StableLego: Stability Analysis of Block Stacking Assembly

TL;DR

This work introduces StableLego, a stability analysis framework for block stacking that uses a force-balancing optimization grounded in rigid-block equilibrium (RBE). By encoding static equilibrium as part of an optimization objective and enforcing a comprehensive set of physical constraints, the method can analyze arbitrary Lego-like assemblies—including non-single-connected designs—and identify weak points. A large-scale StableLego dataset (50k+ layouts) is provided with per-object stability inferences to benchmark analysis methods. Experiments on hand-crafted designs and the dataset show that the approach achieves high solvability and accuracy, outperforming baseline RBE methods, and extending to extensions such as arbitrary orientations, external weights, and palletization. The work offers a practical, scalable tool for design verification and robotic planning in construction-like tasks.

Abstract

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 \textit{StableLego}: 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.

Figures (12)

• Figure 1: Examples of valid and invalid Lego designs. The left and right columns are valid designs and the middle column shows collapsing designs.
• Figure 2: Illustration of the force model of Lego assembly.
• Figure 3: Illustrations of the single-connected assumption. (1) A single-connected design. (2) An assembly design that is not single-connected. (3) A 3D model generated by generative AI. (4) The Lego design of the generated structure. White: floating bricks.
• Figure 4: Comparison of the proposed stability analysis (i.e., first row) and the EB (i.e., second row). The analysis results from left to right correspond to the structures shown in \ref{['fig:1', 'fig:2', 'fig:3', 'fig:4', 'fig:5', 'fig:6']}. Black: bricks with less internal stress; Red: bricks experiencing higher stress; White: collapsing bricks.
• Figure 5: Example valid designs in the StableLEGO dataset.