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This paper introduces SOPO-CD, a sequential optimization framework that reformulates robotic object packing as a differentiable nonlinear optimization problem, overcoming the limitations of traditional heuristic and learning-based methods. By leveraging convex decomposition, the authors achieve a remarkable 100x speedup in optimal placement computations compared to classical grid search methods, enabling efficient packing of irregularly shaped objects in tightly constrained spaces. The framework's versatility is showcased through its application to various packing scenarios, including 2D Tangram, 2D Tetris, and 3D Bin Packing, as well as a real-world demonstration with a robotic hand.
Achieving a 100x speedup in optimal object placement could revolutionize robotic packing efficiency in logistics and manufacturing.
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.
