We study the problem of path planning with soft homology constraints on a surface topologically equivalent to a disk with punctures. Specifically, we propose an algorithm, named $\Hstar$, for the efficient computation of a path homologous to a user-provided reference path. We show that the algorithm can generate a suite of paths in distinct homology classes, from the overall shortest path to the shortest path homologous to the reference path, ordered both by path length and similarity to the reference path. Rollout is shown to improve the results produced by the algorithm. Experiments demonstrate that $\Hstar$ can be an efficient alternative to optimal methods, especially for configuration spaces with many obstacles.

翻译：我们研究了在拓扑等价于带孔洞圆盘的曲面上进行软同调约束路径规划的问题。具体而言，我们提出了一种名为 $\Hstar$ 的算法，用于高效计算与用户提供的参考路径同调的路径。我们证明该算法能够生成一系列处于不同同调类中的路径，从全局最短路径到与参考路径同调的最短路径，这些路径可按路径长度及与参考路径的相似度进行排序。实验表明，滚动优化策略能够进一步提升算法生成的结果。测试结果证明，$\Hstar$ 可作为最优方法的有效替代方案，尤其在包含大量障碍物的构型空间中表现突出。