Parameterized verification of algorithms for oblivious robots on a ring

Abstract

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 parameterized 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.

Optimally Gathering Two Robots

“…However, we expect the complexity of the proof to go beyond what is tractable by a human, and would like to consider the possibility of using formal methods. Currently, modelchecking [15,4,17,21] and program synthesis [6,19] cannot scale to an arbitrary number of robots, and proof assistant techniques [2,11,10,3] do not yet permit to reason about the ASYNC model. Most likely, solving self-stabilizing gathering with n robots in ASYNC will require significant advances in mobile robot formalization.…”

On the Encoding and Solving of Partial Information Games

“…We partly use notations defined in [27]. We consider a fixed number of k > 0 robots evolving on a ring of fixed size n ≥ k. We denote by R the set of considered robots.…”

Continuous vs. Discrete Asynchronous Moves: A Certified Approach for Mobile Robots

“…Formal methods encompass a long-lasting path of research that is meant to overcome errors of human origin. Unsurprisingly, this mechanised approach to protocol correctness was successively used in the context of mobile robots [9,20,6,1,35,16,5,37,2,38,3].…”

“…However, those approaches are limited to small instances with few robots. Generalising to an arbitrary number of robots with similar approaches is doubtful as Sangnier et al [38] proved that safety and reachability problems become undecidable in the parameterised case.…”