I've created a simple Proof-of-concept for grid-like movement on a physics object. It's made up of two objects, the physics object itself, and a sprite object which is tracked to the position of the physics object. The position tracking is modified with expressions to allow the sprite object to only be positioned in the 16x16 area of the screen the physics object is inside of,. Thus giving the sprite grid-like movements.
In case you want to see it in action, or look at the behaviors for use in your own games, here's a link to the testhttp://flowlab.io/game/play/999491