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Tabletop Object Rearrangement: Structure, Complexity, and Efficient Combinatorial Search-Based Solutions

Kai Gao

TL;DR

This thesis delivers a comprehensive treatment of tabletop object rearrangement (TORO) across multiple workspace and manipulator configurations. It first establishes the NP-hardness of running buffer minimization (MRB) in TORE and develops scalable exact algorithms for both labeled and unlabeled settings, linking MRB to linear vertex ordering and FVS-based bounds. It then extends to internal buffers with TORI via lazy buffer verification (TRLB), introducing preprocessing, heterogeneous object support (HeTORI), and weighted planning strategies that integrate with Monte Carlo Tree Search and MCTS. The work further advances dual-arm coordination (CDR) with a GPU-accelerated task-and-motion pipeline (MODAP), providing robust scheduling, buffer management, and real-time control, and explores mobile tabletop rearrangement with ORLA* (lazy A*), including StabilNet-based stability predictions for general shapes. Collectively, these contributions yield high-quality, scalable planning and execution methods for dense, constrained tabletop rearrangements with single, dual, and mobile manipulators, demonstrated through extensive simulations and hardware experiments. The findings suggest that practical TORO instances exhibit small MRB on average, while the proposed lazy-buffer techniques enable near-optimal planning in challenging, cluttered environments with real-time applicability.

Abstract

This thesis provides an in-depth structural analysis and efficient algorithmic solutions for tabletop object rearrangement with overhand grasps (TORO), a foundational task in advancing intelligent robotic manipulation. Rearranging multiple objects in a confined workspace presents two primary challenges: sequencing actions to minimize pick-and-place operations - an NP-hard problem in TORO - and determining temporary object placements ("buffer poses") within a cluttered environment, which is essential yet highly complex. For TORO with available external free space, this work investigates the minimum buffer space, or "running buffer size," required for temporary relocations, presenting both theoretical insights and exact algorithms. For TORO without external free space, the concept of lazy buffer verification is introduced, with its efficiency evaluated across various manipulator configurations, including single-arm, dual-arm, and mobile manipulators.

Tabletop Object Rearrangement: Structure, Complexity, and Efficient Combinatorial Search-Based Solutions

TL;DR

This thesis delivers a comprehensive treatment of tabletop object rearrangement (TORO) across multiple workspace and manipulator configurations. It first establishes the NP-hardness of running buffer minimization (MRB) in TORE and develops scalable exact algorithms for both labeled and unlabeled settings, linking MRB to linear vertex ordering and FVS-based bounds. It then extends to internal buffers with TORI via lazy buffer verification (TRLB), introducing preprocessing, heterogeneous object support (HeTORI), and weighted planning strategies that integrate with Monte Carlo Tree Search and MCTS. The work further advances dual-arm coordination (CDR) with a GPU-accelerated task-and-motion pipeline (MODAP), providing robust scheduling, buffer management, and real-time control, and explores mobile tabletop rearrangement with ORLA* (lazy A*), including StabilNet-based stability predictions for general shapes. Collectively, these contributions yield high-quality, scalable planning and execution methods for dense, constrained tabletop rearrangements with single, dual, and mobile manipulators, demonstrated through extensive simulations and hardware experiments. The findings suggest that practical TORO instances exhibit small MRB on average, while the proposed lazy-buffer techniques enable near-optimal planning in challenging, cluttered environments with real-time applicability.

Abstract

This thesis provides an in-depth structural analysis and efficient algorithmic solutions for tabletop object rearrangement with overhand grasps (TORO), a foundational task in advancing intelligent robotic manipulation. Rearranging multiple objects in a confined workspace presents two primary challenges: sequencing actions to minimize pick-and-place operations - an NP-hard problem in TORO - and determining temporary object placements ("buffer poses") within a cluttered environment, which is essential yet highly complex. For TORO with available external free space, this work investigates the minimum buffer space, or "running buffer size," required for temporary relocations, presenting both theoretical insights and exact algorithms. For TORO without external free space, the concept of lazy buffer verification is introduced, with its efficiency evaluated across various manipulator configurations, including single-arm, dual-arm, and mobile manipulators.

Paper Structure

This paper contains 102 sections, 14 theorems, 26 equations, 76 figures, 3 tables, 16 algorithms.

Table of Contents

  1. Introduction and Background
  2. Running Buffer Minimization (RBM) for TORO with External Buffers (TORE)
  3. Motivation
  4. Related Work
  5. TORO with External Buffer Space (TORE)
  6. Labeled TORO with External Buffers
  7. Unlabeled TORO with External Buffers
  8. Structural Analysis and NP-Hardness
  9. Running Buffer versus Total Buffer
  10. Running Buffers and Linear Vertex Ordering
  11. Intractability of Computing MRB
  12. Lower and Upper Bounds on MRB
  13. Intrinsic MRB Lower Bounds
  14. Upper Bounds on MRB for URBM
  15. Algorithms for TORE
  16. ...and 87 more sections

Key Result

Proposition 2.3.1

$G^{\,\ell}$ fully captures the information needed to solve the tabletop rearrangement problem with external buffers moving objects from $\mathcal{A}_s$ to $\mathcal{A}_g$.

Figures (76)

  • Figure 1: A TORO instance where the three soda cans are to be rearranged from the left configuration to the right configuration.
  • Figure 2: [Left] PyBullet setup for the Cooperative Multi-Robot Rearrangement problem, where only a portion of the environment (the region between two white lines) is reachable by both arms. [Right] Handoff operation at a pre-computed pose above the environment.
  • Figure 3: An example of the Mobile Robot Tabletop Rearrangement (MoTaR) setup.
  • Figure 4: A 7-object labeled instance with uniform cylinders; we will use this instance as a running example. (a) The unshaded discs (as projections of cylinders) represent the start arrangement $\mathcal{A}_s$ and the shaded discs represent the goal arrangement $\mathcal{A}_g$. (b) The corresponding labeled dependency graph. (c) The corresponding unlabeled dependency graph, which is bipartite and planar.
  • Figure 5: Two configurations of the setup given in \ref{['fig:toro']} and the corresponding dependency graphs.
  • ...and 71 more figures

Theorems & Definitions (24)

  • Proposition 2.3.1
  • Proposition 2.3.2
  • Proposition 2.3.3
  • Lemma 2.4.1
  • proof
  • Theorem 2.4.1
  • proof
  • Theorem 2.4.2
  • proof
  • Proposition 2.5.1
  • ...and 14 more