3 research outputs found
Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard
In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots of two different sizes. That is, within one class of robots, where a class is given by the robots\u27 size, any robot can be moved to any of the corresponding target positions. We prove that the decision problem of whether there exists a schedule moving the robots to the target positions is PSPACE-hard
Near-Optimal Min-Sum Motion Planning for Two Square Robots in a Polygonal Environment
Let be a planar polygonal environment
(i.e., a polygon potentially with holes) with a total of vertices, and let
be two robots, each modeled as an axis-aligned unit square, that can
translate inside . Given source and target placements
of and , respectively, the goal is to
compute a \emph{collision-free motion plan} , i.e., a motion
plan that continuously moves from to and from to
so that and remain inside and do not collide with
each other during the motion. Furthermore, if such a plan exists, then we wish
to return a plan that minimizes the sum of the lengths of the paths traversed
by the robots, . Given and a parameter , we present an
-time -approximation algorithm
for this problem. We are not aware of any polynomial time algorithm for this
problem, nor do we know whether the problem is NP-Hard. Our result is the first
polynomial-time -approximation algorithm for an optimal motion
planning problem involving two robots moving in a polygonal environment.Comment: The conference version of the paper is accepted to SODA 202