FEDOR, which stands for Final Experimental Demonstration Object Research, will be tested to see how well it can perform operating in microgravity conditions.
It will be working alongside a human crew for two weeks.
Sitting in the commander’s seat, holding a small Russian flag in its right hand, Fedor sent out a tweet shortly after the orbiting saying that the first part of on board tests went as planned.
"The first part of the flight tests was carried out in accordance with the flight mission," the tweet said.
"He carried out the collection, processing and transmission to the MCC of telemetric data on the operation of the LV, on-board systems of the ship, overloads, temperature and humidity conditions.
"The ship is in the calculated orbit.
"Everything is normal."
Roscosmos also tweeted out a spectacle of the launch.
The Soyuz capsule, which typically carries a space crew, blasted off from the Russia-leased launch pad in Kazakhstan at 8.38am (0338 GMT) on Thursday carrying the robot.
The new booster rocket is expected to replace the Soyuz-FG rocket next year.