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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… (More)

This paper introduces the RoboCast communication abstraction. The RoboCast allows a swarm of non oblivious, anonymous robots that are only endowed with visibility sensors and do not share a common coordinate system, to asynchronously exchange information. We propose a generic framework that covers a large class of asynchronous communication algorithms and… (More)

—We study distributed coordination among autonomous mobile robots, focussing on the problem of gathering the robots at a single location. The gathering problem has been solved previously using deterministic algorithms even for robots that are anonymous, oblivious, disoriented, and operate in the semi-synchronous ATOM model. However these solutions require… (More)

In this paper, we consider the problem of formation of a series of geometric patterns [4] by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either assumed to have distinct identifiers or to be completely anonymous. To generalize these results and to better understand… (More)

We study the convergence problem in fully asynchronous, uni-dimensional robot networks that are prone to Byzantine (i.e. malicious) failures. In these settings, oblivious anonymous robots with arbitrary initial positions are required to eventually converge to an a apriori unknown position despite a subset of them exhibiting Byzantine behavior. Our… (More)

The k-set agreement problem is a generalization of the consensus problem. Namely, assuming each process proposes a value, each non-faulty process has to decide a value such that each decided value was proposed, and no more than k different values are decided. This is a hard problem in the sense that it cannot be solved in asynchronous systems as soon as k… (More)