Sequential Object Placement Optimization with Convex Decomposition

2026-08-25

AI Summary

本文通过引入SOPO-CD框架，将物体放置问题转化为可微非线性优化问题，解决了机器人在处理不规则形状物体时的高效打包难题。

Abstract

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.

Problem

• robotic object packing
• combinatorial search
• irregularly shaped objects
• spatial discretization resolution

Innovation

• SOPO-CD
• sequential optimization
• differentiable nonlinear optimization
• convex decomposition
• custom solver