2,458 research outputs found

    Optimal byzantine resilient convergence in oblivious robot networks

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    Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious-- they do not recall the past computations -- and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. We draw a connection between the convergence problem in robot networks, and the distributed \emph{approximate agreement} problem (that requires correct processes to decide, for some constant ϵ\epsilon, values distance ϵ\epsilon apart and within the range of initial proposed values). Surprisingly, even though specifications are similar, the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings. The proposed algorithm tolerates f Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks, (3f+1)-sized in semi-synchronous networks. These bounds are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots

    Optimal Byzantine Resilient Convergence in Asynchronous Robot Networks

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    We propose the first deterministic algorithm that tolerates up to ff byzantine faults in 3f+13f+1-sized networks and performs in the asynchronous CORDA model. Our solution matches the previously established lower bound for the semi-synchronous ATOM model on the number of tolerated Byzantine robots. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space

    Fault-Tolerant Dispersion of Mobile Robots

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    We consider the mobile robot dispersion problem in the presence of faulty robots (crash-fault). Mobile robot dispersion consists of k≤nk\leq n robots in an nn-node anonymous graph. The goal is to ensure that regardless of the initial placement of the robots over the nodes, the final configuration consists of having at most one robot at each node. In a crash-fault setting, up to f≤kf \leq k robots may fail by crashing arbitrarily and subsequently lose all the information stored at the robots, rendering them unable to communicate. In this paper, we solve the dispersion problem in a crash-fault setting by considering two different initial configurations: i) the rooted configuration, and ii) the arbitrary configuration. In the rooted case, all robots are placed together at a single node at the start. The arbitrary configuration is a general configuration (a.k.a. arbitrary configuration in the literature) where the robots are placed in some l<kl<k clusters arbitrarily across the graph. For the first case, we develop an algorithm solving dispersion in the presence of faulty robots in O(k2)O(k^2) rounds, which improves over the previous O(f⋅min(m,kΔ))O(f\cdot\text{min}(m,k\Delta))-round result by \cite{PS021}. For the arbitrary configuration, we present an algorithm solving dispersion in O((f+l)⋅min(m,kΔ,k2))O((f+l)\cdot\text{min}(m, k \Delta, k^2)) rounds, when the number of edges mm and the maximum degree Δ\Delta of the graph is known to the robots
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