Reaching approximate agreement in the presence of faults
Journal of the ACM (JACM)
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Distributed Algorithms
Information and Computation
Fault-tolerant gathering algorithms for autonomous mobile robots
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Convergence of autonomous mobile robots with inaccurate sensors and movements
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Optimal resilience asynchronous approximate agreement
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
On the feasibility of gathering by autonomous mobile robots
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Optimal Byzantine Resilient Convergence in Asynchronous Robots Networks
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Byzantine Convergence in Robot Networks: The Price of Asynchrony
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Pattern formation through optimum matching by oblivious CORDA robots
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Optimal exploration of small rings
Proceedings of the Third International Workshop on Reliability, Availability, and Security
Optimal probabilistic ring exploration by semi-synchronous oblivious robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
The Gathering Problem for Two Oblivious Robots with Unreliable Compasses
SIAM Journal on Computing
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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 prove ([4]) 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 and (4f + 1)-sized in asynchronous networks. The bounds obtained for the ATOM model are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots.