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

arXiv: https://arxiv.org/abs/2605.17800 · HTML: https://mlsanity.com/paper/2605.17800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 9 of 9)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Robot Operating System 2: Design, Architecture, and Uses In The Wild](https://mlsanity.com/paper/2211.07752/) (2022)
- [You Only Demonstrate Once: Category-Level Manipulation from Single Visual Demonstration](https://mlsanity.com/paper/2201.12716/) (2022)
- [ASAP: Automated Sequence Planning for Complex Robotic Assembly with Physical Feasibility](https://mlsanity.com/paper/2309.16909/) (2023)
- [Multi-Object Rearrangement with Monte Carlo Tree Search:A Case Study on Planar Nonprehensile Sorting](https://mlsanity.com/paper/1912.07024/) (2019)
- [Complexity Results and Fast Methods for Optimal Tabletop Rearrangement with Overhand Grasps](https://mlsanity.com/paper/1711.07369/) (2017)
- [A Framework for Fine Robotic Assembly](https://mlsanity.com/paper/1509.04806/) (2015)
- [Persistent Homology for Effective Non-Prehensile Manipulation](https://mlsanity.com/paper/2202.02937/) (2022)
- [Object Rearrangement with Nested Nonprehensile Manipulation Actions](https://mlsanity.com/paper/1905.07505/) (2019)

## Abstract (arXiv)

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.