6 research outputs found
Positional Encoding by Robots with Non-Rigid Movements
Consider a set of autonomous computational entities, called \emph{robots},
operating inside a polygonal enclosure (possibly with holes), that have to
perform some collaborative tasks. The boundary of the polygon obstructs both
visibility and mobility of a robot. Since the polygon is initially unknown to
the robots, the natural approach is to first explore and construct a map of the
polygon. For this, the robots need an unlimited amount of persistent memory to
store the snapshots taken from different points inside the polygon. However, it
has been shown by Di Luna et al. [DISC 2017] that map construction can be done
even by oblivious robots by employing a positional encoding strategy where a
robot carefully positions itself inside the polygon to encode information in
the binary representation of its distance from the closest polygon vertex. Of
course, to execute this strategy, it is crucial for the robots to make accurate
movements. In this paper, we address the question whether this technique can be
implemented even when the movements of the robots are unpredictable in the
sense that the robot can be stopped by the adversary during its movement before
reaching its destination. However, there exists a constant ,
unknown to the robot, such that the robot can always reach its destination if
it has to move by no more than amount. This model is known in
literature as \emph{non-rigid} movement. We give a partial answer to the
question in the affirmative by presenting a map construction algorithm for
robots with non-rigid movement, but having bits of persistent memory and
ability to make circular moves
Asynchronous Gathering of Robots with Finite Memory on a Circle under Limited Visibility
Consider a set of mobile entities, called robots, located and operating
on a continuous circle, i.e., all robots are initially in distinct locations on
a circle. The \textit{gathering} problem asks to design a distributed algorithm
that allows the robots to assemble at a point on the circle. Robots are
anonymous, identical, and homogeneous. Robots operate in a deterministic
Look-Compute-Move cycle within the circular path. Robots agree on the clockwise
direction. The robot's movement is rigid and they have limited visibility
, i.e., each robot can only see the points of the circle which is at an
angular distance strictly less than from the robot.
Di Luna \textit{et al}. [DISC'2020] provided a deterministic gathering
algorithm of oblivious and silent robots on a circle in semi-synchronous
(\textsc{SSync}) scheduler. Buchin \textit{et al}. [IPDPS(W)'2021] showed that,
under full visibility, robot model with \textsc{SSync}
scheduler is incomparable to robot (robots are silent but have
finite persistent memory) model with asynchronous (\textsc{ASync}) scheduler.
Under limited visibility, this comparison is still unanswered. So, this work
extends the work of Di Luna \textit{et al}. [DISC'2020] under \textsc{ASync}
scheduler for robot model
Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults
A set of mobile robots is placed at points of an infinite line. The robots
are equipped with GPS devices and they may communicate their positions on the
line to a central authority. The collection contains an unknown subset of
"spies", i.e., byzantine robots, which are indistinguishable from the
non-faulty ones. The set of the non-faulty robots need to rendezvous in the
shortest possible time in order to perform some task, while the byzantine
robots may try to delay their rendezvous for as long as possible. The problem
facing a central authority is to determine trajectories for all robots so as to
minimize the time until the non-faulty robots have rendezvoused. The
trajectories must be determined without knowledge of which robots are faulty.
Our goal is to minimize the competitive ratio between the time required to
achieve the first rendezvous of the non-faulty robots and the time required for
such a rendezvous to occur under the assumption that the faulty robots are
known at the start. We provide a bounded competitive ratio algorithm, where the
central authority is informed only of the set of initial robot positions,
without knowing which ones or how many of them are faulty. When an upper bound
on the number of byzantine robots is known to the central authority, we provide
algorithms with better competitive ratios. In some instances we are able to
show these algorithms are optimal
Meeting in a Polygon by Anonymous Oblivious Robots
The Meeting problem for searchers in a polygon (possibly with
holes) consists in making the searchers move within , according to a
distributed algorithm, in such a way that at least two of them eventually come
to see each other, regardless of their initial positions. The polygon is
initially unknown to the searchers, and its edges obstruct both movement and
vision. Depending on the shape of , we minimize the number of searchers
for which the Meeting problem is solvable. Specifically, if has a
rotational symmetry of order (where corresponds to no
rotational symmetry), we prove that searchers are sufficient, and
the bound is tight. Furthermore, we give an improved algorithm that optimally
solves the Meeting problem with searchers in all polygons whose
barycenter is not in a hole (which includes the polygons with no holes). Our
algorithms can be implemented in a variety of standard models of mobile robots
operating in Look-Compute-Move cycles. For instance, if the searchers have
memory but are anonymous, asynchronous, and have no agreement on a coordinate
system or a notion of clockwise direction, then our algorithms work even if the
initial memory contents of the searchers are arbitrary and possibly misleading.
Moreover, oblivious searchers can execute our algorithms as well, encoding
information by carefully positioning themselves within the polygon. This code
is computable with basic arithmetic operations, and each searcher can
geometrically construct its own destination point at each cycle using only a
compass. We stress that such memoryless searchers may be located anywhere in
the polygon when the execution begins, and hence the information they initially
encode is arbitrary. Our algorithms use a self-stabilizing map construction
subroutine which is of independent interest.Comment: 37 pages, 9 figure
Deterministic Rendezvous of Asynchronous Bounded-Memory Agents in Polygonal Terrains
International audienc