I think the posters here who could advise on that might first want to know what the existing floor is, so they could also advise on how to change it to something that's slip resistant. Could you give some details on what your existing flooring is? Photos would help.
The reason I asked about the wheels is that I've noticed sometimes there's more pressure put on the front wheels because the person relies on them more when the rear legs aren't wheeled. I was wondering if there was a possibility that unequal pressure on the floors was causing some breakage.