In 2013 I initiated an honours project to build a cat robot that could land on its feet when dropped from an upside-down position. (Progress is going well at time of writing.)
Science Daily has a write-up on a bio-mimic walking cat robot (with obligatory YouTube video). Haven’t read the paper yet but the shock-absorbing legs look nicely done. I don’t have much opinion yet on artificial muscles; it seems a shame to stick to the old motors’n’gears approach (which is what we’ve done for our own cat), but it doesn’t seem like anything more `realistic’ is useable yet.
`Cheetah’ is a similar robot by Boston Dynamics that can outrun Usain Bolt. Fastest legged robot, they say.