Enumeration of the Non-Isomorphic Configurations for a Reconfigurable Modular Robot with Square-Cubic-Cell Modules

Jinguo Liu,Shugen Ma,Yuechao Wang,Yangmin Li

doi:10.5772/10489

Abstract

Configuration of a reconfigurable modular system is a tough issue because the possible configurations or structures grow exponentially with the number of modules. A library of the non-isomorphic configurations should be set up as a database for configuration design and control. In this paper, we propose a matrix-based enumerating approach for the non-isomorphic configurations of a reconfigurable modular robot system with square-cubic-cell(SCC) modules. Each SCC module considered in this study includes a cubic module body and four connectors on its lateral surfaces. Since it has a square lattice like 2D projection, configuration matrices are proposed to represent the topological information of the modular robot. Thus reconfiguration and enumeration can be programmed by matrix computation in simulation. According to combinational principle, recursive algorithms are used to find out all non-isomorphic configurations. Enumerating result for a multi-module SCC system is provided as an example. Potential applications of this approach to other reconfigurable systems with lattice-form or cubic-form modules are discussed as well. As an application, enumeration of the multi-module CONRO robot also proves the validity of this method.

Highlights

Since some of them can be projected onto a 2D plane like a rectangle or a square lattice, we propose a technique by using configuration matrices to represent the non‐isomorphic configurations of a reconfigurable modular robot with square‐cubic‐cell(SCC) modules
We have proposed a matrix‐based enumerating approach for the non‐isomorphic configurations of a reconfigurable modular robot system with square‐cubic‐cell (SCC) modules
Since the SCC module has a lattice‐like 2D projection, configuration matrices have been proposed to represent the topological information of the modular robot

Summary

Introduction

The reconfigurable modular robot is a kind of biologically inspired robot that can be reconfigured and reassembled to fulfil various natural environmental tasks, which has been widely studied for many applications in areas of deep sea exploration, space exploration, urban search and rescue, and many other situations (e.g., Fukuda and Nakagawa, 1988, 1990; Groß et al, 2006; Liu et al, 2004, 2005, 2008; Rus and Chirikjian, 2001; Shen et al, 2006; Yim et al, 2000a, 2003; Zykov et al, 2005). Reconfigurable modular robots can be mainly divided into chain‐type reconfigurable systems (e.g., CEBOT (Fukuda and Nakagawa, 1990), CONRO (Castano and Will, 2001), SuperBot (Shen et al, 2006), Polypod (Casal and Yim, 1999), PolyBot (Yim et al, 2000b), AMOEBA‐I (Liu et al, 2008) ) and lattice‐type ones (e.g., Telecube (Vassilvitskii et al, 2002), I‐Cube (Ünsal and Khosla, 2000), Metamorphic(Chirikjian,1994), Molecule (Kotay, 1998), Crystalline(Rus and Vona, 2001), Fracta (Murata, 1994), Gear‐Type Unit (Tokashiki et al.,2003), ATRON (Østergaard et al, 2006), Riken Vertical (Hosokawa et al, 1998)). Since some of them can be projected onto a 2D plane like a rectangle or a square lattice, we propose a technique by using configuration matrices to represent the non‐isomorphic configurations of a reconfigurable modular robot with square‐cubic‐cell(SCC) modules.

Results

Conclusion