid cells with connection relations in the grid structure are divided into one group, and the grid cells between different groups do not have any connection relations. Let M_eIs divided into K groups, and K is a positive integer. As shown in fig. 5, the target region has two groups (K ═ 2) of internal obstacles

And

the grid cells filled with empty dots in fig. 5 represent the surrounding grid of two sets of internal obstacles in the target area.

2.1.2 the initialization index value k is 1.

2.1.6 finding all grid cells directly adjacent to G from the set G of grid cells to be covered, locating the found grid cells directly adjacent to G in Sun_kThe grid cell in (a) is saved to a set ad of grid cells directly adjacent to (g)_g。

2.1.9 if g is at the traversal start, put g to the end of order, from Sur_kMiddle deletion g, g equals ad_gThe grid unit with the minimum number value in the middle number is turned to the step 2.1.6; if g is not at the traversal starting point, go to step 2.1.10.

2.1.11 if g_nextThe number of barrier grid cells in the directly adjacent grid cells is more than or equal to 2, g is pressed into a stack item, and the step 2.1.12 is carried out; if g is_nextIn directly adjacent grid cellsThe number of grid cells is less than 2, and the process directly goes to step 2.1.12.

2.1.14 order Sur_kGet sure ═ order, get sure_kAnd saving the data to the surrounding grid set Sur, and updating the index value k to k + 1. If K is larger than K, all the surrounding grid cells are traversed and sorted. As shown in fig. 5, the arrow direction indicates the traversal and sorting direction of the bounding grid, and when k is 1, the traversal is performed

Surrounding grid of { g }₁，g₂，g₃，g₄，g₅，g₇，g₁₂，g₁₁，g₁₀，g₁₅，g₁₆，g₁₇，g₂₀，g₂₅，g₃₂，g₃₁，g₃₀，g₂₄，g₂₉，g₂₈，g₂₃，g₁₉，g₁₄，g₉，g₆Is traversed when k is 2

Surrounding grid of { g }₃₈，g₃₉，g₄₀，_g41，g₄₅，g₅₀，g₄₉，g₄₈，g₄₇，g₄₄}. When Sur ═ Sur₁，...，Sur_k，...，Sur_KK is more than or equal to 1 and less than or equal to K, and the step 2.2 is carried out; otherwise, go to step 2.1.3 and continue to traverse the surrounding grid cells of the internal obstacle.

Where num (G) denotes the number of grid cells in G (num (G) 46 in fig. 4),

denotes the jth grid cell G in G_jJ is 1. ltoreq. num (G). For example, grid cell g in FIG. 4₂₀Of directly adjacent grid cells

Wherein the content of the first and second substances,

denotes the jth grid cell G in G_jIs selected. For example, grid cell g in FIG. 4₂₀Set of diagonally adjacent grid cells

2.4 in the area Coverage algorithm research field, when the target area is divided by square grids, the default unmanned aerial vehicle movement rule is to move from the grid cell where the current position is located to the directly adjacent grid cell, and cannot directly reach the diagonally adjacent grid cell of the grid cell where the current position is located, see the Coverage Path Planning Under the Energy Constraint and the Coverage published by Minghan Wei and Volkan Isler on international robot and automation society (ICRA 2018). According to the rule that the unmanned aerial vehicle moves from the grid cell where the current position is located to the directly adjacent grid cell, the shortest distance from each grid cell to be covered to the starting point S in the G is calculated, namely G₁，...，g_j，...g_num(G)The minimum number of grid cells that need to be passed to S is recorded as

Wherein the content of the first and second substances,

denotes the jth grid cell G in G_jThe shortest distance to S. The numerical marks on the grid to be covered as in fig. 6 represent the shortest distance of the corresponding grid cell to the starting point. For example, the starting point S is the grid cell g in FIG. 4₃₇I.e., the grid cell numbered 0 in fig. 6; grid g₁Shortest distance to starting point

And thirdly, calculating a flight path set P of the unmanned aerial vehicle by adopting a shadow following method. Flight path aggregationP is the path from the start point to the start point for each round trip of the drone, i.e. P ═ P₁，...，p_i，...p_N}. Wherein p is_iAnd the path from the starting point to the starting point after the unmanned aerial vehicle starts from the starting point for the ith time and executes the covering task is shown, N shows the total times of reciprocating the starting point when the unmanned aerial vehicle completely covers the target area, and i is more than or equal to 1 and less than or equal to N. p is a radical of_iConsisting of grid cells traversed by the unmanned aerial vehicle during flight, i.e.

Wherein, g_imRepresents p_iM-th grid cell of (1), num (p)_i) Represents p_iTotal number of middle grid cells. The unmanned plane completely covers the target area after N times of starting points, i.e.

