Path planning for multiple robots (MRPP) represents a task of finding non-colliding paths for robots through which they can navigate from their initial positions to specified goal positions. The problem is usually modeled using undirected graphs where robots move between vertices across edges. Contemporary optimal solving algorithms include dedicated search-based methods, that solve the problem directly, and compilation-based algorithms that reduce MRPP to a different formalism for which an efficient solver exists, such as constraint programming (CP), mixed integer programming (MIP), or Boolean satisfiability (SAT). In this paper, we enhance existing SAT-based algorithm for MRPP via spartification of the set of candidate paths for each robot from which target Boolean encoding is derived. Suggested sparsification of the set of paths led to smaller target Boolean formulae that can be constructed and solved faster while optimality guarantees of the approach have been kept.
翻译:多机器人的路径规划( MRPP) 是一项为机器人找到非对称路径的任务, 机器人可以从最初的位置导航到指定的目标位置。 问题通常使用非定向图形模型, 机器人在边缘之间移动。 当代最佳解算法包括专门的搜索方法, 直接解决问题, 以及基于编译的算法, 将MRP降低为不同的形式主义, 并存在高效的解算法, 例如制约程序( CP)、 混合整流程序( MIP) 或 Boolean 相对性( SAT ) 。 在本文中, 我们通过分割每个机器人的候选路径集来强化基于 SAT MOPP 的现有算法, 从而生成目标 Boolean 编码 。 建议的路径集解压缩到小目标 Boolean 公式, 可以更快地构建和解决, 同时保存了方法的最佳性保证 。