"Bedder Frames" - Digital Fabrication final project proposal

For my final project, I'd like to approach an idea that a friend and I have shared for the past few years, but have not had the design resources to tackle: a more useful bedframe for the itinerant student and post-grad.

The vision is to make it compact and portable, so as not to be a hassle while transferring from dorm to dorm and apartment to apartment. 

The current options are not too attractive:

The original inspiration was a Hoberman Sphere: 

Hoberman Sphere

Hoberman Sphere

I'd like to use the collapsable design to mimic a frame like the one below:

My preliminary model in Vectorworks shows the points at which each section will cross: