194 research outputs found
Optimal byzantine resilient convergence in oblivious robot networks
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 , values distance
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
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
A unified approach for different tasks on rings in robot-based computing systems
International audienceA set of autonomous robots have to collaborate in order to accomplish a common task in a ring-topology where neither nodes nor edges are labeled. We present a unified approach to solve three important problems: the exclusive perpetual exploration, the exclusive perpetual search and the gathering problems. In the first problem, each robot aims at visiting each node infinitely often; in perpetual graph searching, the team of robots aims at clearing the whole network infinitely often; and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the Look-Compute- Move distributed computing model where the robots cannot communicate but can perceive the positions of other robots. Each robot is equipped with visibility sensors and motion actuators, and it operates in asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are anonymous, oblivious, uniform (execute the same algorithm) and have no common sense of orientation. In this setting, we devise algorithms that, starting from an exclusive rigid (i.e. aperiodic and asymmetric) configuration, solve the three above problems in anonymous ring-topologies
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