97 research outputs found
k-Color Multi-Robot Motion Planning
We present a simple and natural extension of the multi-robot motion planning
problem where the robots are partitioned into groups (colors), such that in
each group the robots are interchangeable. Every robot is no longer required to
move to a specific target, but rather to some target placement that is assigned
to its group. We call this problem k-color multi-robot motion planning and
provide a sampling-based algorithm specifically designed for solving it. At the
heart of the algorithm is a novel technique where the k-color problem is
reduced to several discrete multi-robot motion planning problems. These
reductions amplify basic samples into massive collections of free placements
and paths for the robots. We demonstrate the performance of the algorithm by an
implementation for the case of disc robots and polygonal robots translating in
the plane. We show that the algorithm successfully and efficiently copes with a
variety of challenging scenarios, involving many robots, while a simplified
version of this algorithm, that can be viewed as an extension of a prevalent
sampling-based algorithm for the k-color case, fails even on simple scenarios.
Interestingly, our algorithm outperforms a well established implementation of
PRM for the standard multi-robot problem, in which each robot has a distinct
color.Comment: 2
Motion Planning for Unlabeled Discs with Optimality Guarantees
We study the problem of path planning for unlabeled (indistinguishable)
unit-disc robots in a planar environment cluttered with polygonal obstacles. We
introduce an algorithm which minimizes the total path length, i.e., the sum of
lengths of the individual paths. Our algorithm is guaranteed to find a solution
if one exists, or report that none exists otherwise. It runs in time
, where is the number of robots and is the total
complexity of the workspace. Moreover, the total length of the returned
solution is at most , where OPT is the optimal solution cost. To
the best of our knowledge this is the first algorithm for the problem that has
such guarantees. The algorithm has been implemented in an exact manner and we
present experimental results that attest to its efficiency
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
We consider the following motion-planning problem: we are given unit
discs in a simple polygon with vertices, each at their own start position,
and we want to move the discs to a given set of target positions. Contrary
to the standard (labeled) version of the problem, each disc is allowed to be
moved to any target position, as long as in the end every target position is
occupied. We show that this unlabeled version of the problem can be solved in
time, assuming that the start and target positions are at
least some minimal distance from each other. This is in sharp contrast to the
standard (labeled) and more general multi-robot motion-planning problem for
discs moving in a simple polygon, which is known to be strongly NP-hard
Pebble Motion on Graphs with Rotations: Efficient Feasibility Tests and Planning Algorithms
We study the problem of planning paths for distinguishable pebbles
(robots) residing on the vertices of an -vertex connected graph with . A pebble may move from a vertex to an adjacent one in a time step provided
that it does not collide with other pebbles. When , the only collision
free moves are synchronous rotations of pebbles on disjoint cycles of the
graph. We show that the feasibility of such problems is intrinsically
determined by the diameter of a (unique) permutation group induced by the
underlying graph. Roughly speaking, the diameter of a group is the
minimum length of the generator product required to reach an arbitrary element
of from the identity element. Through bounding the diameter of this
associated permutation group, which assumes a maximum value of , we
establish a linear time algorithm for deciding the feasibility of such problems
and an algorithm for planning complete paths.Comment: WAFR submissio
Motioning connected subgraphs into a graph
In this paper we study connected subgraphs and how to motion them inside a
connected graph preserving the connectivity. We determine completely the group
of movements.Comment: 17 pages, 18 figure
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