The self-reconfiguration of large swarms of modular robotic units from one object into another is an intricate problem whose critical parameter that must be optimized is the time required to perform a transformation. Various optimizations methods have been proposed to accelerate transformations, as well as techniques to engineer the shape itself, such as scaffolding which creates an internal object structure filled with holes for easing the motion of modules. In this paper, we propose a novel deterministic and distributed method for rapidly constructing the scaffold of an object from an organized reserve of modules placed underneath the reconfiguration scene. This innovative scaffold design is parameterizable and has a face-centered-cubic lattice structure made from our rotating-only micro-modules. Our method operates at two levels of planning, scheduling the construction of components of the scaffold to avoid deadlocks at one level, and handling the navigation of modules and their coordination to avoid collisions in the other. We provide an analysis of the method and perform simulations on shapes with an increasing level of intricacy to show that our method has a reconfiguration time complexity of $O(\sqrt[3]{N})$ time steps for a subclass of convex shapes, with N the number of modules in the shape. We then proceed to explain how our solution can be further extended to any shape.

大型模块化机器人单元从一个对象到另一个对象的自我重新配置是一个复杂的问题，必须优化的关键参数是执行转换所需的时间。已经提出了各种优化方法来加速转换，以及提出了对形状本身进行工程设计的技术，例如脚手架，该脚手架创建了一个内部对象结构，该内部对象结构填充有孔以减轻模块的运动。在本文中，我们提出了一种新颖的确定性和分布式方法，该方法可以从放置在重新配置场景下的模块的有组织储备中快速构建对象的脚手架。这种创新的支架设计是可参数化的，并且具有由我们仅旋转的微型模块制成的面心立方晶格结构。我们的方法在两个计划层面上运作，安排脚手架组件的构造以避免在一个级别上出现死锁，并处理模块的导航及其协调，以避免在另一个级别上发生冲突。我们提供了对该方法的分析，并对形状进行了模拟，并增加了复杂度，以表明我们的方法的重新配置时间复杂度为$Ø（\sqrt[3]{ñ}）$凸形状子类的时间步长，其中N个形状为模块。然后，我们继续说明如何将我们的解决方案进一步扩展为任何形状。