I have had my eye on something like this for a while, I would like to make an animated object that follows you around, while looking at developer forums I came across a cat rig that somebody made, unfortunately I couldn’t find the post because I lost it. It would be great if somebody could help. Though this dose not even have to be a block, it could be a person or anything else.
Well… if you want a block to follow you like most simulators, try using bodyforce and bodygyro 
if you want something like what you showed, you’d have to treat the cat as a NPC and use pathfindingService. And check for whenever it is moving, play an animation.
If you’re expecting inheritence (for multiple different types of pets with different attributes) check out OOP. It would work nicely in this scenrio.
Alright, I will try and work with the path finding service.
Remember if you’re planning to have a lot of pets moving at the same time, the pathfinding service provided by Roblox may be overkill.
nah, I just thought of one pet following a person…