We present a planner for large-scale (un)labeled object sorting tasks, which uses two types of manipulation actions: overhead grasping and planar pushing. The grasping action offers completeness guarantee under mild assumptions, and planar pushing is an acceleration strategy that moves multiple objects at once. Our main contribution is twofold: (1) We propose a bilevel planning algorithm. Our high-level planner makes efficient, near-optimal choices between pushing and grasping actions based on a cost model. Our low-level planner computes one-step greedy pushing or grasping actions. (2) We propose a novel low-level push planner that can find one-step greedy pushing actions in a semi-discrete search space. The structure of the search space allows us to efficient We show that, for sorting up to objects, our planner can find near-optimal actions with seconds of computation on a desktop machine.
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