Most of the previous studies on mobile robot path planning consider the obstacles as polygons. However, the complex shaped obstacles should be considered as curves rather than polygons, since the latter may result in non-optimal paths. Three new algorithms are proposed for finding the shortest path of a mobile robot among curved obstacles: TAD which uses a tangent drawing method, TRAD which uses trapezoidal decomposition, and TAD-TRAD which uses a combination of the TAD and the TRAD algorithms. The time complexities of the TAD algorithm, the TRAD algorithm, and the TAD-TRAD algorithm are $O(n^3\log n)$, $O(n\log n)$, and $O(n{(\log n)}^2)$ respectively, where $n$ is the total number of arcs in all the obstacles. The TAD and the TAD-TRAD algorithms compute an optimal shortest path, whereas the TRAD algorithm computes an approximate shortest path, among curved obstacles. The TAD algorithm has a lower time complexity than existing algorithms which are implemented for the computation of the optimal shortest path. The TRAD algorithm has a lower time complexity than existing algorithms which compute an approximate shortest path and the TAD-TRAD algorithm has a lower time complexity than existing algorithms which compute an optimal shortest path. The experimental comparison of the TAD, TRAD, and TAD-TRAD algorithms on 200 randomly generated problems shows that the TAD-TRAD algorithm has the least running time. Moreover, the TAD-TRAD algorithm computes an optimal path using a lesser number of tangents and with lesser time complexity when experimental comparisons are performed with existing algorithms in the literature.

以前关于移动机器人路径规划的大部分研究都将障碍物视为多边形。然而，复杂形状的障碍物应被视为曲线而不是多边形，因为后者可能导致非最佳路径。三个新的算法提出了用于发现弯曲障碍物之间的移动机器人的最短路径：TAD其使用TA ngent d rawing方法，TRAD其使用TRA pezoidal d ecomposition，和TAD-TRAD它使用TAD和TRAD的组合算法。TAD算法、TRAD算法和TAD-TRAD算法的时间复杂度为$哦(n^3\mathrm{日志}n)$, $哦(n\mathrm{日志}n)$， 和 $哦(n{(\mathrm{日志}n)}^2)$ 分别，其中 $n$是所有障碍物中弧的总数。TAD 和 TAD-TRAD 算法计算最佳最短路径，而 TRAD 算法计算弯曲障碍物中的近似最短路径。TAD 算法的时间复杂度低于为计算最优最短路径而实现的现有算法。TRAD算法的时间复杂度低于计算近似最短路径的现有算法，TAD-TRAD算法的时间复杂度低于计算最优最短路径的现有算法。TAD、TRAD和TAD-TRAD算法在200个随机生成问题上的实验对比表明，TAD-TRAD算法的运行时间最短。而且，