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Rendezvous and Merging for Two Metamorphic Robotic Systems without Global Compass

Ryonosuke Yamada, Tomoyuki Usami, Yukiko Yamauchi

TL;DR

This work addresses distributed coordination of two metamorphic robotic systems (MRSs) without a global compass. It introduces a path-based rendezvous algorithm that forces two $5$-module MRSs to gather and observe all modules, followed by a label- and view-driven merge algorithm that connects the two MRSs into a single connected system. The authors prove that $5$ modules per MRS are necessary for rendezvous in their model and provide detailed procedures to handle symmetry, collisions, and deadlocks, achieving merging under specified visibility. This constitutes the first known result on distributed coordination of multiple MRSs and lays groundwork for multi-MRS building blocks, with potential implications for leader election, synchronization, and fault-tolerant coordination in metamorphic robotics.

Abstract

A metamorphic robotic system (MRS) consists of anonymous modules, each of which autonomously moves in the 2D square grid by sliding and rotation with keeping connectivity among the modules. Existing literature considers distributed coordination among modules so that they collectively form a single MRS. In this paper, we consider distributed coordination for two MRSs. We first present a rendezvous algorithm that makes the two MRSs gather so that each module can observe all the other modules. Then, we present a merge algorithm that makes the two MRSs assemble and establish connectivity after rendezvous is finished. These two algorithms assume that each MRS consists of five modules, that do not have a common coordinate system. Finally, we show that five modules for each MRS is necessary to solve the rendezvous problem. To the best of our knowledge, our result is the first result on distributed coordination of multiple MRSs.

Rendezvous and Merging for Two Metamorphic Robotic Systems without Global Compass

TL;DR

This work addresses distributed coordination of two metamorphic robotic systems (MRSs) without a global compass. It introduces a path-based rendezvous algorithm that forces two -module MRSs to gather and observe all modules, followed by a label- and view-driven merge algorithm that connects the two MRSs into a single connected system. The authors prove that modules per MRS are necessary for rendezvous in their model and provide detailed procedures to handle symmetry, collisions, and deadlocks, achieving merging under specified visibility. This constitutes the first known result on distributed coordination of multiple MRSs and lays groundwork for multi-MRS building blocks, with potential implications for leader election, synchronization, and fault-tolerant coordination in metamorphic robotics.

Abstract

A metamorphic robotic system (MRS) consists of anonymous modules, each of which autonomously moves in the 2D square grid by sliding and rotation with keeping connectivity among the modules. Existing literature considers distributed coordination among modules so that they collectively form a single MRS. In this paper, we consider distributed coordination for two MRSs. We first present a rendezvous algorithm that makes the two MRSs gather so that each module can observe all the other modules. Then, we present a merge algorithm that makes the two MRSs assemble and establish connectivity after rendezvous is finished. These two algorithms assume that each MRS consists of five modules, that do not have a common coordinate system. Finally, we show that five modules for each MRS is necessary to solve the rendezvous problem. To the best of our knowledge, our result is the first result on distributed coordination of multiple MRSs.
Paper Structure (8 sections, 3 theorems, 14 figures, 2 algorithms)

This paper contains 8 sections, 3 theorems, 14 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Metamorphic robotic system
  4. Problem definitions
  5. Rendezvous algorithm
  6. Merge algorithm
  7. Impossibility
  8. Conclusion

Key Result

Theorem 1

Two MRSs each of which consists of five modules not equipped with the global compass can solve the rendezvous problem from an arbitrary initial configuration, where the state of each MRS is not symmetric in a field of size $w \times h$ ($w \neq h$).

Figures (14)

  • Figure 1:
  • Figure 3:
  • Figure 5:
  • Figure 7: Paths on the field. $(a)$ Path $A$. $(b)$ Path $B$. $(c)$ Forward move on path $A$. $(d)$ Backward move on path $B$.
  • Figure 8:
  • ...and 9 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3