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

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

Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

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

Synchronous Robots vs Asynchronous Lights-Enhanced Robots on Graphs

AbstractIn this paper, we consider the distributed setting of computational mobile entities, called robots, that have to perform tasks without global coordination. Depending on the environment as well as on the robots' capabilities, tasks might be accomplished or not.In particular, we focus on the well-known scenario where the robots reside on the nodes of a graph and operate in Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of robots positions (Look), decides whether to move toward some edge of the graph (Compute), and in the positive case it performs an instantaneous move along the computed edge (Move).We then compare two basic models: in the first model robots are fully synchronous, while in the second one robots are asynchronous and lights-enhanced, that is, each robot is equipped with a constant number of lights visible to all other robots. The question whether one model is more powerful than the other in terms of computable tasks has been considered in [Das et al., Int.'l Conf. on Distributed Computing Systems, 2012] but for robots moving on the Euclidean plane rather than on a graph.We provide two different tasks, and show that on graphs one task can be solved in the fully synchronous model but not in the asynchronous lights-enhanced model, while for the other task the converse holds. Hence we can assert that the fully synchronous model and the asynchronous lights-enhanced model are incomparable on graphs. This opens challenging directions in order to understand which peculiarities make the models so different