378 research outputs found
Gathering on Rings for Myopic Asynchronous Robots With Lights
We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M_{init}, which denotes the number of nodes between two border nodes, and O_{init}, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if M_{init} or O_{init} is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility
Gathering an even number of robots in an odd ring without global multiplicity detection
We propose a gathering protocol for an even number of robots in a ring-shaped
network that allows symmetric but not periodic configurations as initial
configurations, yet uses only local weak multiplicity detection. Robots are
assumed to be anonymous and oblivious, and the execution model is the non-
atomic CORDA model with asynchronous fair scheduling. In our scheme, the number
of robots k must be greater than 8, the number of nodes n on a network must be
odd and greater than k+3. The running time of our protocol is O(n2)
asynchronous rounds.Comment: arXiv admin note: text overlap with arXiv:1104.566
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
Gathering over Meeting Nodes in Infinite Grid
The gathering over meeting nodes problem asks the robots to gather at one of
the pre-defined meeting nodes. The robots are deployed on the nodes of an
anonymous two-dimensional infinite grid which has a subset of nodes marked as
meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They
operate under an asynchronous scheduler. They do not have any agreement on a
global coordinate system. All the initial configurations for which the problem
is deterministically unsolvable have been characterized. A deterministic
distributed algorithm has been proposed to solve the problem for the remaining
configurations. The efficiency of the proposed algorithm is studied in terms of
the number of moves required for gathering. A lower bound concerning the total
number of moves required to solve the gathering problem has been derived
Asynchronous Gathering in a Torus
We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots.
Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network
Model Checking of Robot Gathering
Recent advances in distributed computing highlight models and algorithms for autonomous mo- bile robots that self-organize and cooperate together in order to solve a global objective. As results, a large number of algorithms have been proposed. These algorithms are given together with proofs to assess their correctness. However, those proofs are informal, which are error prone. This paper presents our study on formal verification of mobile robot algorithms. We first propose a formal model for mobile robot algorithms on anonymous ring shape network under multiplicity and asynchrony assumptions. We specify this formal model in Maude, a specification and pro- gramming language based on rewriting logic. We then use its model checker to formally verify an algorithm for robot gathering problem on ring enjoys some desired properties. As the result of the model checking, counterexamples have been found. We detect the sources of some unforeseen design errors. We, furthermore, give our interpretations of these errors
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