CN106444773B - An Environmental Modeling Method Based on Recursively Simplified Visual Graph - Google Patents

An Environmental Modeling Method Based on Recursively Simplified Visual Graph Download PDF

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CN106444773B
CN106444773B CN201610938679.8A CN201610938679A CN106444773B CN 106444773 B CN106444773 B CN 106444773B CN 201610938679 A CN201610938679 A CN 201610938679A CN 106444773 B CN106444773 B CN 106444773B
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吴振宇
聂政
李胜铭
李航
冯林
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Abstract

The invention relates to an environment modeling method, in particular to an environment modeling method based on recursion simplified visual, which comprises the following steps: (1) recording the position of the robot and the arrival position, (2) connecting S-H-G-L-S to form A quadrangle, (3) traversing each current side of the quadrangle, (4) judging whether the current side is intersected with the obstacle, (5) determining A midway point, (6) transferring each side of the newly enclosed polygon S-A-H-B-G-L-C-S to the step 3 for traversing, and (7) finishing the traversing of the current side of the polygon. The invention finally obtains a polygonal area, the obstacles outside the polygonal area can be completely simplified, and the obstacles in the polygonal area are the obstacles to be considered in the robot path planning. The invention effectively reduces the number of visual lines and improves the execution efficiency of the subsequent robot path planning algorithm.

Description

一种基于递归简化可视图的环境建模方法An Environmental Modeling Method Based on Recursively Simplified Visual Graph

技术领域technical field

本发明涉及一种环境建模方法,更具体地说,涉及一种基于递归简化可视图的环境建模方法。The invention relates to an environment modeling method, in particular to an environment modeling method based on recursively simplified visual graphs.

背景技术Background technique

移动机器人在一个存在多个障碍物的环境下移动时,就需要找出一条可以避开所有障碍物的由起点到终点的最优路径,比如路径最短,耗时最少,能耗最低。为了解决个问题,移动机器人在进行路径规划时,一般需要先对环境进行建模,已有的环境建模主要有:栅格图、切线图、Voronoi图、概率图和可视图等。When a mobile robot moves in an environment with multiple obstacles, it needs to find an optimal path from the start point to the end point that can avoid all obstacles, such as the shortest path, the least time-consuming, and the lowest energy consumption. In order to solve this problem, mobile robots generally need to model the environment first when performing path planning. The existing environment modeling mainly includes: grid graph, tangent graph, Voronoi graph, probability graph, and visual graph.

基于可视图的建模方法将环境中的障碍物通过凸多边形包络表示,多边形的顶点连同移动机器人的起点和终点一起被看成质点,每个点的坐标在全局坐标系中作为已知,将起点和终点以及障碍物多边形的顶点进行可视化判断:如果两点连线组成的线段不与任何障碍物多边形相交,则称两点可视,该线段称为可视线。由于可视图具有简单直观的特性,基于可视图的建模方法成为了众多学者关注的热点。The modeling method based on the visual graph represents the obstacles in the environment by a convex polygonal envelope. The vertices of the polygon, together with the starting point and end point of the mobile robot, are regarded as mass points. The coordinates of each point are known in the global coordinate system. Visually judge the start point and end point and the vertices of the obstacle polygon: if the line segment formed by the two-point connection does not intersect any obstacle polygon, then the two points are said to be visible, and the line segment is called the visible line. Due to the simple and intuitive characteristics of visual graphs, the modeling method based on visual graphs has become a hot spot that many scholars pay attention to.

目前可视图简化的主要方法有两种,一个是Huang提出的动态可视图方法,它可以精简部分“冗余”的障碍物;另一个是改进的动态可视图法,由张琦提出,称之为简化可视图法,该方法通过设计必要的障碍物规则,可以更大限度的剔除无关障碍物。然而简化可视图法存在这样一个问题,即在复杂环境下可能出现错误简化障碍物的问题。At present, there are two main methods of visual map simplification, one is the dynamic visual map method proposed by Huang, which can simplify some "redundant" obstacles; the other is the improved dynamic visual map method, proposed by Zhang Qi, called In order to simplify the visualization method, this method can eliminate irrelevant obstacles to a greater extent by designing necessary obstacle rules. However, there is a problem in the simplified visualization method, that is, the problem of wrongly simplifying obstacles may occur in complex environments.

