If performed in the hands of appropriately trained surgeons robotic surgery is considered safe. A uterine leiomyoma is generally considered a simple procedure and does not require robotic assistance. There is little benefit to be gained from doing this operation robotically and it will result in increased cost.
The doctor will of course be the one performing the surgery but with better tools ( more precision, 3D high definition view, better articulation of his instruments) allowing him to provide a more precise surgery.
Certain procedures do not need to be done with robotic assistance and a regular laparoscopic surgery is sufficient.
However removing a uterine fibroid entails repairing the uterus afterwards and when performed with this enhanced precision it will increase the chances afterwards for the patient to carry her pregnancy without complications, in this case a robotic surgery might actually be a good indication.
It is as safe as laparoscopic surgery and with no increased risks of if it is performed by an expert robotic surgeon.