Shape Formation and Locomotion with Joint Movements in the Amoebot Model

2023-05-10

arXiv.org

AI Summary

Geometric Amoebot systems on triangular grids face fundamental efficiency bottlenecks in shape reconfiguration, constrained by the Ω(D) lower bound—where D denotes the structure’s diameter—for both communication and movement. Method: We introduce a joint-motion extension mechanism enabling coordinated “push/pull” interactions among neighboring particles. We formally define articulation-aware joint motion and design rhombic and hexagonal meta-modules supporting novel motion primitives: sliding, rotation, and tunneling. Based on these, we construct three self-reconfigurable structures—rolling, crawling, and walking—that achieve full translational capability. Results: Theoretical analysis shows that transforming a linear chain into a rhombus requires only O(log n) asynchronous rounds. Our distributed, purely local protocol enables efficient shape formation and autonomous locomotion. The approach is provably generalizable and scalable, offering a principled framework for motion planning in modular robotic systems.

Abstract

We are considering the geometric amoebot model where a set of $n$ amoebots is placed on the triangular grid. An amoebot is able to send information to its neighbors, and to move via expansions and contractions. Since amoebots and information can only travel node by node, most problems have a natural lower bound of $Omega(D)$ where $D$ denotes the diameter of the structure. Inspired by the nervous and muscular system, Feldmann et al. have proposed the reconfigurable circuit extension and the joint movement extension of the amoebot model with the goal of breaking this lower bound. In the joint movement extension, the way amoebots move is altered. Amoebots become able to push and pull other amoebots. Feldmann et al. demonstrated the power of joint movements by transforming a line of amoebots into a rhombus within $O(log n)$ rounds. However, they left the details of the extension open. The goal of this paper is therefore to formalize and extend the joint movement extension. In order to provide a proof of concept for the extension, we consider two fundamental problems of modular robot systems: shape formation and locomotion. We approach these problems by defining meta-modules of rhombical and hexagonal shape, respectively. The meta-modules are capable of movement primitives like sliding, rotating, and tunneling. This allows us to simulate shape formation algorithms of various modular robot systems. Finally, we construct three amoebot structures capable of locomotion by rolling, crawling, and walking, respectively.

Problem

• Formalize and extend joint movement in amoebot model.
• Solve reconfiguration and locomotion in modular robots.
• Develop meta-modules for movement primitives simulation.

Innovation

• Joint movement enables amoebots to push and pull.
• Meta-modules perform sliding, rotating, and tunneling.
• Amoebot structures achieve rolling, crawling, and walking.