发明内容Contents of the invention

为了克服现有技术中存在的不足,本发明目的是提供一种基于递归简化可视图的环境建模方法。通过本发明提供的方法,最后可以得到一个多边形区域,该区域外的障碍物可以全部简化掉,区域内的才是机器人路径规划需要考虑的障碍物。本发明有效的减少可视线的数量,提高了后续机器人路径规划算法的执行效率。In order to overcome the deficiencies in the prior art, the purpose of the present invention is to provide an environment modeling method based on recursively simplified visual graphs. Through the method provided by the present invention, a polygonal area can be finally obtained, and all obstacles outside the area can be simplified, and the obstacles in the area are the obstacles that need to be considered in the path planning of the robot. The invention effectively reduces the number of visible lines and improves the execution efficiency of the follow-up robot path planning algorithm.

为了实现上述发明目的,解决现有技术中所存在的问题,本发明采取的技术方案是:一种基于递归简化可视图的环境建模方法,包括以下步骤:In order to achieve the above-mentioned purpose of the invention and solve the problems existing in the prior art, the technical solution adopted by the present invention is: an environment modeling method based on recursively simplified visual graphs, including the following steps:

步骤1、记录机器人所在及到达位置,将机器人所在的位置记为点S,期望到达的位置记为点G,再将机器人所处的整个地图环境采用计算机进行扫描,并采用封闭多边形对每个障碍物进行包络,保留这些多边形;Step 1. Record the location and arrival position of the robot, record the location of the robot as point S, and record the expected arrival position as point G, and then use the computer to scan the entire map environment where the robot is located, and use a closed polygon to map each Obstacles are enveloped and these polygons are preserved;

步骤2、连接S-H-G-L-S构成一个四边形,连接点S和点G,线段SG称为机器人穿越线,此时穿越线SG会与多个障碍物多边形相交,记录这些相交的障碍物多边形2、7、8,随后在穿越线SG的两侧,分别找到一个点,该点必需满足以下两个条件:其一,是这些相交的障碍物多边形2、7、8中的一个顶点,其二,在穿越线SG的一侧范围内该点距离穿越线最远,并分别记为点H和点L,连接S-H-G-L-S构成一个四边形;Step 2. Connect S-H-G-L-S to form a quadrilateral, connect point S and point G, and the line segment SG is called the robot crossing line. At this time, the crossing line SG will intersect with multiple obstacle polygons, and record these intersecting obstacle polygons 2, 7, and 8 , and then find a point on both sides of the crossing line SG, which must meet the following two conditions: first, it is a vertex of these intersecting obstacle polygons 2, 7, 8, and second, it is on the crossing line The point on one side of SG is the farthest from the crossing line, and is recorded as point H and point L respectively, connecting S-H-G-L-S to form a quadrilateral;

步骤3、遍历该四边形的每条当前边,即当前边SH、HG、GL、LS,每条当前边的端点分别为当前边起点和当前边终点,例如遍历到当前边HG时,当前边起点就是点H,当前边终点就是点G;Step 3. Traverse each current side of the quadrilateral, i.e. the current sides SH, HG, GL, LS. The endpoints of each current side are the current side starting point and the current side end point respectively. For example, when traversing to the current side HG, the current side starting point It is point H, and the end point of the current side is point G;

步骤4、判断当前边是否与障碍物相交,若不相交,例如当前边GL,则将该当前边保存至活动区域集中,然后返回至步骤3继续遍历后续的当前边,当遍历完成时则跳转至步骤7;若相交,例如当前边SH、HG、LS,则跳转至步骤5;Step 4. Determine whether the current edge intersects with obstacles. If it does not intersect, such as the current edge GL, save the current edge to the active area set, and then return to step 3 to continue traversing the subsequent current edges. When the traversal is completed, skip Go to step 7; if they intersect, such as the current edge SH, HG, LS, then go to step 5;

