X*: Anytime Multiagent Planning With Bounded Search
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Multi-agent planning in dynamic domains is a challenging problem: the size of the configuration space increases exponentially in the number of agents, and plans need to be re-evaluated periodically to account for moving obstacles. However, we have two key insights that hold in several domains: 1) conflicts between multi-agent plans often have geometrically local resolutions within a small repair window, even if such local resolutions are not globally optimal; and 2) the partial search tree for such local resolutions can then be iteratively improved over successively larger windows to eventually compute the global optimal plan. Building upon these two insights, we introduce a sparse, anytime variant of the A* planner, which we call X* (Expanding A*). X* operates by planning for each agent individually and forming local repair windows around collisions, repairing agents within that window. If time allows, X* grows the window and repeats. X* implements two novel techniques to reduce the computational cost compared to joint A*: 1) it preserves the partial X* search trees and priority queues between iterations of window growth; and 2) it defers explicit joint state enumeration until necessary. By preserving the search tree, X* significantly out-performs joint A* and a naïve window-growing A* algorithm. By deferring explicit joint state enumeration, X* reduces the number of priority queue operations by several orders of magnitude compared to a joint A* planner. We present empirical results from several domains, showing that X* outperforms existing state-of-the-art joint planners for sparse anytime multi-agent planning with optimality convergence.
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