Efficient reconfiguration of lattice-based modular robots

Abstract

Abstract-Modular robots consist of many small units that attach together and can perform local motions. By combining these motions, we can achieve a reconfiguration of the global shape. The term modular comes from the idea of grouping together a fixed number of units into a module, which behaves as a larger individual component.Recently, a fair amount of research has focused on Crystalline robots, whose units (and modules) fit on a cubic lattice. When the proper module size is formed, these robots can reconfigure in linear time within a rather physically restrictive model, or in O(log n) time in a more unrestricted theoretical model.In this paper, we show that the results for Crystalline robots also apply to two other modular robots: M-TRAN and Molecube. The common requirement, for each robot type, is that a fixed number of units combine to create modules of specified shapes. In this way, we are able to simulate the actions of Crystalline modules. Previous reconfiguration bounds thus transfer automatically, as long as the robots are composed of the module shapes that we specify.

Terminating distributed construction of shapes and patterns in a fair solution of automata

“…This means that nodes (representing monomers there) are capable of firing transition rules that apart from changing their state can also change their relative position to neighboring nodes. This core characteristic brings the Nubot model closer to reconfigurable robotics (see, e.g., [5]) and active programmable matter (see, e.g., [15,36]) models. In contrast, reconfiguration in our model is passive, meaning that all mobility is controlled by the environment and the nodes can only "decide" whether to connect or disconnect whenever they are given the opportunity to interact.…”

“…4 We should mention that part of the ideas related to the pixel-encoding and the TM operating on pixels have been inspired by similar constructions of Woods et al [43]. 5 G is the shape of a labeled square S ∈ L in case L is defined in terms of such squares. 6 By "order" of a shape, we mean the number of nodes of the shape.…”

A new meta-module for efficient reconfiguration of hinged-units modular robots

“…In order to prove Lemma 1 for Molecubes, we follow the lemmata structure proposed in [1], whose proofs admit a straightforward adaptation to our design of the arm. Following the notation from [1], let J i and O i respectively denote the rotating half and the center of unit U i , and let x(O i ) denote the x-coordinate of O i .…”

“…For example, Kotay and Rus [9] have proposed an expandable and contractible meta-module for Molecules, while Murata and Kurokawa have presented in [12] a small and compact M-TRAN meta-module, but it can only expand and contract in two dimensions. For 3D, the only expanding/contracting M-TRAN meta-module that we are aware of is that of Aloupis et al [1], which is also valid for Molecube [26]. However, the meta-module of [1] is formed by 58 units and the side length of its minimum axis-aligned bounding cube when expanded is 32 units.…”

“…For 3D, the only expanding/contracting M-TRAN meta-module that we are aware of is that of Aloupis et al [1], which is also valid for Molecube [26]. However, the meta-module of [1] is formed by 58 units and the side length of its minimum axis-aligned bounding cube when expanded is 32 units. In addition, it is much less compact than the one by Murata and Kurokawa, making it less robust.…”