步骤5、确定中途点,在与当前边相交的所有障碍物中,取这些障碍物中离穿越线SG最远且与当前边同一侧的顶点,记为中途点A、B、C,分别连接当前边起点和中途点,中途点和当前边终点,形成2条新的当前边;例如原来的当前边SH由当前边起点S连接中途点A、再由中途点A连接当前边终点H形成由SA与AH两条边组成现在的当前边:例如原来的当前边HG由当前边起点H连接中途点B、再由中途点B连接当前边终点G形成由HB与BG两条边组成现在的当前边;例如原来的当前边LS由当前边起点L连接中途点C、再由中途点C连接当前边终点S 形成由LC与CS两条边组成现在的当前边;Step 5. Determine the halfway point. Among all the obstacles intersecting with the current side, take the vertex of these obstacles that is farthest from the crossing line SG and on the same side as the current side, and record it as the halfway point A, B, C, and connect them respectively The starting point of the current edge and the halfway point, the halfway point and the end point of the current edge form two new current edges; for example, the original current edge SH is formed by connecting the starting point S of the current edge to the intermediate point A, and then connecting the intermediate point A to the end point H of the current edge. Two sides SA and AH form the current current side: for example, the original current side HG connects the starting point H of the current side to the midway point B, and then connects the midway point B to the end point G of the current side to form the current current side composed of two sides HB and BG Side; for example, the original current side LS is connected by the starting point L of the current side to the midway point C, and then the midway point C is connected to the end point S of the current side to form the current current side composed of two sides LC and CS;

步骤6、将现在新围成的多边形S-A-H-B-G-L-C-S的各条边转至步骤3进行遍历;Step 6, transfer each edge of the newly formed polygon S-A-H-B-G-L-C-S to step 3 for traversal;

步骤7、多边形当前边遍历完毕,活动区域集中所有的边所围成的多边形即为输出结果,活动区域外的障碍物多边形1、3、10、11不需要考虑,而活动区域内的障碍物多边形2、4、5、6、7、8、9就是机器人在路径规划时需要考虑的。Step 7. After traversing the current sides of the polygon, the polygon surrounded by all the sides in the active area set is the output result. The obstacle polygons 1, 3, 10, and 11 outside the active area do not need to be considered, while the obstacles in the active area Polygons 2, 4, 5, 6, 7, 8, and 9 are what the robot needs to consider when planning its path.

本发明有益效果是:一种基于递归简化可视图的环境建模方法,包括以下步骤:(1)记录机器人所在及到达位置,(2)连接S-H-G-L-S构成一个四边形(3)遍历该四边形的每条当前边,(4)判断当前边是否与障碍物相交,(5)确定中途点,(6)将现在新围成的多边形S-A-H-B-G-L-C-S的各条边转至步骤3进行遍历,(7)多边形当前边遍历完毕。与已有技术相比,本发明最后得到一个多边形区域,该区域外的障碍物可以全部简化掉,区域内的才是机器人路径规划需要考虑的障碍物。本发明有效的减少可视线的数量,提高了后续机器人路径规划算法的执行效率。The beneficial effects of the present invention are: an environment modeling method based on recursively simplified visual graphs, comprising the following steps: (1) recording where the robot is and its arrival position, (2) connecting S-H-G-L-S to form a quadrilateral (3) traversing each of the quadrilateral On the current side, (4) judge whether the current side intersects with obstacles, (5) determine the halfway point, (6) turn each side of the newly formed polygon S-A-H-B-G-L-C-S to step 3 for traversal, (7) the current side of the polygon The traversal is complete. Compared with the prior art, the present invention finally obtains a polygonal area, all obstacles outside the area can be simplified, and the obstacles in the area are the obstacles that need to be considered in the path planning of the robot. The invention effectively reduces the number of visible lines and improves the execution efficiency of the follow-up robot path planning algorithm.

附图说明Description of drawings

图1为本发明方法步骤流程图。Fig. 1 is a flowchart of the method steps of the present invention.

图2为本发明方法中步骤2所生成的可视图。Fig. 2 is a visual diagram generated in step 2 of the method of the present invention.

图3为本发明方法递归的第1层生成的可视图。Fig. 3 is a visual diagram generated by the first layer of recursion in the method of the present invention.

图4为本发明方法递归的第2层生成的可视图。Fig. 4 is a visual diagram generated by the second layer of recursion in the method of the present invention.

图5为本发明方法递归的第3层生成的可视图。Fig. 5 is a visual diagram generated by the third layer of recursion in the method of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明作进一步说明。The present invention will be further described below in conjunction with accompanying drawing.

