Morphology Transformation of Underwater Self-Reconfigurable Modular Robots via Heterogeneous Decomposition and Distributed Control

Abstract

This paper addresses the morphology transformation problem of an underwater self-reconfigurable modular robotic system. Morphology decomposition and reconnections are reduced to mitigate transformation failures and the overhead of underwater wireless communication, giving rise to subgraph matching problems. We propose an efficient probabilistic decomposition method by constraining the search depth of maximal common subgraphs of the initial and goal morphologies. The computational complexity reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{2})$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula>. The decomposition yields a swarm of heterogeneous clusters, which are interconnected modular robots of varying quantities. The heterogeneity makes the exchange of clusters’ designated positions in the goal morphology not immediately feasible. Subsequently, we present Distributed Control with minimal In-situ task Refinement (DCIR). DCIR is proven to ensure collision-free and deadlock-free morphology transformation. The numerical simulations involving up to 641 modular robots and experiments on 6 robots have shown that DCIR scales well with the number of modular robots, runs in real time, and reduces traveling distances by at least 14% and communication costs by about half, compared to the distributed control with homogeneous task exchange and the modified surface sliding method. Note to Practitioners—This paper presents a distributed control approach to transform the morphologies. Considering the limited communication bandwidth, the disconnections between modular robots are minimized. The proposed distributed control approach refines tasks locally to transform the morphologies, and it scales well to the number of modular robots. This effort is orthogonal to the existing studies on the structures of the modular system. However, the positioning of the underwater robots in this study was assumed known or given by an underwater motion capture system, and it should be further investigated.