The method updates the shadow path while calculating the target grid unit, so that the unmanned aerial vehicle can return to the starting point along the shadow path when the energy is insufficient, and executes the covering task while not damaging the continuity of the uncovered target area, thereby improving the covering efficiency of a single unmanned aerial vehicle and reducing the times of the unmanned aerial vehicle for returning to and fro the starting point. The finite airborne Energy of the unmanned aerial vehicle is represented by a finite flight distance D, which is an assumption in the Coverage Planning and Coverage Under Energy Constraint of the information Constraint of the application published by Minghan Wei and Volkan Isler in the International society of robotics and Automation (ICRA 2018). The limited flying distance D is converted into the maximum flying grid unit number B of the unmanned aerial vehicle through the side length R of the grid unit, so that the requirement of the maximum flying grid unit number B of the unmanned aerial vehicle is met

As shown in fig. 7, the specific steps of calculating P by using the shadow following method are as follows:

3.1 let the drone start from the starting point, i.e. initialize the bits of the drone's current grid cell gSetting as S; initializing a flight path set P { } of the unmanned aerial vehicle; the number i of times of starting and returning the unmanned aerial vehicle is initialized is 1. Let path p traverse the starting point the ith time_iThe unmanned plane starts from the starting point grid unit; let shadow path p_wAnd (S) indicating that the unmanned aerial vehicle returns to the starting grid unit along the shadow path. Initializing all grid cells in the mesh cell set G to be covered to be in an uncovered state, and setting the state (G) of the current grid cell G to be in a covered state, that is, making the state (G) be covered. Initializing remaining flight capabilities B of the drone_restB, i.e. the number of mesh cells that the drone can fly remaining is equal to the maximum number of flyable mesh cells of the drone at the initial state.

The method comprises the following specific steps:

3.3.6 according to path p_iThe last grid cell in (b) gets the last covered grid cell p_i(end) connecting g and p_i(end) constitutes a line segment and is extended along the line segment from g outwards (i.e. in the direction opposite to the line segment), the extended line being a ray starting from g. And rotating the extension line clockwise by taking the g as a center and the direction of the extension line as an initial direction. According to the extension line and ad_gGiven ad in the order of grid cell intersection in_gThe grid cell ordering in (1). Extension line and ad_gThe earlier the grid cells in (A) intersect, then ad_gThe higher the priority of the grid cell in (b). Due to ad_gThe grid cells in (1) are all the grid cells directly adjacent to g or the grid cells with equal distances to g, so that the situation that two or more grid cells are positioned on a scanning line at the same time does not occur in the scanning process. Fetching ad_gThe grid cell with the highest medium priority is used as g_next。

3.4 according to g_nextFinding an updated value for a shadow path

3.4.2 if

The last grid unit of (3) goes to the step 3.4.3; otherwise, go to step 3.4.4.

3.4.3 if

Does not contain g_nextIndicate deleted

3.4.4 if

Last grid cell of

Then along

Returning to the starting grid unit, and turning to step 3.4.8; if it is

If the other uncovered grid cells pass, the step 3.4.5 is carried out.

If it is

Go to step 3.4.9 if there is no grid cell; if it is

And only one grid cell, will

Put the grid cells in

In the last grid cell

Then go to step 3.4.9; if it is

If there are more grid cells satisfying the condition, go to step 3.4.6.

3.4.6 calculation

Grid cells of (1) to

Last grid cell of

The distance of (c). The shorter the distance is,

the grid cell priorities in (1) are the same. Deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority. If it is

Only one grid cell in the grid array, then put the grid cell into

Then go to step 3.4.9; if not, then,

there are multiple grid cells with the highest priority, go to step 3.4.7.

3.4.7 calculation

To S. The further away the distance is from the ground,

the higher the grid cell priority in (c). Deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority. If it is

Has only one grid cell, and places the grid cell into

Then go to step 3.4.9; otherwise, go to step 3.4.8.

3.4.8 connecting g and g_nextComposing a line segment and following the line segment from g_nextExtending outwards (i.e. in the direction opposite to the line segment) by g_nextIs the ray of origin. In g_nextThe direction of the extension line is the starting direction, and the extension line is rotated clockwise. According to an extension line and

the order of grid cell intersection in (1)

The grid cell ordering in (1). Extension line and

the earlier the grid cells in (A) intersect, then

The higher the priority of the grid cell in (b). Due to the fact that

Put the grid cell with the highest medium priority to

And a rear face.

To preserve

The original value of (a).

