Several surgical robots get the FDA 510(k) clearance, which means they are proven to be equivalent to the already-approved surgical techniques.
Here is a story behind the FDA approval. ISS could not get through FDA approval procedures because they claimed their surgical robot, robodoc, used a new kind of surgical techniques. They changed their claim and applied for the FDA 510(k). Finally, they got the FDA approval. The FDA 510(k) document of the robodoc can be found at the following link:
Since the robodoc succeeded in getting the FDA 510(k), other surgical robots including da Vinci have followed the FDA 510(k) approval path.