Hypergraph-based Multi-Robot Task and Motion Planning

We present a multi-robot task and motion planning method that, when applied to the rearrangement of objects by manipulators, produces solution times up to three orders of magnitude faster than existing methods. We achieve this improvement by decomposing the planning space into subspaces for independent manipulators, objects, and manipulators holding objects. We represent this decomposition with a hypergraph where vertices are substates and hyperarcs are transitions between substates. Existing methods use graph-based representations where vertices are full states and edges are transitions between states. Using the hypergraph reduces the 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 scale exponentially in the number of robots and objects. Additionally, the hypergraph provides a structure to reason over varying levels of (de)coupled spaces and transitions between them enabling a hybrid search of the planning space. We show that similar gains can be achieved for other multi-robot task and motion planning problems.