3.4.10 if

Last grid cell of

Begin to put the ordered surrounding grid cells in order

And a rear face. Note that g here_nextIs not put into

Rear, to avoid repeated coverage g_next. In the invention, under the condition of fully considering the obstacle scene, the shadow path adds the surrounding grid into the shadow path, so that the overlapping of the shadow path and the covered grid unit is avoided, and the coverage efficiency of the unmanned aerial vehicle is improved, as shown in fig. 8. FIGS. 8(a) and 8(b) are partial views of FIG. 4, with FIGS. 8(a) and 8(b) being formed by the grid cell to be covered { g } in FIG. 4₃₇，g₃₈，g₃₉，g₄₀，g₄₁，g₄₃，g₄₄，g₄₅，g₄₆，g₄₇，g₄₈，g₄₉，g₅₀And internal obstaclesPhysical grid cell

And (4) forming. FIG. 8(a) is a schematic diagram of one embodiment in which no bounding grid is added to the shadow path. If there are no uncovered adjacent grid cells around the current grid cell, a part of the grid cells in the shadow path overlap with the covered grid cells, i.e., the solid line arrow and the dashed line arrow in fig. 8(a) pass through the same grid cell. The shaded grid cells in fig. 8(a) represent obstacle grid cells, solid arrows represent that the drone flies from the current grid cell to the target grid cell, and the grid cells passed by the drone are filled with solid dots to represent a covered state; the drone returns to the starting point along the dashed arrow, uncovered grid cells passing in the return process are filled with empty dots and the grid cells passing in the return process are also marked as covered. FIG. 8(b) is a schematic diagram of one embodiment of adding a bounding grid to a shadow path. As shown in fig. 8(b), the shaded filled grid cells represent obstacle grid cells, the solid arrows represent that the drone flies from the current grid cell to the target grid cell, and the passing grid cells are filled with solid dots to represent a covered state; the dotted arrow indicates that the unmanned aerial vehicle returns to the starting point from the current position according to the shadow path to supplement energy. In fig. 8(b), the shadow path adds the bounding grid to the shadow path, so as to avoid overlapping of the shadow path and the covered grid cell, that is, the grid cell passed by the dotted arrow and the grid cell passed by the solid arrow in fig. 8(b) are not overlapped. Compared with the method that no surrounding grid is added into the shadow path in fig. 8(a), fig. 8(b) improves coverage efficiency of the drone while satisfying the remaining uncovered target area, that is, in the case that the number of arrows is equal, the number of grid units covered by fig. 8(b) is greater than that covered by fig. 8(a), and the number of grids filled with solid dots and hollow dots in fig. 8(b) is greater than that filled with solid dots and hollow dots in fig. 8 (a).

The method comprises the following steps:

Go back to the starting point, i.e. satisfy

representing the slave target grid cell g_nextTo

Last grid cell of

The shortest distance of (d);

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (c). Updating the remaining flight capacity of the drone, i.e. order B_rest＝B_rest-len(g，g_next) (ii) a Update nobodyThe machine moves from the grid unit where the current position is located to the target grid unit, namely, g is set as g_next(ii) a Updating the grid unit where the current position of the unmanned aerial vehicle is located to be in a coverage state, namely, commanding state (g) to be covered; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell; update the shadow path to

Returning to the starting point, the step 3.5.2 is carried out.

3.5.2 if the remaining flight capability of the drone can support the drone to fly from g to g_nextAnd along

Go back to the starting point, i.e. satisfy

Wherein the content of the first and second substances,

indicating the grid cell g from the current position_nextTo

Last grid cell of

The shortest distance of (d);

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (c). Updating the remaining flight capacity of the drone, i.e. order B_rest＝B_rest-len(g，g_next) (ii) a The unmanned aerial vehicle moves from the grid unit where the current position is located to the target grid unit, namely, g is set as g_next(ii) a Updating the grid unit where the current position of the unmanned aerial vehicle is located to be in a covered state, namely, enabling state (g) to be covered; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell of (a); update the shadow path to

Returning to the starting point, go to step 3.5.3.

3.5.3 at this time, the remaining flight energy of the drone is not enough to support the drone to proceed to perform the coverage task, and the drone must follow the shadow path p_wReturning to the starting point to supplement energy, the method comprises the following steps: p is to be_wThe grid cells in (1) are added to the path p of the ith round-trip starting point from back to front in sequence_iAnd setting each added grid cell to a covered state; after the unmanned aerial vehicle returns to the starting point, the path index value i is updated to i +1, and the ith path and the shadow path are initialized to p_i＝{g}，p_w-g; the residual flight capacity of the unmanned aerial vehicle at the starting point is equal to the maximum flyable grid unitNumber B_restGo to step 3.5.4.

70 target areas are randomly arranged, and the side length of each target area G is 20R, namely, each row and each column in the target areas have 20 grid units. The obstacle density in the target area, i.e. the percentage of the total number of obstacle meshes in the target area to the total number of meshes in the target area, is set to 10%, 15%, 20%, 25%, 30%, 35%, 40%, respectively. Ten target areas were randomly generated at each density, and 70 target areas were generated for testing the present invention. The flight capability of the unmanned aerial vehicle is set to be B80. The experimental software system environment is the Wuban 16.04 version (namely Ubuntu 16.04, a version of the Linux system), an Intel i7-9750H processor is mounted, the frequency of the processor is 2.6GHz, and the RAM size is 16 GB.

Based on the known target area and the Constraint of limited flight capability, a Planning algorithm (CFA algorithm for short) given by an article (Coverage Path Planning and covering Under Energy Constraint) published by Minghan Wei and Volkan Isler in International Congress of robots and Automation (ICRA 2018) and a shadow following single unmanned plane area Coverage Path Planning method (SF for short) provided by the invention are compared.

Fig. 9 is a comparison of the number of times the drone starts and returns to the origin and the total length of the flight path for the invention (SF) and CFA algorithms. Fig. 9(a) is a comparison graph of the total length of the flight path of the drone covering the target area obtained by the present invention and the CFA algorithm under the environment with different obstacle densities; fig. 9(b) is a comparison graph of the number of times of energy replenishment from the starting point of the round trip when the drone covers the target area, obtained by the (SF) and CFA algorithms of the present invention, in an environment with different obstacle densities. The horizontal axis in fig. 9(a) and 9(b) represents the obstacle density in the target region. In each of the obstacle densities in fig. 9(a) and 8(b), the solid line represents the result of the CFA algorithm, and the broken line represents the result of the path following algorithm proposed by the present invention.

The ordinate of fig. 9(a) represents the total path length of the drone coverage target area. The error bars at each obstacle density connected by the solid line in fig. 9(a) represent intervals of the minimum value and the maximum value of the total flight path length of the unmanned aerial vehicle in ten scenes where the density is the same and the obstacles are random, and the intersection points of the error bars and the solid line represent the average value of the flight path length of the unmanned aerial vehicle at the corresponding obstacle density; the error bars at each obstacle density connected by the dotted line in fig. 9(a) represent intervals between the minimum value and the maximum value of the total flight path length of the unmanned aerial vehicle in the SF algorithm in ten scenes where the density is the same and the obstacles are random, and the intersection points of the error bars and the dotted line represent the average value of the flight path lengths of the unmanned aerial vehicle at the corresponding obstacle density. Under the same target area, the shorter the total path length of the unmanned aerial vehicle is, the higher the coverage efficiency of the unmanned aerial vehicle is. As can be seen from fig. 9(a), compared with the CFA algorithm, the invention significantly reduces the length of the drone required to fly to cover the target area, and improves the coverage efficiency of the drone.

The ordinate of fig. 9(b) represents the number of times of energy replenishment from the round trip start point when the drone covers the target area. The error bars at each obstacle density connected by the solid line in fig. 9(b) represent intervals between the minimum value and the maximum value of the number of the unmanned aerial vehicle round-trip start points in ten scenes in which the density is the same and the obstacles are random in the CFA algorithm, and the intersection points of the error bars and the solid line represent the average value of the number of the unmanned aerial vehicle round-trip start points at the corresponding obstacle density; in fig. 9(b), the error bars at each obstacle density connected by the dotted line represent the intervals between the minimum value and the maximum value of the number of the unmanned aerial vehicle round trip start points in the SF algorithm in ten scenes in which the density is the same and the obstacles are random, and the intersection point of the error bar and the solid line represents the average value of the number of the unmanned aerial vehicle round trip start points at the corresponding obstacle density. Under the same target area, the number of times that the unmanned aerial vehicle comes and goes to the starting point is less, which shows that the unmanned aerial vehicle uses less energy to complete the coverage of the same target area, namely the higher the energy utilization rate of the unmanned aerial vehicle is, the higher the coverage efficiency is. As can be seen from fig. 9(b), compared with the CFA algorithm, the present invention uses fewer times of round trip starting points in the process of covering the target area, which shows that the unmanned aerial vehicle can complete the coverage task of the target area with less energy, and improves the energy utilization rate of the unmanned aerial vehicle.

