The game was fun as I do enjoy the linked movement mechanics. Unfortunately you can collide with the obstacles even when it seems you shouldn't (You can get offset from the grid it seems). Fixing that would make it waaay better because it can be frustrating when you have the solution then you get stuck on the edge of a door or something like that.
And as a nitpick, it would be good if there was some indicator for their direction besides color. A lot of games do this with two characters which is pretty easy to track, but with four it can be a bit confusing.
I hope that doesn't sound harsh (It's hard to tell how I sound over written word). I'm just trying to provide constructive criticism.
Oh, and I forgot to add that the game looks nice!