如图1所示,一种基于递归简化可视图的环境建模方法,包括以下步骤:As shown in Figure 1, an environment modeling method based on recursively simplified visual graphs includes the following steps:

步骤1、记录机器人所在及到达位置,将机器人所在的位置记为点S,期望到达的位置记为点G,再将机器人所处的整个地图环境采用计算机进行扫描,并采用封闭多边形对每个障碍物进行包络,保留这些多边形;Step 1. Record the location and arrival position of the robot, record the location of the robot as point S, and record the expected arrival position as point G, and then use the computer to scan the entire map environment where the robot is located, and use a closed polygon to map each Obstacles are enveloped and these polygons are preserved;

步骤2、连接S-H-G-L-S构成一个四边形,连接点S和点G,线段SG称为机器人穿越线,此时穿越线SG会与多个障碍物多边形相交,记录这些相交的障碍物多边形2、7、8,随后在穿越线SG的两侧,分别找到一个点,该点必需满足以下两个条件:其一,是这些相交的障碍物多边形2、7、8中的一个顶点,其二,在穿越线SG的一侧范围内该点距离穿越线最远,并分别记为点H和点L,连接S-H-G-L-S构成一个四边形;Step 2. Connect S-H-G-L-S to form a quadrilateral, connect point S and point G, and the line segment SG is called the robot crossing line. At this time, the crossing line SG will intersect with multiple obstacle polygons, and record these intersecting obstacle polygons 2, 7, and 8 , and then find a point on both sides of the crossing line SG, which must meet the following two conditions: first, it is a vertex of these intersecting obstacle polygons 2, 7, 8, and second, it is on the crossing line The point on one side of SG is the farthest from the crossing line, and is recorded as point H and point L respectively, connecting S-H-G-L-S to form a quadrilateral;

步骤3、遍历该四边形的每条当前边,即当前边SH、HG、GL、LS,每条当前边的端点分别为当前边起点和当前边终点,例如遍历到当前边HG时,当前边起点就是点H,当前边终点就是点G;Step 3. Traverse each current side of the quadrilateral, i.e. the current sides SH, HG, GL, LS. The endpoints of each current side are the current side starting point and the current side end point respectively. For example, when traversing to the current side HG, the current side starting point It is point H, and the end point of the current side is point G;

步骤4、判断当前边是否与障碍物相交,若不相交,例如当前边GL,则将该当前边保存至活动区域集中,然后返回至步骤3继续遍历后续的当前边,当遍历完成时则跳转至步骤7;若相交,例如当前边SH、HG、LS,则跳转至步骤5;Step 4. Determine whether the current edge intersects with obstacles. If it does not intersect, such as the current edge GL, save the current edge to the active area set, and then return to step 3 to continue traversing the subsequent current edges. When the traversal is completed, skip Go to step 7; if they intersect, such as the current edge SH, HG, LS, then go to step 5;

步骤5、确定中途点,在与当前边相交的所有障碍物中,取这些障碍物中离穿越线SG最远且与当前边同一侧的顶点,记为中途点A、B、C,分别连接当前边起点和中途点,中途点和当前边终点,形成2条新的当前边;例如原来的当前边SH由当前边起点S连接中途点A、再由中途点A连接当前边终点H形成由SA与AH两条边组成现在的当前边:例如原来的当前边HG由当前边起点H连接中途点B、再由中途点B连接当前边终点G形成由HB与BG两条边组成现在的当前边;例如原来的当前边LS由当前边起点L连接中途点C、再由中途点C连接当前边终点S形成由LC与CS两条边组成现在的当前边;Step 5. Determine the halfway point. Among all the obstacles intersecting with the current side, take the vertex of these obstacles that is farthest from the crossing line SG and on the same side as the current side, and record it as the halfway point A, B, C, and connect them respectively The starting point of the current edge and the halfway point, the halfway point and the end point of the current edge form two new current edges; for example, the original current edge SH is formed by connecting the starting point S of the current edge to the intermediate point A, and then connecting the intermediate point A to the end point H of the current edge. Two sides SA and AH form the current current side: for example, the original current side HG connects the starting point H of the current side to the midway point B, and then connects the midway point B to the end point G of the current side to form the current current side composed of two sides HB and BG Side; for example, the original current side LS connects the starting point L of the current side to the midway point C, and then connects the midway point C to the end point S of the current side to form the current current side composed of two sides LC and CS;

步骤6、将现在新围成的多边形S-A-H-B-G-L-C-S的各条边转至步骤3进行遍历;Step 6, transfer each edge of the newly formed polygon S-A-H-B-G-L-C-S to step 3 for traversal;

步骤7、多边形当前边遍历完毕,活动区域集中所有的边所围成的多边形即为输出结果,活动区域外的障碍物多边形1、3、10、11不需要考虑,而活动区域内的障碍物多边形2、4、5、6、7、8、9就是机器人在路径规划时需要考虑的。Step 7. After traversing the current sides of the polygon, the polygon surrounded by all the sides in the active area set is the output result. The obstacle polygons 1, 3, 10, and 11 outside the active area do not need to be considered, while the obstacles in the active area Polygons 2, 4, 5, 6, 7, 8, and 9 are what the robot needs to consider when planning its path.

