Can I draw 2,2A current at 9V with AA batteries?
For high current drain applications you are best to use NiMH rechargeable cells, which have a lower ESR than most alkaline cells and so can deliver higher currents. 2.2A is not a problem, and is often done in RC cars. This datasheet shows that a 1300mAh cell is rated for up to 3C discharge rate, which is 3.9A. At 2C (2.6A) you should get nearly 30 minutes of use. Higher capacity cells are available.

The only issue is that NiMH cells are only 1.2V per cell, so 8 cells give you 9.6V which may be too much for your motors. Check the spec for your motors to see if they can operate from 9.6V.