# StableLego: Stability Analysis of Block Stacking Assembly

arXiv: https://arxiv.org/abs/2402.10711 · HTML: https://mlsanity.com/paper/2402.10711/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2024.

## Built on by (most cited first, 9 of 9)

- [Generating Physically Stable and Buildable Brick Structures from Text](https://mlsanity.com/paper/2505.05469/) (2025)
- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
- [Physics-Aware Combinatorial Assembly Sequence Planning using Data-free Action Masking](https://mlsanity.com/paper/2408.10162/) (2024)
- [Rollback-Free Stable Brick Structures Generation](https://mlsanity.com/paper/2605.06947/) (2026)
- [BrickAnything: Geometry-Conditioned Buildable Brick Generation with Structure-Aware Tokenization](https://mlsanity.com/paper/2605.26182/) (2026)
- [AssemblyComplete: 3D Combinatorial Construction with Deep Reinforcement Learning](https://mlsanity.com/paper/2410.15469/) (2024)
- [Prompt-to-Product: Generative Assembly via Bimanual Manipulation](https://mlsanity.com/paper/2508.21063/) (2025)
- [CRAG: Can 3D Generative Models Help 3D Assembly?](https://mlsanity.com/paper/2602.22629/) (2026)
- [ScaffoldM3C: A Multimodal Sequential Monte Carlo Framework for Generative Stable Construction Planning](https://mlsanity.com/paper/2610.00487/) (2026)

## Abstract (arXiv)

Structural stability is a necessary condition for successful construction of an assembly. However, designing a stable assembly requires a non-trivial effort since a slight variation in the design could significantly affect the structural stability. To address the challenge, this paper studies the stability of assembly structures, in particular, block stacking assembly. The paper proposes a new optimization formulation, which optimizes over force balancing equations, for inferring the structural stability of 3D block stacking structures. The proposed stability analysis is verified on hand-crafted Lego examples. The experiment results demonstrate that the proposed method can correctly predict whether the structure is stable. In addition, it outperforms the existing methods since it can accurately locate the weakest parts in the design, and more importantly, solve any given assembly structures. To further validate the proposed method, we provide textitStableLego: a comprehensive dataset including 50k+ 3D objects with their Lego layouts. We test the proposed stability analysis and include the stability inference for each corresponding object in StableLego. Our code and the dataset are available at https://github.com/intelligent-control-lab/StableLego.