机器人避障问题模型研究
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摘要
研究机器人避障最短路径问题,主要研究1个区域存在12个障碍物,从点O出发避开障碍物分别到达目的地点A,B,C的最短路径。限定区域内的最短路径由2部分组成的:一部分是平面上的自然最短路径(即直线段),另一部分是限定区域的部分边界(圆弧部分),这2部分是相切且互相连接的。可以认为最短路径一定是由线段和圆弧构成,因此建立线圆结构。对于从出发点到目的地的路径采取2种方案:第1种方案,在拐点和节点都采用最小转弯半径的形式;第2种方案,适当扩大拐点处的转弯半径,使得机器人能够沿直线通过途中的目标点。然后建立了最优化模型对比,最后对2种方案分别进行求解。因为区域面积很大而限定圆半径至少为10,通过近似比较估算得出较优的最短路线方案。结论:无论路径多么复杂,都可以将路径划分为若干个线圆结构来求解,利用数学几何运算、直线关系以及Mathematics工具,来分析在问题中出现的3种具体的线圆结构情形,从而得到最短路径。
This paper studies the robot obstacle-avoiding shortest path problem,twelve obstacles of a region. From the point of view of O to avoiding obstacles respectively at the place of destination A,B,C of the shortest path. We analyze the re- stricted shortest path within the region which is composed of two parts: one part is plane natural shortest path( i. e. straight line),the other part is limited to part of the boundary region. The two parts is the tangent,connected to each other. We can think of the shortest path is composed of line segments and circular arc,hence the establishment of round wire struc- ture. From the starting point to the destination path we take two kinds of schemes. The first scheme,the inflection point and the node with the minimum turning radius of the form; the second kind of scheme is the turning radius at the turning point,so the robot can get along through a straight route to the target point,and then the contrast optimization model is es- tablished. Because the area is large and limited radius of at least 10,is estimated by approximate shortest route plan better, no matter how complicated this path is,it can be divided into a plurality of the path line of the round structure to solve the mathematics,geometry,linear relationship and mathematics tool,to analyze three kinds of concrete line which appear in the problem of circular structure,so as to get the shortest path.
This paper studies the robot obstacle-avoiding shortest path problem,twelve obstacles of a region. From the point of view of O to avoiding obstacles respectively at the place of destination A,B,C of the shortest path. We analyze the re- stricted shortest path within the region which is composed of two parts: one part is plane natural shortest path( i. e. straight line),the other part is limited to part of the boundary region. The two parts is the tangent,connected to each other. We can think of the shortest path is composed of line segments and circular arc,hence the establishment of round wire struc- ture. From the starting point to the destination path we take two kinds of schemes. The first scheme,the inflection point and the node with the minimum turning radius of the form; the second kind of scheme is the turning radius at the turning point,so the robot can get along through a straight route to the target point,and then the contrast optimization model is es- tablished. Because the area is large and limited radius of at least 10,is estimated by approximate shortest route plan better, no matter how complicated this path is,it can be divided into a plurality of the path line of the round structure to solve the mathematics,geometry,linear relationship and mathematics tool,to analyze three kinds of concrete line which appear in the problem of circular structure,so as to get the shortest path.
引文
[1]谭永基.数学模型[M].上海:复旦大学出版社,2011.
[2]尤承业.解析几何[M].北京:北京大学出版社,2004.
[3]霍迎辉,张连明,杨宜民.移动机器人路径规划的最短切线路径算法[J].自动化与信息工程,2003(1):10-12.
[4]周培德.计算几何—算法与设计[M].北京:清华大学出版社,2005.
[2]尤承业.解析几何[M].北京:北京大学出版社,2004.
[3]霍迎辉,张连明,杨宜民.移动机器人路径规划的最短切线路径算法[J].自动化与信息工程,2003(1):10-12.
[4]周培德.计算几何—算法与设计[M].北京:清华大学出版社,2005.