We present a multi-robot task and motion planning method that, when applied to the rearrangement of objects by manipulators, results in solution times up to three orders of magnitude faster than existing methods and successfully plans for problems with up to twenty objects, more than three times as many objects as comparable methods. We achieve this improvement by decomposing the planning space to consider manipulators alone, objects, and manipulators holding objects. We represent this decomposition with a hypergraph where vertices are decomposed elements of the planning spaces and hyperarcs are transitions between elements. Existing methods use graph-based representations where vertices are full composite spaces and edges are transitions between these. Using the hypergraph reduces the representation size of the planning space-for multi-manipulator object rearrangement, the number of hypergraph vertices scales linearly with the number of either robots or objects, while the number of hyperarcs scales quadratically with the number of robots and linearly with the number of objects. In contrast, the number of vertices and edges in graph-based representations scales exponentially in the number of robots and objects. We show that similar gains can be achieved for other multi-robot task and motion planning problems.

翻译：我们提出一种多机器人任务与运动规划方法，在机械臂对物体进行重排时，其求解速度比现有方法快三个数量级，并能成功规划包含多达二十个物体的问题，可处理物体数量是同类方法的三倍以上。这一改进源于将规划空间分解为三个独立部分：机械臂本身、物体、以及机械臂抓取物体的组合状态。我们用超图表示这种分解：顶点为规划空间的分解元素，超弧为元素间的转移关系。现有方法采用基于图的表示，其中顶点为完整复合空间，边为空间间的转移。超图降低了规划空间的表示规模——对于多机械臂物体重排问题，超图顶点数与机器人或物体数量呈线性关系，超弧数与机器人数量呈二次关系、与物体数量呈线性关系。相比之下，基于图的表示中顶点和边的数量随机器人和物体数量呈指数增长。我们证明，这种性能增益同样适用于其他多机器人任务与运动规划问题。