Will there be a hierarchy among robots, once they become more common and self-aware?

Think a couple years in the future, when robotic technology is a bit more advanced than it is today. Robots will work with and talk to each other. Supposedly they will be in service to mankind, but we cannot be sure.

Will these robots have a caste system among themselves?

For example, will mobile robots look down on fixed position robots? Will multi-function robots feel they are superior to single function robots? Will robots made primarily of plastic feel inferior to robots made mostly of steel?

How will robots classify themselves? Will they develop a self-image, and will that make them feel superior? Will there be robot-bullies?