The exercises called the "5 Tibetans" or the "5 Rites" make an excellent warm-up for meditation. They are helpful to do on a daily basis anyway even if they aren't really Tibetan.

Usually I read for drowsiness to visualize bright light, but that doesn't help much. Imagining sitting on a telephone pole in an earthquake doesn't do it for me either. Recently I read that holding your breath is a good wake-up for drowsiness in meditation, but I haven't tried it. At this point if I'm that tired I just go to sleep and use reiki as I drift off. Something to keep in mind when you are falling asleep in meditation is that fighting it often just makes it many times worse than it otherwise would be. Be patient and watch yourself falling asleep. Remember, if you can achieve mind awake / body asleep on a regular basis that this can really help with astral projection and wake-induced lucid dreaming.