  Motion planning problems can be simplified by admissible projections of the
configuration space to sequences of lower-dimensional quotient-spaces, called
sequential simplifications. To exploit sequential simplifications, we present
the Quotient-space Rapidly-exploring Random Trees (QRRT) algorithm. QRRT takes
as input a start and a goal configuration, and a sequence of quotient-spaces.
The algorithm grows trees on the quotient-spaces both sequentially and
simultaneously to guarantee a dense coverage. QRRT is shown to be (1)
probabilistically complete, and (2) can reduce the runtime by at least one
order of magnitude. However, we show in experiments that the runtime varies
substantially between different quotient-space sequences. To find out why, we
perform an additional experiment, showing that the more narrow an environment,
the more a quotient-space sequence can reduce runtime.
