How do I make a sprite trace my movement?

Dunno how complicated this would be to make, but here goes. I want to make, for example, a companion for my top-down character that traces all the character's steps but I have no idea how to do this. The tracing should be very precise and mimic all of the player's movements so the companion wouldn't get stuck into anything. Any help? Is there a custom behavior for this kind of stuff? Or what would be the best way to create this kind of system?

You can do this by Pathfinding behavior in Construct 2 or by third-party plugin MoveTo by Rex.Rainbow.