  This work proposes a method for effectively computing manipulation paths to
rearrange similar objects in a cluttered space. The solution can be used to
place similar products in a factory floor in a desirable arrangement or for
retrieving a particular object from a shelf blocked by similarly sized objects.
These are challenging problems as they involve combinatorially large,
continuous configuration spaces due to the presence of multiple moving bodies
and kinematically complex manipulators. This work leverages ideas from
algorithmic theory, multi-robot motion planning and manipulation planning to
propose appropriate graphical representations for this challenge. These
representations allow to quickly reason whether manipulation paths allow the
transition between entire sets of objects arrangements without having to
explicitly enumerate the path for each pair of arrangements. The proposed
method also allows to take advantage of precomputation given a manipulation
roadmap for transferring a single object in the same cluttered space. The
resulting approach is evaluated in simulation for a realistic model of a Baxter
robot and executed in open-loop on the real system, showing that the approach
solves complex instances and is promising in terms of scalability and success
ratio.