The shadow following single unmanned aerial vehicle area coverage path planning method provided by the invention is described in detail above. The principles and embodiments of the present invention are explained herein, with the above description being included to assist in understanding the core concepts of the present invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

Claims

1. A shadow following single unmanned aerial vehicle area coverage path planning method is characterized by comprising the following steps:

firstly, preprocessing a known target area; the target area comprises the boundary of the area to be covered, the position of an obstacle in the area to be covered and the position of a starting point, and the charging station is arranged at the starting point; dividing the target area T into square grid units with the same shape and size in a decomposition mode; the side length of the grid unit is marked as R, and the R is determined according to the capacity of the airborne sensor and the task requirement; grid cells g and barrier grid cells m to be covered; a set formed by grid cells G to be covered is marked as a set G of the grid cells to be covered, and a set formed by barrier grid cells M is marked as a set M of the barrier grid cells; wherein, there is a grid cell in G as the starting point, note as S; the unmanned aerial vehicle starts from S to execute a coverage task, and returns to S when the energy is insufficient or the task is finished; the grid cells in M are divided into two categories: set of boundary obstacles M_dAnd an interior barrierSet of obstacles M_e；M_dIncluding grid cells having a connection relationship with the target area boundary and grid cells having a connection relationship with other boundary barrier grid cells, denoted m_d(ii) a Except that M_dThe rest grid cells in M are internal obstacle grid cells M_eForm an internal obstacle set M_e(ii) a Here, the connection relationship includes a direct adjacent relationship and an oblique adjacent relationship; directly adjacent means that the center distance of two grid cells is equal to R; diagonally adjacent means that the center distance of two grid cells is equal to

2.1 Collection of M from internal obstacles_eThe connection relationship between the grid cells in (1) will be M_eThe grid units in the system are divided into K groups, K is a positive integer, surrounding grids of the internal obstacle grid units in each group are respectively calculated and are sorted in a clockwise direction, the sorted surrounding grids are placed into a surrounding grid set Sur, and Sur is { Sur ═ Sur [, and the surrounding grids are sorted in a clockwise direction₁，...，Sur_k，...，Sur_K}，1≤k≤K，Sur_kA set of k-th ordered bounding grids; surrounding grid fingers and M_eAny grid unit in the grid structure has a grid unit to be covered in a connection relation;

2.2 statistics of grid cells G in the set G of grid cells to be covered₁，...，g_j，...g_num(G)Respectively storing the directly adjacent grid cells to g₁，...，g_j，...g_num(G)Of directly adjacent grid cells

Where num (G) represents the number of grid cells in G,

denotes the jth grid cell G in G_jJ is more than or equal to 1 and less than or equal to num (G);

2.3 statistics of grid cells G in the set G of grid cells to be covered₁，...，g_j，...g_num(G)Storing the oblique adjacent grid cell to g₁，...，g_j，...g_num(G)Set of diagonally adjacent grid cells

Wherein the content of the first and second substances,

denotes g_jThe diagonal adjacent grid cell set;

2.4 according to the rule that the unmanned aerial vehicle moves from the grid cell where the current position is located to the directly adjacent grid cell, calculating the shortest distance from each grid cell to be covered to the starting point S in G, namely G₁，...，g_j，...g_num(G)The minimum number of grid cells that need to be passed to S is recorded as

Obtaining the shortest distance set dis from the grid unit to be covered to the starting point

Wherein the content of the first and second substances,

denotes g_jThe shortest distance to S; the unmanned aerial vehicle moves from the grid cell where the current position is located to the directly adjacent grid cell according to the movement rule, and cannot directly reach the obliquely adjacent grid cell of the grid cell where the current position is located;

thirdly, calculating a flight path set P of the unmanned aerial vehicle by adopting a shadow following method; p is composed of the path from the drone to the starting point every round trip, i.e. P ═ P₁，...，p_i，...p_N}；p_iThe path from the starting point to the starting point after the unmanned aerial vehicle starts from the starting point for the ith time and executes the covering task is shown, N shows the total times of reciprocating the starting point when the unmanned aerial vehicle completely covers the target area, and i is more than or equal to 1 and less than or equal to N; p is a radical of_iConsisting of grid cells traversed by the unmanned aerial vehicle during flight, i.e.

Wherein, g_imRepresents p_iM-th grid cell of (1), num (p)_i) Represents p_iThe total number of middle grid cells; the unmanned plane completely covers the target area after N times of starting points, namely p₁∪...∪p_i∪...∪p_NG; updating a shadow path while calculating a target grid unit, and representing the limited airborne energy of the unmanned aerial vehicle by using a limited flight distance D; d is converted into the maximum flying grid unit number B of the unmanned aerial vehicle through the grid unit side length R, so that the requirement of

The method for calculating P by adopting the shadow following method comprises the following steps:

3.1 starting the unmanned aerial vehicle from a starting point, namely initializing the position of a current grid unit g of the unmanned aerial vehicle to be S; initializing a flight path set P { } of the unmanned aerial vehicle; initializing the number i of times that the unmanned aerial vehicle returns to the starting point to be 1; let path p traverse the starting point the ith time_iThe unmanned plane starts from the starting point grid unit; let shadow path p_wThe unmanned plane returns to the starting point grid unit along the shadow path; initializing all grid cells in G to be in an uncovered state, and setting the state (G) of the current grid cell G to be in a covered state, namely, making the state (G) be covered; initializing remaining flight capabilities B of the drone_rest＝B；

