Answers

I have seen some extremely nice patio umbrellas with large bases that can cover quite a large area on a patio. These do not attach to the home and usually do not attract HOA disaprovals. I'd also recommend observing some of your neighbors and see what they have done to create shade on their patio. Finally contact your HOA and see what they suggest.   

Stores like menards and home depots, etc. do in fact sell some things like these. If you're looking to have someone out to install, and do everything for you, you can try US Patio Systems. They have great products, great staff, and they're great with timing!

Unfortunately we do not do any type of awnings. What i would do is call the HOA and ask them what they allow back there.