Coming as an Android user converted in the last year from Apple (not really a fan, but I preferred them for my purposes then - irrelevant story), I have yet to find an android app that I like as much as the ones I used to use on my iPod Touch (Sleep Cycles and Sleep Sound Recorder by Viaden).
However, "Sleep Time" by Azumio, Inc.♦ is pretty good. I'm rather pleased with it.
On Android, I have tried "Sleep Cycles Alarm Free" by Roger Fortet,♣ which I did not like much, but you can feel free to try if you want..
I also tried "Sleep Cycle" by Nova.Labs♠, which was alright, and may or may not be what you were looking for, as well. It was a simpler design, only functioning as a cycles calculator and making the assumption that your cycle is exactly the average, at 90 minutes but letting you adjust the cycle length at the beginning to account for the time you estimate it takes you to fall asleep.
As for "Sleep Time," it analyzes your sleep pattern and allows you to set an alarm to get you up at a time within a set space of time near your cycle peak (you may choose 0 minutes -normal alarm, 10 minute, 20 minute, or 30 minute spans of time in which the alarm will wake you up, based on the data it collects using your movements to determine your cycles).
As far as I know, all three of the Android apps I mentioned are free (although I downloaded them a while ago and they may not be anymore...) and I have linked to them below so you may try them out and see for yourself.
Good luck, I hope you find what you are looking for and that I was somewhat helpful in that.
♦
https://play.google.com/store/apps/details?id=com.azumio.android.sleeptime
♣
https://play.google.com/store/apps/details?id=free.sleepcyclesapp.lite
♠
https://play.google.com/store/apps/details?id=com.blogspot.novalabsandroid.sleepeasy