Do I have to register the robot anywhere?

As an operator, generally not. As an importer or economic operator placing on the market, yes.

Anyone placing electrical equipment or batteries on the market in Germany for the first time must register before the first delivery – for electrical equipment and batteries with Stiftung EAR, for packaging in the packaging register (Verpackungsregister).

These registrations are a prerequisite for sales, not formalities to be completed afterwards. If they are missing, a sales ban and fines may follow.

Which further obligations arise from the role of importer is set out under Who is liable if I import a robot directly from abroad?.