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

Parameterized Verification of Algorithms for Oblivious Robots on a Ring

We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameter-ized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies

Finding Water on Poleless Using Melomaniac Myopic Chameleon Robots

In 2042, the exoplanet exploration program, launched in 2014 by NASA, finally discovers a new exoplanet so-called Poleless, due to the fact that it is not subject to any magnetism. A new generation of autonomous mobile robots, called M2C (for Melomaniac Myopic Chameleon), have been designed to find water on Poleless. To address this problem, we investigate optimal (w.r.t., visibility range and number of used colors) solutions to the infinite grid exploration problem (IGE) by a small team of M2C robots. Our first result shows that minimizing the visibility range and the number of used colors are two orthogonal issues: it is impossible to design a solution to the IGE problem that is optimal w.r.t. both parameters simultaneously. Consequently, we address optimality of these two criteria separately by proposing two algorithms; the former being optimal in terms of visibility range, the latter being optimal in terms of number of used colors. It is worth noticing that these two algorithms use a very small number of robots, respectively six and eight

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

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