Animating between two sets of Auto Layout constraints is quite simple.

All you have to do is update your installed/configured constraints and then call layoutIfNeeded inside of a UIView.animateWith* closure.

class DoorsViewController: UIViewController {
    var open: Bool = false {
        didSet { transition() }
    }

    func transition() {
        self.view.layoutIfNeeded() // force layout before animating

        UIView.animateWithDuration(0.4) {
            // change constraints inside animation block
            self.updateConstraintsForDoors()

            // force layout inside animation block
            self.view.layoutIfNeeded()
        }
    }

    func updateConstraintsForDoors() {
        leftDoorHorizontalConstraint.constant = open ? -16 : -leftDoorView.bounds.size.width
        rightDoorHorizontalConstraint.constant = open ? -16 : -rightDoorView.bounds.size.width
    }
}

Download sample project