Reconfiguration of 3D Crystalline Robots Using O(log n) Parallel Moves

TL;DR

This paper presents a parallel reconfiguration algorithm for 3D crystalline robots that reduces the transformation time from linear to logarithmic parallel steps, enabling near-instantaneous shape changes.

Contribution

It introduces the first parallel algorithm achieving O(log n) reconfiguration steps for crystalline robots, significantly improving reconfiguration speed.

Findings

Reconfiguration can be achieved in O(log n) parallel steps.

Total operations increase to Theta(n log n).

First theoretical model for near-instantaneous reconfigurable robots.

Abstract

We consider the theoretical model of Crystalline robots, which have been introduced and prototyped by the robotics community. These robots consist of independently manipulable unit-square atoms that can extend/contract arms on each side and attach/detach from neighbors. These operations suffice to reconfigure between any two given (connected) shapes. The worst-case number of sequential moves required to transform one connected configuration to another is known to be Theta(n). However, in principle, atoms can all move simultaneously. We develop a parallel algorithm for reconfiguration that runs in only O(log n) parallel steps, although the total number of operations increases slightly to Theta(nlogn). The result is the first (theoretically) almost-instantaneous universally reconfigurable robot built from simple units.