3.2 if grid cells in an uncovered state exist in the G, turning to the step 3.3; otherwise, the target area is completely covered, and the step 3.6 is carried out;

3.3 according to the position of the current grid cell g of the unmanned aerial vehicle, the coverage state of the target area and the information of the obstacles, calculating the grid cell g of the unmanned aerial vehicle going to next step_nextThe position of (a);

3.4 according to g_nextFinding an updated value for a shadow path

is to consider the shadow path update values of the surrounding grid cells;

3.5 remaining flight capability B according to unmanned aerial vehicle_restUpdating the position of the current grid cell g of the drone and the shadow path p_wThe method comprises the following steps:

Go back to the starting point, i.e. satisfy

Updating the remaining flight capacity of the drone, i.e. commandingB_rest＝B_rest-len(g，g_next) (ii) a Updating the unmanned aerial vehicle to move from the grid unit where the current position is located to the target grid unit, namely, making g equal to g_next(ii) a Updating the grid unit where the current position of the unmanned aerial vehicle is located to be in a coverage state, namely, commanding state (g) to be covered; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell; update the shadow path to

Returning to the starting point, and turning to the step 3.5.2; said len (g, g)_next) Indicating the grid cell g from which the current position is located to the target grid cell g_nextThe shortest distance of the first and second electrodes,

representing the slave target grid cell g_nextTo

Last grid cell of

The shortest distance of the first and second electrodes,

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (d);

Go back to the starting point, i.e. satisfy

Updating the remaining flight capacity of the drone, i.e. order B_rest＝B_rest-len(g，g_next) (ii) a The unmanned aerial vehicle moves from the grid unit where the current position is located to the target grid unit, namely, g is set as g_next(ii) a Updating the grid unit where the current position of the unmanned aerial vehicle is located to be in a covered state, namely, enabling state (g) to be covered; adding the grid unit g where the current position of the unmanned aerial vehicle is located into the path p of the ith round-trip starting point_iBehind the last grid cell of (a); update the shadow path to

Returning to the starting point, turning to step 3.5.3; the above-mentioned

Indicating the grid cell g from the current position_nextTo

Last grid cell of

The shortest distance of (d);

represents from

Last grid cell of

Through

Of a grid cell to

First grid cell of

The shortest distance of (d);

3.5.3 at this time, the remaining flight energy of the unmanned aerial vehicle is not enough to support the unmanned aerial vehicle to continue to advance to execute the covering task, and the unmanned aerial vehicle follows the shadow path p_wReturning to the starting point to supplement energy, the method comprises the following steps: p is to be_wThe grid cells in (1) are added to the path p of the ith round-trip starting point from back to front in sequence_iAnd setting each added grid cell to a covered state; after the unmanned aerial vehicle returns to the starting point, the path index value i is updated to i +1, and the ith path and the shadow path are initialized to p_i＝{g}，p_w-g; the remaining flight capacity of the unmanned plane at the starting point is equal to the maximum flying grid cell number B_restTurning to step 3.5.4 when the result is B;

3.5.4 if the surrounding grid cell with some group of obstacles in the surrounding grid cell set Sur is in a covering state, deleting the group of surrounding grid cells from Sur, and going to the step 3.2;

3.6 the target area is completely covered, the number of times N of the starting point of the single unmanned aerial vehicle is obtained, the number is i, and the covering path is stored as P, P₁，...，p_i，...，p_N}，1≤i≤N；

Fourthly, outputting the times N of the unmanned aerial vehicle to return the starting point and a flight path P for executing the covering task, wherein the unmanned aerial vehicle follows the path in the flight path P and follows the secondary path P₁To p_NThe order of execution of the overlay tasks.

2. The shadow following single unmanned aerial vehicle area coverage path planning method of claim 1, wherein the side length of the grid unit

h is the flying height of the unmanned aerial vehicle, and alpha is the visual field range of the airborne camera on the unmanned aerial vehicle.

