基于凸分解的序列物体放置优化

中文摘要 AI 辅助

机器人物体装箱是物流、工业等领域机器人部署的核心挑战，原因在于组合搜索的维度灾难，以及处理不规则形状物体的动态和接触约束的难度。当前的启发式方法和基于学习的方法假设空间的离散化分辨率有限，且随着离散化精度提高，计算效率会变得极低。在本研究中，我们通过引入SOPO-CD（一种序列优化框架）来消除这些假设，该框架将物体放置问题建模为分解自由空间中的可微非线性优化问题。我们证明，将凸物体放置在凸包内，本质上是将物体的顶点约束在凸包内，这些约束及其导数可以写成闭式形式，且计算耗时在200纳秒以内。我们实现了一个自定义求解器，该求解器能在毫秒级时间内实现紧密约束空间内的最优放置，与经典网格搜索方法相比，速度提升了100倍。我们将该框架推广到二维七巧板、二维俄罗斯方块和三维装箱问题中，展示了优异的计算性能和装箱效用，还演示了使用Allegro Hand机械臂和Xarm机械臂在线解决真实七巧板谜题的过程。

英文摘要

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 collision constraints for irregularly shaped objects. Current heuristic and learning-based methods mainly assume a limited spatial discretization resolution of space, and computation becomes extremely inefficient as discretization accuracy increases. In this work, we eliminate this assumption by introducing SOPO-CD, which frames sequential object placement as a differentiable nonlinear optimization problem with hard constraints in a decomposed free space. We formulate the constraints of placing a convex object inside a convex hull as constraining the vertices of the object to lie inside the convex hull. The constraints and their derivatives can be written in closed form and calculated efficiently. We implement a custom solver that achieves local-optimal placements within tightly constrained space in milliseconds; a $50 \times$ speedup compared to a fine-grained grid search method. We evaluate our framework on 2D Tangram, 2D Tetris, and 3D Bin Packing, and have demonstrated strong computational performance and packing utility. We also demonstrate its real-world applicability for solving the Tangram puzzle using a robot equipped with a dexterous hand.

发表机构

• Lund University（隆德大学）
• Robotics Institute Germany（德国机器人研究所）

机构由 AI 辅助整理，请以论文原文为准。