We introduce Lazy-DaSH, an improvement over the recent state of the art multi-robot task and motion planning method DaSH, which scales to more than double the number of robots and objects compared to the original method and achieves an order of magnitude faster planning time when applied to a multi-manipulator object rearrangement problem. We achieve this improvement through a hierarchical approach, where a high-level task planning layer identifies planning spaces required for task completion, and motion feasibility is validated lazily only within these spaces. In contrast, DaSH precomputes the motion feasibility of all possible actions, resulting in higher costs for constructing state space representations. Lazy-DaSH maintains efficient query performance by utilizing a constraint feedback mechanism within its hierarchical structure, ensuring that motion feasibility is effectively conveyed to the query process. By maintaining smaller state space representations, our method significantly reduces both representation construction time and query time. We evaluate Lazy-DaSH in four distinct scenarios, demonstrating its scalability to increasing numbers of robots and objects, as well as its adaptability in resolving conflicts through the constraint feedback mechanism.

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.