Deterministic scaffold assembly by self-reconfiguring micro-robotic swarms

Abstract

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(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.

3D Coating Self-Assembly for Modular Robotic Scaffolds

“…This work is a follow-up of our previous work on the coordinated construction of the scaffold of objects by 3D Catom modules mentioned in the introduction, which was demonstrated in [13] for the asynchronous construction of square pyramids of various sizes and later generalized to a large class of convex objects in [15].…”

“…Furthermore, self-reconfiguration is usually painfully slow, as the constraints imposed on the motion of the modules makes it extremely tedious to reach a high number of modules moving around the robot in parallel without dramatically increasing the risk of collisions between modules or deadlocks. Accordingly, we have shown in [13] and [15] that unprecedented self-reconfiguration speeds could be achieved thanks to two propositions we made. First, engineering the † All authors are with Univ.…”

“…Lastly, assembly decisions can be made by the distributed robotic units on the fly by relying on a set of local neighborhood rules that describe the order and constraints under which a module of the shape must attract neighbors and by resolving global constraints through communication [16,15,13]. Our present work belongs to the latter category.…”

“…• The reconfiguration occurs in a sandbox environment, as introduced in [13,15], which means that there is a reserve of modules below the ground of the reconfiguration scene and that can supply modules at any time to various ground locations of the scene (cf. the gray modules and tile branches in Figure 3.a/b).…”

“…Indeed, let us consider a single source of sandbox modules at the base of the scaffold, or rather a single source per disjoint component of the object, and where modules are introduced at regular intervals leaving only one free position between them, forming a train of modules. Let t i the time at which the coating position number i in the assembly order is filled, and assuming that it would take a constant number of time steps c (realistically 2 to 4) for the next module along the train to take its position, then: Our self-reconfiguration algorithm for building the scaffold of a shape has been shown to have an O( 3 √ N) reconfiguration time for all semi-convex shapes, i.e., having no vertical concavities, and with no hole between the sandbox and the shape [15]. This makes the total reconfiguration time O(n coating ) + O( 3 √ n scaffold ), or O(n coating+scaffold ) for that class of shape.…”