In the past few years, we have covered a whole host of fancy telepresence robots here. Not all of them have an open platform. The Ubbo is an open source telepresence robot for work, school, and everything in between. It comes with mecanum wheels and modular design.
You can add sensors and robotic arms to do more with this robot. The Ubbo can run for 6 hours on battery. It ships with Arduino, Android, and Ruby source code.