Cycloid gearboxes are nifty, so I'd use any valid excuse to put one on a robot. Even so, with the number of COTS parts available these days, it's probably going to be a lot easier and cheaper to build a high reduction mechanism with gearboxes/chain/sprockets.
I spent a little while trying to figure out the math behind the gear profiles for these last year, and learned a bit. As I recall, I wasn't able to track down the exact profiles they use in the industry. The profile for the funny shaped gear is constructed as shown below, and the 'ring' gear is typically made of a set of round bearings (note in the second photo below).
Sifting through some of my old files turned up these; feel free to peruse. This is a two stage version that doesn't use rollers for the ring gear, so friction is expected to be an issue. Equations are set up in solidworks models, and values calculated with the spreadsheet. The me-from-the-past should have commented on things better, but apparently he didn't care enough to do so. If someone has experience with designing these things, critique and explanation on correct design approach would be wonderful.