任意距离下Dubins最短路径研究

Research on Shortest Path in Any Distance Based on Dubins Method

为快速寻找同一平面内连接带方向两点的最短路径,针对两点距离较短时需考虑因素较多的问题,推导了短距离条件下不同情况Dubins路径的分段连续计算公式,并在此基础上证明了任意距离条件下的Dubins最短路径;完善了Dubins最短路径理论,推动Dubins路径在航迹规划等实际问题中更加广泛的应用,试验结果证明当带方向两点位置确定时根据结论可快速获得连接两点的最短路径。

Given two points by any distance in a plane,each with a prescribed direction of motion in it,the question of finding the shortest smooth path of bounded curvature that joins them widely exist. In terms of short distance,many factors should be taken into account. To solve this problem,a kind of piecewise continuous differentiable function is firstly given to compute distance of dubins road in shorter distance. Based on this result,the shortest path chosen from the dubins’ set is proved by any distance in this paper. This result sheds light on the nature of factors affecting the length of paths in the Dubins problem by any distance,and is useful for further extensions. At last,experimentation is taken to prove that the shortest path can be attained quickly when the position of two points with direction are given.