Ring Exploration with Oblivious Myopic Robots

The exploration problem in the discrete universe, using identical oblivious asynchronous robots without direct communication, has been well investigated. These robots have sensors that allow them to see their environment and move accordingly. However, the previous work on this problem assume that robots have an unlimited visibility, that is, they can see the position of all the other robots. In this paper, we consider deterministic exploration in an anonymous, unoriented ring using asynchronous, oblivious, and myopic robots. By myopic, we mean that the robots have only a limited visibility. We study the computational limits imposed by such robots and we show that under some conditions the exploration problem can still be solved. We study the cases where the robots visibility is limited to 1, 2, and 3 neighboring nodes, respectively.Comment: (2012

Optimal torus exploration by oblivious robots

International audienceWe deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size ℓ×L, where 7≤ℓ≤L, by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots

Uniform multi-agent deployment on a ring

AbstractWe consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges.The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring. We show that if either the ring is unoriented, or the visibility range is less than ⌊n/k⌋, this is an impossible mission for the agents. Then, for an oriented ring and V≥⌈n/k⌉, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread.The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference

Optimal Torus Exploration by Oblivious Robots

International audienceWe consider autonomous robots that are endowed with motion actuators and visibility sensors. The robots we consider are weak, i.e., they are anonymous, uniform, unable to explicitly communicate, and oblivious (they do not remember any of their past actions). In this paper, we propose an optimal (w.r.t. the number of robots) solution for the terminating exploration of a torus-shaped network by a team of $k$ such robots. In more details, we first show that it is impossible to explore a simple torus of arbitrary size with (strictly) less than four robots, even if the algorithm is probabilistic. If the algorithm is required to be deterministic, four robots are also insufficient. This negative result implies that the only way to obtain an optimal algorithm (w.r.t. the number of robots participating to the algorithm) is to make use of probabilities. Then, we propose a probabilistic algorithm that uses four robots to explore all simple tori of size $\ell \times L$, where $7 \leq \ell \leq L$. Hence, in such tori, four robots are necessary and sufficient to solve the (probabilistic) terminating exploration. As a torus can be seen as a 2-dimensional ring, our result shows, perhaps surprisingly, that increasing the number of possible symmetries in the network (due to increasing dimensions) does not come at an extra cost w.r.t. the number of robots that are necessary to solve the problem

A Certified Universal Gathering Algorithm for Oblivious Mobile Robots

We present a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. To our knowledge, this is the first certified positive (and constructive) result in the context of oblivious mobile robots. It demonstrates both the effectiveness of the approach to obtain new algorithms that are truly generic, and its managability since the amount of developped code remains human readable

Terminating Exploration Of A Grid By An Optimal Number Of Asynchronous Oblivious Robots

International audienceWe consider swarms of asynchronous oblivious robots evolving into an anonymous grid-shaped network. In this context, we investigate optimal (w.r.t. the number of robots) deterministic solutions for the terminating exploration problem. We first show lower bounds in the semi-synchronous model. Precisely, we show that at least three robots are required to explore any grid of at least three nodes, even in the probabilistic case. Then, we show that at least four (resp. five) robots are necessary to deterministically explore a (2,2)-Grid (resp. a (3,3)-Grid). We then propose deterministic algorithms in the asynchronous model. This latter being strictly weakest than the semi-synchronous model, all the aforementioned bounds still hold in that context. Our algorithms actually exhibit the optimal number of robots that is necessary to explore a given grid. Overall, our results show that except in two particular cases, three robots are necessary and sufficient to deterministically explore a grid of at least three nodes and then terminate. The optimal number of robots for the two remaining cases is four for the (2,2)-Grid and five for the (3,3)-Grid, respectively

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

Certified Universal Gathering in R2R^2 for Oblivious Mobile Robots

We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework. As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a two-dimensional Euclidean space. In more details, we provide a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160

On the Synthesis of Mobile Robots Algorithms: the Case of Ring Gathering

International audienceRecent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs.This paper is the first to propose a formal framework to automatically design distributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolving on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size)