Line-Recovery by Programmable Particles

Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line shape, used as a tool for the construction of more complex configurations. We present a solution to the line recovery problem by the non-faulty anonymous particles; the solution works regardless of the initial distribution and number $f<n-4$ of faults, of the local orientations of the non-faulty entities, and of the number of non-faulty entities activated in each round (i.e., semi-synchronous adversarial scheduler)

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

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks

Exploration of Finite 2D Square Grid by a Metamorphic Robotic System

We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules. The number of possible shapes of a metamorphic robotic system grows as the number of modules increases. The shape of the system serves as its memory and shows its functionality. We consider the effect of global compass on the minimum number of modules necessary to explore a finite 2D square grid. We show that if the modules agree on the directions (north, south, east, and west), three modules are necessary and sufficient for exploration from an arbitrary initial configuration, otherwise five modules are necessary and sufficient for restricted initial configurations

Deaf, Dumb, and Chatting Robots, Enabling Distributed Computation and Fault-Tolerance Among Stigmergic Robot

We investigate ways for the exchange of information (explicit communication) among deaf and dumb mobile robots scattered in the plane. We introduce the use of movement-signals (analogously to flight signals and bees waggle) as a mean to transfer messages, enabling the use of distributed algorithms among the robots. We propose one-to-one deterministic movement protocols that implement explicit communication. We first present protocols for synchronous robots. We begin with a very simple coding protocol for two robots. Based on on this protocol, we provide one-to-one communication for any system of n \geq 2 robots equipped with observable IDs that agree on a common direction (sense of direction). We then propose two solutions enabling one-to-one communication among anonymous robots. Since the robots are devoid of observable IDs, both protocols build recognition mechanisms using the (weak) capabilities offered to the robots. The first protocol assumes that the robots agree on a common direction and a common handedness (chirality), while the second protocol assumes chirality only. Next, we show how the movements of robots can provide implicit acknowledgments in asynchronous systems. We use this result to design asynchronous one-to-one communication with two robots only. Finally, we combine this solution with the schemes developed in synchronous settings to fit the general case of asynchronous one-to-one communication among any number of robots. Our protocols enable the use of distributing algorithms based on message exchanges among swarms of Stigmergic robots. Furthermore, they provides robots equipped with means of communication to overcome faults of their communication device

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

Asynchronous approach in the plane: A deterministic polynomial algorithm

In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other's range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed. Let $\Delta$ and $l$ be the initial distance separating the agents and the length of the shortest label, respectively. Assuming that $\Delta$ and $l$ are unknown to both agents, does there exist a deterministic approach algorithm always working at a cost that is polynomial in $\Delta$ and $l$? In this paper, we provide a positive answer to the above question by designing such an algorithm