求加权着色图全局最优路的广义A* 算法
A Generalized A* Algorithm for Finding Globally Optimal Paths in Weighted Colored Graphs
摘要：
搜索空间的几何信息和语义信息对于一个好的计划是必不可少的。我们将这些属性编码在一个加权彩色图（边权重的几何信息和边和顶点颜色的语义信息）中，并提出了一个广义A*，以找到最短路径的路径集合中包含最少的低排名的颜色边缘。我们证明了这个类序A*（COA*）算法的完整性和最优性，关于这里定义的最优性的概念。COA* 的效用在三元图中进行了数值验证，该三元图具有可行的、不可行的和未知的顶点和边缘，用于2D移动机器人、3D机器人手臂和具有有限传感能力的5D机器人手臂的情况。我们比较COA* 的结果，定期的A* 算法，后者发现最短路径，无论不确定性，我们表明，COA* 占主导地位的A* 解决方案，在寻找不确定的路径。
英文摘要：
Both geometric and semantic information of the search space is imperative for a good plan. We encode those properties in a weighted colored graph (geometric information in terms of edge weight and semantic information in terms of edge and vertex color), and propose a generalized A* to find the shortest path among the set of paths with minimal inclusion of low-ranked color edges. We prove the completeness and optimality of this Class-Ordered A* (COA*) algorithm with respect to the hereto defined notion of optimality. The utility of COA* is numerically validated in a ternary graph with feasible, infeasible, and unknown vertices and edges for the cases of a 2D mobile robot, a 3D robotic arm, and a 5D robotic arm with limited sensing capabilities. We compare the results of COA* to that of the regular A* algorithm, the latter of which finds the shortest path regardless of uncertainty, and we show that the COA* dominates the A* solution in terms of finding less uncertain paths.
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