Which variables are controlled in the mammalian womb to ensure a healthy environment?
It seems you are referring to this recent advance:

http://www.sciencemag.org/news/2017/04/fluid-filled-biobag-allows-premature-lambs-develop-outside-womb
https://www.nature.com/articles/ncomms15112

Involving putting premature lambs (delivered via caesarean) in bags of nutritive fluid and connecting the umbilical cord to an apparatus to oxygenate the blood.

Your question asks which variables are controlled in a mammalian womb, which I think is a misleading way to look at what a womb does and thus what the difficulties are with reproducing it. Namely, it makes it sound like the womb is a container whose purpose is to keep environmental variables (temperature, pressure, etc) at a good value for the development of a fetus. The problem is the womb doesn't just contain the fetus, it feeds it via the placenta. And the placenta is a structure built by fetus during embryogenesis, that connects to the lining of the uterus and enmeshes itself with it so that there is a huge surface of contact between the blood vessels of the mother and the blood vessels of the placenta, so oxygen and nutrients can pass through the mother's blood vessels to the placenta's and from there to the fetus via the umbilical cord. This allows the fetus to get all the nutrients and oxygen it needs to develop.

The "Biobag" these researchers created for these lambs is designed for fetuses who are advanced enough in their development that the main problem they have with surviving outside the womb is that their lungs are immature; the main purpose of this contraption is to allow oxygenation via their umbilical cord while keeping their lungs filled with fluid. And it also seems like they're being fed via that fluid, which suggests they're mature enough to get nutrition via their digestive system.

The paper gives quite a few details of the challenges involved in even that comparatively low level of uterine service. Infection, setting up the cannulas and oxygenating system so that the blood flow is just right and doesn't overtax the fetal heart, making sure there is no clotting, haemorrhage or brain damage...

I imagine the main challenge of making an actual artificial womb that's usable from implantation on would be emulating implantation itself, with artificial endometrial lining that a placenta could naturally develop in and intermingle its blood vessels with and somehow accurately reproducing the flow of blood that's necessary to feed the placenta. If we assume an artificial womb for a fetus that already has an umbilical cord, so we basically need to emulate the placenta's job not the uterus', but can be used earlier than Partrige et al's Biobag, then I imagine all the concerns they had about cannula size and getting the blood flow just right would be a million times harder with tinier, less-mature umbilical cords and fetuses. Not to mention if they need to put nutrients in the blood and not just oxygen.