Pilates in its most basic form could have been designed for that description. If you have enough space to lie down in, you can do a routine. Pilates focuses on providing strong abs and other core muscles which then support the lower back preventing back injury.
I've just discovered a series of free video podcasts available on itunes from
pilatesonfifth.com (and its
sister website) that include a set of 10 minute and 30 minute sessions, and individual exercises in separate videos. You should look at the 'Mat' exercises which use no equipment.
Although you can get equipment to perform pilates with, the basics use the resistance of gravity to provide the work content.