Recent advancements in robotics enable robots to accomplish complex assembly tasks. However, designing an assembly requires a non-trivial effort since a slight variation in the design could significantly affect the task feasibility. It is critical to ensure the physical feasibility of the assembly design so that the assembly task can be successfully executed. To address the challenge, this paper studies the physical stability of assembly structures, in particular, block stacking assembly, where people use cubic blocks to build 3D structures (e.g., Lego constructions). 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 tested and verified on hand-crafted Lego examples. The experiment results demonstrate that the proposed stability analysis can correctly predict whether the structure is stable. In addition, it outperforms the existing methods since it can locate the weakest parts in the design, and more importantly, solve any given assembly structure. To further validate the proposed analysis formulation, we provide StableLego: a comprehensive dataset including more than 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.

翻译：近期机器人技术的进展使得机器人能够完成复杂的装配任务。然而，装配设计需要耗费大量精力，因为设计中的微小变化可能显著影响任务可行性。确保装配设计的物理可行性对于成功执行装配任务至关重要。为解决这一挑战，本文研究了装配结构的物理稳定性，特别是积木堆叠结构（即人们使用立方体砖块构建三维结构，例如乐高积木）。文章提出了一种新的优化公式，通过优化力平衡方程来推断三维积木堆叠结构的结构稳定性。该稳定性分析方法在手工艺品乐高示例上进行了测试与验证。实验结果表明，所提出的稳定性分析能够正确预测结构是否稳定。此外，该方法优于现有方法，因为它能够定位设计中最薄弱的环节，更重要的是，可以求解任意给定的装配结构。为进一步验证所提出的分析公式，我们提供了StableLego：一个包含超过5万个三维物体及其乐高布局的综合数据集。我们测试了提出的稳定性分析，并将每个对应物体的稳定性推断结果纳入StableLego数据集。我们的代码与数据集可在https://github.com/intelligent-control-lab/StableLego获取。