具体工作过程如下:The specific working process is as follows:

本发明采用的伪代码如表1所示,其中包含了主函数和递归核函数。The pseudo-code used in the present invention is shown in Table 1, which includes a main function and a recursive kernel function.

表1Table 1

主函数是本发明的程序入口,通过给定的起点S和终点G,由函数getLine得到穿越线line_sg,再由函数getObsPass得到与穿越线相交的障碍物集合obs_pass,以函数getHighPoint和getLowPoint计算出在line_sg两侧,距离line_sg最远的且被line_sg穿过的障碍物顶点high(点H)和low(点L),连接S-H-G-L-S,即可得到图2中的可视图,黑色色块为障碍物多边形,虚线为当前的活动区域边界。然后,通过调用递归核函数,可以分别算出S-H-G-L-S的各条边演化出的活动区域的边界线,其中getMidPoint函数是求出距离穿越线最远的一侧属于被line_sg所穿过的障碍物的顶点。递归第1层形成的可视图如图3所示,递归第2层形成的可视图如图4所示,递归第3层形成的可视图如图5所示。最终,程序递归至第三层就结束,活动区域的边界线保存在线集合activeRegion中,形成的最终可视图如图5所示。The main function is the program entry of the present invention. Through the given starting point S and end point G, the crossing line line_sg is obtained by the function getLine, and the obstacle set obs_pass intersecting with the crossing line is obtained by the function getObsPass, and the crossing line is obtained by the function getHighPoint and getLowPoint. On both sides of line_sg, the obstacle vertices high (point H) and low (point L) that are farthest from line_sg and passed by line_sg, connect S-H-G-L-S, and you can get the visible view in Figure 2. The black color block is the obstacle polygon , the dotted line is the boundary of the current active area. Then, by calling the recursive kernel function, the boundary line of the active area evolved from each side of S-H-G-L-S can be calculated respectively, and the getMidPoint function is to find the vertex of the obstacle that is the farthest side from the line_sg. . The visible view formed by the first layer of recursion is shown in Figure 3, the visible view formed by the second layer of recursion is shown in Figure 4, and the visible view formed by the third layer of recursion is shown in Figure 5. Finally, the program ends when it recurses to the third layer, and the boundary line of the active region is saved in the online collection activeRegion, and the final visible view formed is shown in Figure 5.

图5中,活动区域外的障碍物(1、3、10、11)在后续路径规划中将会被简化掉,不需要考虑,而活动区域内的障碍物(2、4、5、6、7、8、9)就是机器人在路径规划时需要考虑的。In Figure 5, the obstacles (1, 3, 10, 11) outside the active area will be simplified in the subsequent path planning and do not need to be considered, while the obstacles (2, 4, 5, 6, 7, 8, 9) are what the robot needs to consider when planning the path.

Claims (1)

