High grip floor washable/brushable for Dogs in house?

Tue 5 Dec 2023, 13:58 (last edited on Tue 5 Dec 2023, 14:07)

We have found that the tiled downstairs rooms are very slippery particularly for the dogs (apart from one patch of filthy old carpet about 10x10' left by builders in part of our "new" Living room-  made from knocking two rooms together downstairs -  that we have left in situ so the dogs have an area to play vigorously upon). The Laminate floors upstairs are not good and grippy for the dogs as well but that flooring will have to remain. The stair treads are mahogany or similar hardwood and slippy too. 

In particular, the ageing Goldendoodle is beginning to find the lack of traction on most floors and the wooden stairs is straining his joints - particularly his rear hips.

Even though both are non-shedding Poodle crosses the sheer quantity of very fine dust they track in is boggling! The remaining patch of carpet makes it clear that laying more cannot be the way forward - we'd be just as well off with a beaten earth floor from the old days, or need to employ a cleaner to thoroughly vacuum twice a day. Over much of downstairs we did - years BD (before dogs) - put down tiles with a scattering of higher-grip particles in the glaze, but that was never noticeably much better, and over the nearly 20 years we've been here the surface of most areas has been eroded to a low-grip condition that isn't good for the dogs' welfare (or come to that, mine with growing mobility problems from youthful injuries now roosting).

Does anyone know of a higher grip or friction flooring material that is easily brushable and washable to put down instead, and something for the wooden stairs (traversing which the elder dog looks very hip-strainingly awkward particularly going downwards upon)? On the stairs front we've found a semi-transparent sticky tape upon Amazon to put over the treads, which will look messy but is possibly a way forward for those, but a nicer looking solution would be good. But the general flooring downstairs?

For nearly 2 years since creating the new bigger room downstairs we've been living in a mess of real scruffy rough cut carpet scraps, ragged tile edges and patches of levelling concrete and skimpily patch-painted walls with un-replaced ancient furniture, being held up at an impasse. Anyone able to enlighten us with suggestions?