In certain embodiments, a robotic attacher performs a method of attaching and detaching a cup from the teats of a dairy livestock in the sequence of right front teat, left front teat, left rear teat, and right rear teat. The method comprises the steps of determining a reference point and then, for each teat, positioning the cup relative to the reference point, determining a location of the teat, attaching the cup to the teat, and detaching the cup from the teat. In certain alternate embodiments, the sequence of attaching and detaching the cup comprises left front teat, right front teat, right rear teat, and left rear teat.