Optimal Knock-Pick Planning for Tightly Packed Tabletop Blocks With Parallel Grippers

TL;DR

This paper introduces an optimal planning method for rearranging densely packed tabletop blocks using a combination of knock and pick actions, enabling efficient manipulation when traditional methods are infeasible.

Contribution

It formulates the knock-pick problem, introduces a directional knock primitive, and develops a polynomial-time algorithm for optimal action planning in dense object arrangements.

Findings

Efficient polynomial-time computation of optimal plans using maximum-weight perfect matching.

Successful experiments demonstrating scalability in synthetic and simulated environments.

Theoretical insights towards combining prehensile and non-prehensile manipulation strategies.

Abstract

Rearranging densely packed tabletop objects is challenging when parallel-gripper picks are infeasible without sufficient clearance around an object. This work studies the problem characteristics for practically motivated settings with uniformly sized blocks placed at planar tabletop grid locations. Since purely prehensile removal can become infeasible, a directional knock primitive is therefore introduced and the optimal knock-pick variant of the problem is formulated. The work proposes a series of abstractions wherein minimal constraining gadgets are covered to identify the necessary knocks. Utilizing a maximum-weight perfect matching on a graphical abstraction yields efficient polynomial-time computation of the optimal plan that minimizes the number of actions. Experiments are reported for increasing grid sizes in synthetic settings as well as in IsaacSim. The theoretical observations provide a promising stepping stone towards rigorously building efficient manipulation strategies that interleave prehensile and non-prehensile actions.