Optimal Rendezvous L-Algorithms for Asynchronous Mobile Robots with External-Lights

We study the Rendezvous problem for two autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible in a basic model when robots have no lights, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights of various types with a constant number of colors. If robots can observe not only their own lights but also other robots\u27 lights, their lights are called full-light. If robots can only observe the state of other robots\u27 lights, the lights are called external-light. This paper focuses on robots with external-lights in asynchronous settings and a particular class of algorithms called L-algorithms, where an L-algorithm computes a destination based only on the current colors of observable lights. When considering L-algorithms, Rendezvous can be solved by robots with full-lights and three colors in general asynchronous settings (called ASYNC) and the number of colors is optimal under these assumptions. In contrast, there exist no L-algorithms in ASYNC with external-lights regardless of the number of colors. In this paper, extending the impossibility result, we show that there exist no L-algorithms in so-called LC-1-Bounded ASYNC with external-lights regardless of the number of colors, where LC-1-Bounded ASYNC is a proper subset of ASYNC and other robots can execute at most one Look operation between the Look operation of a robot and its subsequent Compute operation. We also show that LC-1-Bounded ASYNC is the minimal subclass in which no L-algorithms with external-lights exist. That is, Rendezvous can be solved by L-algorithms using external-lights with a finite number of colors in LC-0-Bounded ASYNC (equivalently LC-atomic ASYNC). Furthermore, we show that the algorithms are optimal in the number of colors they use

RENDEZVOUS OF AUTONOMOUS MOBILE ROBOTS WITH STATES

We study a Rendezvous problem for 2 autonomous mobile robots in asynchronous setting with persistent memory called light. It is known that Rendezvous is impossible when robots have no lights in basic common models, even if the system is semi-synchronous. We show that Rendezvous can be solved with optimal number of states if we consider some restricted class of asynchronous setting. In full-light (the robot can recognize own states and states of others), Rendezvous can be solved with 2 states. In external-light, (the robot can recognize only states of others) Rendezvous can be solved with 4 states or 5 states in self-stabilization. When giving restrictions on the initial states and movement of the robots, Rendezvous can be solved with 3 states in external-light

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure

Brief Announcement: Model Checking Rendezvous Algorithms for Robots with Lights in Euclidean Space

This announces the first successful attempt at using model-checking techniques to verify the correctness of self-stabilizing distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights and presents a generic verification model for the SPIN model checker. It will be presented in full at an upcoming venue

Gathering on Rings for Myopic Asynchronous Robots With Lights

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M_{init}, which denotes the number of nodes between two border nodes, and O_{init}, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if M_{init} or O_{init} is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility