Tip for anyone having trouble: Notice that the drones do not aim at you; instead, they aim for the point where they will collide with you if you do not change direction. Try moving in the same direction as the drones, and they will accelerate more, which will make it easier to make them overshoot you (watch out for rebounds though). Also, it seems their accelerate increase with score, not time, so do not be afraid to take your time collecting points if it makes it easier to dodge them.
To novakaine (and anyone else complaining about trial and error), I'm fairly certain that you generally don't need to know what dots are going to show up. Technically your design should work for ANY combination of dots.