Uniform Circle Formation for Swarms of Opaque Robots with Lights

Abstract

We study the Uniform Circle Formation (UCF) problem for a swarm of n autonomous mobile robots operating in Look-Compute-Move (LCM) cycles on the Euclidean plane. We assume our robots are luminous, i.e. embedded with a persistent light that can assume a color chosen from a fixed palette, and opaque, i.e. not able to see beyond a collinear robot. Robots are said to collide if they share positions or their paths intersect within concurrent LCM cycles. To solve UCF, a swarm of n robots must autonomously arrange themselves so that each robot occupies a vertex of the same regular n-gon not fixed in advance. In terms of efficiency, the goal is to design an algorithm that optimizes (or provides a tradeoff between) two fundamental performance metrics: (i) the execution time and (ii) the size of the color palette. There exists an O(1)-time O(1)-color algorithm for this problem under the fully synchronous and semi-synchronous schedulers and a O(log log n)-time O(1)-color or O(1)-time O( √ n)-color algorithm under the asynchronous scheduler, avoiding collisions. In this paper, we develop a deterministic algorithm solving UCF avoiding collisions in O(1)-time with O(1) colors under the asynchronous scheduler, which is asymptotically optimal with respect to both time and number of colors used, the first such result. Furthermore, the algorithm proposed here minimizes for the first time what we call the computational SEC, i.e. the smallest circular area where robots operate throughout the whole algorithm.

An Enhanced Photonic Quantum Finite Automaton

“…More generally, the Krohn-Rhodes decomposition theorem [27] states that any classical finite automaton can be simulated by composing very "simple" finite automata: one of these simple automata is exactly the one for L m . From this perspective, our photonic quantum automaton could be hardwired into "hybrid" architectures joining classical and quantum components to build very succinct finite state devices operating in environments where dimension and energy absorption are particularly critical issues (e.g., drone or robot-based systems [28]).…”

Circle formation by asynchronous opaque robots on infinite grid

“…Also, they assumed that an inactive robot can sense its vicinity. The closest solution to our problem was studied in [13]; however, they considered the problem under an Fsync scheduler.…”

Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

“…Generally, robots are assumed to be point-like, anonymous (without any distinct identifiers yielding the ability to distinguish one robot from another), and oblivious (without any persistent memory). In order to consider more powerful and realistic models, the luminous robot [11,[20][21][22][25][26][27] has been introduced: robots equipped with a persistent light assuming different colors. Since such a light color is preserved from one look-compute-move cycle to the next one, it can be used as a persistent constant memory and a means of communication as well.…”