3. The shadow following single unmanned aerial vehicle area coverage path planning method according to claim 1, wherein 2.1 steps of the method are based on an internal obstacle set M_eThe pair of connection relations M between the grid cells in (1)_eThe method for grouping the grid cells in the system, respectively calculating the surrounding grid of each group of internal obstacle grid cells and sequencing the surrounding grids in the clockwise direction comprises the following steps:

2.1.1 mixing M_eThe grid cells with the connection relation are divided into one group, and the grid cells among different groups do not have any connection relation; let M_eIs divided into K groups, and K is a positive integer;

2.1.2 initializing index value k is 1;

2.1.3 according to the connection relation of the grid units, finding out the directly adjacent and obliquely adjacent grid units of each grid unit in the k group of internal obstacle grid units, and storing the directly adjacent and obliquely adjacent grid units to the k group of surrounding grid set Sur_kAnd from the set Sur_kDelete the obstacle grid cell; set Sur at this time_kThe grid cells in (1) are surrounding grids of the kth group of internal barrier grids;

2.1.4 according to Sur_kThe positions of the middle grid cells are from bottom to top and from left to right to Sun_kThe grid cells in (1) are sorted and numbered; the grid cell number value at the lower left corner is the smallest; rearranging Sur in ascending order according to numbering value_kA grid cell of (1);

2.1.5 initializing ordered set order { }, initializing grid unit record stack { }, and setting current grid unit position g ═ Sur { }_k[1]I.e. with Sur_kTaking the grid unit with the minimum middle number value as a traversal starting point;

2.1.6 finding all grid cells directly adjacent to G from the set G of grid cells to be covered, locating the found grid cells directly adjacent to G in Sun_kThe grid cell in (a) is saved to a set ad of grid cells directly adjacent to (g)_g；

2.1.7 if ad_gThe grid cells are found in the grid cell, and the step 2.1.8 is carried out; otherwise, G is not directly adjacent to G and is located at Sur_kGo to step 2.1.13;

2.1.8 if ad_gWith only one grid cell, put g to the end of order, from Sur_kDeleting g, when g equals ad_gThe only grid unit in the step (2) is turned to the step (2.1.6); if ad_gTurning to step 2.1.9;

2.1.9 if g is at the traversal start, put g to the end of order, from Sur_kDeleting g, when g equals ad_gThe grid unit with the minimum number value in the middle number is turned to the step 2.1.6; if g is not located at the traversal starting point, turning to the step 2.1.10;

2.1.10 Slave ad_gIn which a grid cell having the same immediate adjacent obstacle grid cell as the last grid cell in the order is selected, denoted g_next；

2.1.11 if g_nextPressing g into the stack top of the stack, and turning to step 2.1.12, wherein the number of barrier grid cells in the directly adjacent grid cells is more than or equal to 2; if g is_nextThe number of the barrier grid cells in the directly adjacent grid cells is less than 2, and the step 2.1.12 is directly carried out;

2.1.13 checking stack information; if no grid cell is stored in the stack, it indicates that the traversal of the surrounding grid cells of the current group of internal obstacles is finished, and go to step 2.1.14; if the stack has grid cells, making g equal to the grid cells at the top of the stack, deleting the grid cells of the stack items, and turning to the step 2.1.6;

2.1.14 order Sur_kGet sure ═ order, get sure_kSaving the data to a surrounding grid set Sun, and updating an index value k to be k + 1; if K is larger than K, all the surrounding grid units are traversed and sorted, and sum is obtained as { sum ═ sum₁，...，Sur_k，...，Sur_KK is more than or equal to 1 and less than or equal to K, and ending; otherwise, go to step 2.1.3.

4. The shadow following single unmanned aerial vehicle area coverage path planning method according to claim 1, wherein the third step requires that distances from all grid cells to be covered to S do not exceed 2B when calculating the flight path set P of the unmanned aerial vehicle by using the shadow following method.

5. The shadow following single unmanned aerial vehicle area coverage path planning method according to claim 1, wherein 3.3 steps of calculating the grid cell g of the unmanned aerial vehicle going to next step according to the position of the current grid cell g of the unmanned aerial vehicle, the coverage state of the target area and the obstacle information_nextThe position method comprises the following steps:

3.3.1 find all grid cells in G that are directly adjacent to G and in an uncovered state, and save to the set of directly adjacent grid cells ad_g；

3.3.2 if ad_gIf the grid cell is an empty set, all grid cells in G with the shortest distance to G and in an uncovered state are found and stored to ad_g；

3.3.3 if ad_gOnly one grid cell in the grid list, the grid cellTarget grid cell g with Yuan as unmanned aerial vehicle_nextAnd ending; if ad_gA plurality of grid cells are arranged in the grid cell, and the step 3.3.4 is carried out;

3.3.4 finding ad_gThe distance from the middle grid cell to the starting point S; the shorter the distance, the higher the priority of the grid cell; the distances are equal, and the priorities of the grid cells are the same; will ad_gDeleting the grid cells with the medium-low priority, and only keeping the grid cells with the highest priority; if ad_gIf there is only one grid cell, the grid cell is used as the target grid cell g of the unmanned plane_nextAnd ending; if ad_gA plurality of grid units with the highest priority are arranged in the grid structure, and the step 3.3.5 is carried out;

