Hi i have had success at this after using several different methods i tried something different .

I used an older computer  that could reconise usb drives  i disconected all hard drives floppys etc  except for the c/d rom drive .plug in the  usb stick and boot computer from ubuntu live c/d  do a normal instilation after choosing the usb as the hard drive --- make a root partition a home partition   and a swap partition--  although ive been told  usbs dont like to be writen to all the time i havent had a problem as yet but my techi nephew  recomended not to install a swap partition and let it use ram as a swap---   i havent tried this yet .But  have had good succes just doing a normal install on to the usb drives .it will also boot up on most computers  although some times  you need to change screen resolution on some machines . you can also  clone the drive to another usb  just in case  it does crash  as they are so cheap  to buy  and just plug it in and up date the clone from time to time from your main usb -- I hope this helps