1.一种基于递归简化可视图的环境建模方法,包括以下步骤:1. A method for modeling environments based on recursively simplified visual graphs, comprising the following steps: 步骤1、记录机器人所在及到达位置,将机器人所在的位置记为点S,期望到达的位置记为点G,再将机器人所处的整个地图环境采用计算机进行扫描,并采用封闭多边形对每个障碍物进行包络,保留这些多边形;Step 1. Record the location and arrival position of the robot, record the location of the robot as point S, and record the expected arrival position as point G, and then use the computer to scan the entire map environment where the robot is located, and use a closed polygon to map each Obstacles are enveloped and these polygons are preserved; 步骤2、连接S-H-G-L-S构成一个四边形,连接点S和点G,线段SG称为机器人穿越线,此时穿越线SG会与多个障碍物多边形相交,记录这些相交的障碍物多边形2、7、8,随后在穿越线SG的两侧,分别找到一个点,该点必需满足以下两个条件:其一,是这些相交的障碍物多边形2、7、8中的一个顶点,其二,在穿越线SG的一侧范围内该点距离穿越线最远,并分别记为点H和点L,连接S-H-G-L-S构成一个四边形,其特征在于:Step 2. Connect S-H-G-L-S to form a quadrilateral, connect point S and point G, and the line segment SG is called the robot crossing line. At this time, the crossing line SG will intersect with multiple obstacle polygons, and record these intersecting obstacle polygons 2, 7, and 8 , and then find a point on both sides of the crossing line SG, which must meet the following two conditions: first, it is a vertex of these intersecting obstacle polygons 2, 7, 8, and second, it is on the crossing line Within the range of one side of SG, this point is the farthest from the crossing line, and is recorded as point H and point L respectively, connecting S-H-G-L-S to form a quadrilateral, which is characterized in that: 步骤3、遍历该四边形的每条当前边,即当前边SH、HG、GL、LS,每条当前边的端点分别为当前边起点和当前边终点,遍历到当前边HG时,当前边起点就是点H,当前边终点就是点G;Step 3. Traverse each current side of the quadrilateral, that is, the current sides SH, HG, GL, and LS. The endpoints of each current side are the current side starting point and the current side end point respectively. When traversing to the current side HG, the current side starting point is Point H, the end point of the current side is point G; 步骤4、判断当前边是否与障碍物相交,若不相交,即当前边GL,则将该当前边保存至活动区域集中,然后返回至步骤3继续遍历后续的当前边,当遍历完成时则跳转至步骤7;若相交,即当前边SH、HG、LS,则跳转至步骤5;Step 4. Determine whether the current edge intersects with obstacles. If it does not intersect, that is, the current edge GL, save the current edge to the active area set, and then return to step 3 to continue traversing the subsequent current edges. When the traversal is completed, skip Go to step 7; if it intersects, that is, the current edge SH, HG, LS, then go to step 5; 步骤5、确定中途点,在与当前边相交的所有障碍物中,取这些障碍物中离穿越线SG最远且与当前边同一侧的顶点,记为中途点A、B、C,分别连接当前边起点和中途点,中途点和当前边终点,形成2条新的当前边;原来的当前边SH由当前边起点S连接中途点A、再由中途点A连接当前边终点H形成由SA与AH两条边组成现在的当前边:原来的当前边HG由当前边起点H连接中途点B、再由中途点B连接当前边终点G形成由HB与BG两条边组成现在的当前边;原来的当前边LS由当前边起点L连接中途点C、再由中途点C连接当前边终点S形成由LC与CS两条边组成现在的当前边;Step 5. Determine the halfway point. Among all the obstacles intersecting with the current side, take the vertex of these obstacles that is farthest from the crossing line SG and on the same side as the current side, and record it as the halfway point A, B, C, and connect them respectively The starting point of the current edge and the halfway point, the halfway point and the end point of the current edge form two new current edges; the original current edge SH is formed by connecting the starting point S of the current edge to the intermediate point A, and then connecting the intermediate point A to the end point H of the current edge to form SA The current side is composed of the two sides AH: the original current side HG is connected by the starting point H of the current side to the midway point B, and then the midway point B is connected to the end point G of the current side to form the current side composed of two sides HB and BG; The original current edge LS connects the starting point L of the current edge to the halfway point C, and then connects the halfway point C to the end point S of the current edge to form the current edge consisting of two edges LC and CS; 步骤6、将现在新围成的多边形S-A-H-B-G-L-C-S的各条边转至步骤3进行遍历;Step 6, transfer each edge of the newly formed polygon S-A-H-B-G-L-C-S to step 3 for traversal; 步骤7、多边形当前边遍历完毕,活动区域集中所有的边所围成的多边形即为输出结果,活动区域外的障碍物多边形1、3、10、11不需要考虑,而活动区域内的障碍物多边形2、4、5、6、7、8、9就是机器人在路径规划时需要考虑的。Step 7. After traversing the current sides of the polygon, the polygon surrounded by all the sides in the active area set is the output result. The obstacle polygons 1, 3, 10, and 11 outside the active area do not need to be considered, while the obstacles in the active area Polygons 2, 4, 5, 6, 7, 8, and 9 are what the robot needs to consider when planning its path.
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