凸分解を用いた逐次物体配置最適化
Sequential Object Placement Optimization with Convex Decomposition
物体配置を微分可能な非線形最適化問題として定式化し、凸包内の頂点制約を閉形式で計算することで、高速かつ高密度なパッキングを実現するフレームワークを提案した。
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著者: Yuezhe Zhang, Xiangyu Lyu, Sohan Rudra, Davide Tateo, Georgia Chalvatzaki
分類: cs.RO
原文アブストラクト
Robotic object packing has been a core challenge for robotic deployment in logistics, industry, etc., due to the curse of dimensionality in combinatorial search and the difficulty of dealing with dynamic and contact constraints for irregularly shaped objects. Current heuristic and learning-based methods assume a limited spatial discretization resolution of space, and computation becomes extremely inefficient as discretization accuracy increases. In this work, we eliminate these assumptions by introducing SOPO-CD, a sequential optimization framework that frames object placement as a differentiable nonlinear optimization problem in a decomposed free space. We prove that placing a convex object inside a convex hull is essentially constraining the vertices of the object inside the convex hull. The constraints and their derivatives can be written in closed form and calculated within $200$ns. We implement a custom solver that achieves optimal placement within tightly constrained space in milliseconds; a $100 \times$ speedup compared to a classical grid search method. We generalize our framework to 2D Tangram, 2D Tetris, and 3D Bin Packing, and have demonstrated strong computational performance and packing utility. We also demonstrate solving a real-world Tangram puzzle online using an Allegro Hand and an Xarm.