Cats and dogs are both known to be very popular pets for humans around the world and have been bred for thousands of years for this purpose.
Destin Sandlin's Slow Motion Flipping Cat Physics | Smarter Every Day 58 includes footage of cats momentarily floating and flailing in aircraft in parabolic flight, and early Soviet spaceflight tests have included dogs in seat belts.
Question: But is there any information at all on the locomotive ability or adaptability of cats and dogs in space? If so, how much?
"Locomotive adaptability" means can they figure out how to move around in some way, given some time. Without the ability to get from point A to point B when they want to, the experience may be quite stressful and they would have to be hand-fed and waste would end up everywhere.
For example: mice seem to have "locomotive adaptability" in that they can work out how to move around. I don't think they were hand-fed the whole time.
Screenshots from Mice aboard the International Space Station
The story describes a test of this waste management system for cats. While the title suggests it's a "space toilet" the principle requires gravity to be present. Thus it has been added to illustrate the problem associated with waste management rather than a solution to it. I have no affiliation with this nor any other space-cat product.