优化3D打印顺序与布局，避免机械臂碰撞。
Object Packing and Scheduling for Sequential 3D Printing: a Linear Arithmetic Model and a CEGAR-inspired Optimal Solver
- 将打印顺序与空间布局建模为线性算术公式。
- 采用基于CEGAR的求解策略，显著提升计算效率。
- 适合需要高精度、多对象连续打印的工业场景。
针对顺序式3D打印中的物体排布与调度问题，本文提出一种组合优化方法。与传统一次性逐层打印不同，顺序打印需确保打印机运动部件不与已打印物体发生碰撞。本文将该问题建模为线性算术公式，并利用满足模理论（SMT）的求解器进行求解。为提升效率，采用受反例引导的抽象精化（CEGAR）技术，避免直接求解复杂公式。该方法有效解决了动态路径规划中的碰撞约束，实现安全高效的打印序列生成。
原文摘要 · Abstract (English)
We address the problem of object arrangement and scheduling for sequential 3D printing. Unlike the standard 3D printing, where all objects are printed slice by slice at once, in sequential 3D printing, objects are completed one after other. In the sequential case, it is necessary to ensure that the moving parts of the printer do not collide with previously printed objects. We look at the sequential printing problem from the perspective of combinatorial optimization. We propose to express the problem as a linear arithmetic formula, which is then solved using a solver for satisfiability modulo theories (SMT). However, we do not solve the formula expressing the problem of object arrangement and scheduling directly, but we have proposed a technique inspired by counterexample guided abstraction refinement (CEGAR), which turned out to be a key innovation to efficiency.
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