3.3.5 calculating ad_gOf the directly adjacent grid cells of each grid cell, located in G and being the sum of the number of covered grid cells and obstacle grid cells; ad (cell-bone growth promoting)_gThe greater the number of covered grid cells and obstacle grid cells around the middle grid cell, the more ads_gThe higher the priority of the middle grid cell; equal number, ad_gThe priorities of the middle grid cells are the same; ad (cell-bone growth promoting)_gOnly the grid cell with the highest priority is reserved; if ad_gIn which there is only one grid cell, set that grid cell to g_nextAnd ending; if ad_gA plurality of grid units with the highest priority are still arranged in the grid cell group, and the step 3.3.6 is carried out;

3.3.6 according to path p_iThe last grid cell in (b) gets the last covered grid cell p_i(end) connecting g and p_i(end) forming a line segment, and making an extension line along the line segment from g to the outside, namely the direction opposite to the line segment, wherein the extension line is a ray taking g as a starting point; rotating the extension line clockwise by taking the g as a center and the direction of the extension line as an initial direction; according to the extension line and ad_gGiven ad in the order of grid cell intersection in_gThe grid cell ordering in (1); extension line and ad_gThe earlier the grid cells in (A) intersect, then ad_gThe higher the priority of the grid cell in (b); fetching ad_gThe grid cell with the highest medium priority is used as g_nextAnd then, the process is ended.

6. The shadow following single unmanned aerial vehicle area coverage path planning method of claim 5, wherein 3.3.2 steps of finding all grid cells in G with shortest distance to G and in uncovered state, and storing to ad_gThe method comprises the following steps:

3.3.2.1, calculating the distance from the grid cell in G to G by: the distance from the grid unit where g is located to the grid unit is equal to 0, and the mark g is 0; the distance from the grid cell directly adjacent to g and not an obstacle to g is equal to 1, and the grid cell marked directly adjacent to g and not an obstacle is 1; traversing the directly adjacent grid cells of the grid cell marked 1, and adding one to the mark value of the grid cell which is not an obstacle and is not marked, namely the distance from the grid cell to g is equal to 2; marking all grid cells in G according to the breadth-first thought to obtain the distance from all grid cells in G to G;

3.3.2.2 if ad_gFor the empty set, starting from the grid cells with the distance to G equal to 2 in G, and searching the grid cells in the uncovered state in G according to the sequence of the distance to G from small to large; when a first uncovered grid cell in the G is found, recording the distance between the found first uncovered grid cell and the G as dis;

7. The shadow following single unmanned aerial vehicle area coverage path planning method according to claim 1, wherein 3.4 steps of 3.4 steps are according to g_nextFinding an updated value for a shadow path_{pwnext1，pw_next2}The method comprises the following steps:

3.4.1 initialization regardless of the shadow path update values surrounding the grid cell_pw_next1＝pw_；

3.4.2 if

In which g is contained_nextDeletion of

The last grid unit of (3) goes to the step 3.4.3; otherwise, turning to the step 3.4.4;

3.4.3 if

Does not contain g_nextTurning to the step 3.4.4; otherwise, go to step 3.4.2;

3.4.4 if

Last grid cell of

And g_nextDirectly adjacent, go to step 3.4.8; if it is

And g_nextNot directly adjacent, and turning to the step 3.4.5;

If it is

Go to step 3.4.9 if there is no grid cell; if it is

And only one grid cell, will

Put the grid cells in

In the last grid cell

Then go to step 3.4.9; if it is

If a plurality of grid units meeting the conditions exist, turning to the step 3.4.6;

3.4.6 calculation

Grid cells of (1) to

Last grid cell of

The distance of (d); the shorter the distance is,

the grid cell priorities in (1) are the same; deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority; if it is

Only one grid cell in the grid array, then put the grid cell into

Then go to step 3.4.9; if not, then,

the step 3.4.7 is carried out when a plurality of grid units with the highest priority exist;

3.4.7 calculation

The distance of the grid cell of (1) to S; the further away the distance is from the ground,

the higher the grid cell priority in (1); deleting

Grid cells of medium to low priority, reserved only

The grid cell with the highest medium priority; if it is

Has only one grid cell, and places the grid cell into

Then go to step 3.4.9; otherwise, go to step 3.4.8;

3.4.8 connecting g and g_nextComposing a line segment and following the line segment from g_nextAn extension line is made in the direction opposite to the line segment and is g_nextA ray as a starting point; in g_nextThe direction of the extension line is the starting direction, and the extension line is rotated clockwise; according to an extension line and