Lazy-DaSH: Lazy Approach for Hypergraph-based Multi-robot Task and Motion Planning

TL;DR

Lazy-DaSH introduces a two-stage, constraint-feedback MR-TMP framework that decouples task and motion planning within a hierarchical hypergraph. By performing task planning and constraint-driven representation expansion before lazy motion validation, it reduces representation size and avoids unnecessary collision checks, yielding substantial gains in scalability and planning speed. The approach demonstrates up to twice as many robots/objects and up to two orders of magnitude faster planning in multi-manipulator rearrangement tasks, including challenging geometric constraints. The work also provides probabilistic completeness assurances under monotone and exhaustive expansion, and validates performance across five scenarios, including a hardware experiment.

Abstract

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.

Figures (8)

• Figure 1: A comparison of the search space scope during the search processes of DaSH and Lazy-DaSH. The introduction of the task space expansion, task query, task constraint detection, task and motion constraint feedback, and lazy motion validation phases distinguishes our approach from DaSH, as highlighted in red. The task query narrows the search space, while lazy motion validation considers only motions in the candidate plan, reducing the computational cost of motion space construction. The task and motion constraint feedback initiates the expansion of the task space and motion space, thereby broadening the search space in the respective planning representations. While both DaSH and Lazy-DaSH iteratively update representations upon plan failure, Lazy-DaSH employs a constraint feedback mechanism within a hierarchical framework to effectively manage both task-level and motion-level constraints, as illustrated in Fig. \ref{['fig:overview']} and Algorithm \ref{['alg:lazy-dash']}.
• Figure 2: Illustration of the hierarchical structure of the proposed Lazy-DaSH, showing two manipulators ($R_1$ and $R_2$) rearranging an object ($O_1$). The task query phase and the task constraint feedback scheme, which distinguish it from DaSH, are highlighted with red lines. This feature is also emphasized in Algorithm \ref{['alg:lazy-dash']}. Each layer of the hierarchy is detailed in corresponding sections. Note that the different types of grasp modes are omitted from these figures to improve clarity of visualization and conceptual explanation.
• Figure 3: Illustration of task conflict detection. In the left figure, $O_1$ and $O_2$ collide at frontier 3, creating a task constraint that blocks the expansion of hyperarcs with $O_1$ at their head. Expansion of such hyperarcs becomes possible only when $O_2$ is absent at the frontier, in accordance with the task constraints.
• Figure 4: Illustration of scheduled adaptive robot coordination.
• Figure 5: Five different types of experiment scenarios. (a) and (b) show "Sorting" scenarios where the initial clusters of objects are represented within colored circles, and each group must be moved to the matching square boxes. (c) and (d) represent "Wall" scenarios, featuring different numbers of walls. (e) and (f) illustrate the "Shelf-wall" scenario, showing the start and goal locations of the blocks. Finally, (g) is the "Lab" scenario, involving 3-axis gantry robots along with descriptions of the problem entities.