  We present a coordination method for multiple mobile manipulators to sort
objects in clutter. We consider the object rearrangement problem in which the
objects must be sorted into different groups in a particular order. In clutter,
the order constraints could not be easily satisfied since some objects occlude
other objects so the occluded ones are not directly accessible to the robots.
Those objects occluding others need to be moved more than once to make the
occluded objects accessible. Such rearrangement problems fall into the class of
nonmonotone rearrangement problems which are computationally intractable. While
the nonmonotone problems with order constraints are harder, involving with
multiple robots requires another computation for task allocation. The proposed
method first finds a sequence of objects to be sorted using a search such that
the order constraint in each group is satisfied. The search can solve
nonmonotone instances that require temporal relocation of some objects to
access the next object to be sorted. Once a complete sorting sequence is found,
the objects in the sequence are assigned to multiple mobile manipulators using
a greedy allocation method. We develop four versions of the method with
different search strategies. In the experiments, we show that our method can
find a sorting sequence quickly (e.g., 4.6 sec with 20 objects sorted into five
groups) even though the solved instances include hard nonmonotone ones. The
extensive tests and the experiments in simulation show the ability of the
method to solve the real-world sorting problem using multiple mobile
manipulators.
