485 research outputs found
Compatibility of convergence algorithms for autonomous mobile robots
We investigate autonomous mobile robots in the Euclidean plane. A robot has a
function called target function to decide the destination from the robots'
positions, and operates in Look-Compute-Move cycles, i.e., identifies the
robots' positions, computes the destination by the target function, and then
moves there. Robots may have different target functions. Let and
be a set of target functions and a problem, respectively. If the robots whose
target functions are chosen from always solve , we say that
is compatible with respect to . If is compatible with respect to
, every target function is an algorithm for (in the
conventional sense). Note that even if both and are algorithms
for , may not be compatible with respect to .
From the view point of compatibility, we investigate the convergence, the
fault tolerant ()-convergence (FC()), the fault tolerant
()-convergence to points (FC()-PO), the fault tolerant
()-convergence to a convex -gon (FC()-CP), and the gathering
problems, assuming crash failures. As a result, we see that these problems are
classified into three groups: The convergence, the FC(1), the FC(1)-PO, and the
FC()-CP compose the first group: Every set of target functions which always
shrink the convex hull of a configuration is compatible. The second group is
composed of the gathering and the FC()-PO for : No set of target
functions which always shrink the convex hull of a configuration is compatible.
The third group, the FC() for , is placed in between. Thus, the
FC(1) and the FC(2), the FC(1)-PO and the FC(2)-PO, and the FC(2) and the
FC(2)-PO are respectively in different groups, despite that the FC(1) and the
FC(1)-PO are in the first group
Minimum algorithm sizes for self-stabilizing gathering and related problems of autonomous mobile robots
We investigate a swarm of autonomous mobile robots in the Euclidean plane. A
robot has a function called {\em target function} to determine the destination
point from the robots' positions. All robots in the swarm conventionally take
the same target function, but there is apparent limitation in problem-solving
ability. We allow the robots to take different target functions. The number of
different target functions necessary and sufficient to solve a problem is
called the {\em minimum algorithm size} (MAS) for . We establish the MASs
for solving the gathering and related problems from {\bf any} initial
configuration, i.e., in a {\bf self-stabilizing} manner. We show, for example,
for , there is a problem such that the MAS for the
is , where is the size of swarm. The MAS for the gathering
problem is 2, and the MAS for the fault tolerant gathering problem is 3, when
robots may crash, but the MAS for the problem of gathering all
robot (including faulty ones) at a point is not solvable (even if all robots
have distinct target functions), as long as a robot may crash
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
- …