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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. |
