Not quite sure what the advantages are, but it's certainly innovative. From the Festo description:
Flying by turning inside-out
SmartInversion is a helium-filled flying object that moves through the air by turning inside-out. This constant, rhythmically pulsating movement is known as inversion and gives the flight model its name. With the intelligent combination of extreme lightweight construction, electric drive units and control and regulation technology, inversion kinematics can be indefinitely maintained to produce motion through the air.
inspiration for new drive concepts
The shape of this flying object is based on the geometrical band devised by Paul Schatz: its middle section, in the form of an articulated ring of six members, detaches itself from a cube and constantly turns inside-out, taking on different geometrical shapes in the process.
With the geometrical band Schatz discovered that the principle of kinematics, which until then had been based on rotation and translation (linear motion), could be extended by a further mode: inversion. With SmartInversion, the engineers and designers are now investigating where and how geometrical inversion can be put to use in technology.