Object rearrangement is a fundamental sub-task in accomplishing a great many physical tasks. As such, effectively executing rearrangement is an important skill for intelligent robots to master. In this study, we conduct the first algorithmic study on optimally solving the problem of Multi-layer Object Rearrangement on a Tabletop (MORT), in which one object may be relocated at a time, and an object can only be moved if other objects do not block its top surface. In addition, any intermediate structure during the reconfiguration process must be physically stable, i.e., it should stand without external support. To tackle the dual challenges of untangling the dependencies between objects and ensuring structural stability, we develop an algorithm that interleaves the computation of the optimal rearrangement plan and structural stability checking. Using a carefully constructed integer linear programming (ILP) model, our algorithm, Stability-aware Integer Programming-based Planner (SIPP), readily scales to optimally solve complex rearrangement problems of 3D structures with over 60 building blocks, with solution quality significantly outperforming natural greedy best-first approaches. Upon the publication of the manuscript, source code and data will be available at https://github.com/arc-l/mort/

翻译：物体重新排列是完成大量物理任务的基础子任务。因此，有效执行重新排列是智能机器人需要掌握的重要技能。在本研究中，我们首次对桌面上多层物体重新排列（MORT）问题的最优求解进行算法研究。该问题中，一次只能移动一个物体，且只有当其他物体不遮挡其顶面时，该物体才能被移动。此外，重新配置过程中的任何中间结构必须物理稳定，即无需外部支撑即可站立。为了应对解开物体间依赖关系与确保结构稳定性的双重挑战，我们开发了一种算法，该算法交替计算最优重新排列方案和结构稳定性检查。通过精心构建的整数线性规划（ILP）模型，我们的算法——基于稳定性感知的整数规划规划器（SIPP）——能够轻松扩展以最优解决包含超过60个构建块的复杂3D结构重新排列问题，其解的质量显著优于自然的贪心最佳优先方法。手稿发表后，源代码和数据将在 https://github.com/arc-l/mort/ 提供。