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

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

Formal Methods for Mobile Robots

International audienceMost existing work in the literature typically ensures the correctness of mobile robot protocols via ad hoc handwritten proofs, which are both cumbersome and error-prone.This paper surveys state-of-the-art results about applying formal methods approaches (namely, model-checking, program synthesis, and proof assistants) to the context of mobile robot networks. Those methods already proved useful for bug-hunting in published literature, designing correct-by-design optimal protocols, and certifying impossibility results and protocols

[Invited Paper] Formal Methods for Mobile Robots: Current Results and Open Problems

International audienceMobile robot networks emerged in the past few years as a promising distributed computing model. Existing work in the literature typically ensures the correctness of mobile robot protocols via ad hoc handwritten proofs, which are both cumbersome and error-prone.This paper surveys state-of-the-art results about applying formal methods approaches (namely, model-checking, program synthesis, and proof assistants) to the context of mobile robot networks. Those methods already proved useful for bug-hunting in published literature, designing correct-by-design optimal protocols, and certifying impossibility results.We also present related open questions to further develop this path of research