Past two companies hired me specifically for UAV projects, so my professional experience has been in this field- however, it is so wide, that you can easily branch out:
* design one-off test hardware for various bench/field tests where an off the shelf solution doesn't fit (custom thrust stand, spring constant measurement jig to determine properties of vibration isolation solutions, simple blackbody for QA to determine if the LWIR payload meets specifications)
* like physics/control systems? Lot of work on tuning PID controllers, implementing simulators for pure SWEs to not crash your expensive prototypes
* hmm, it looks like we have excessive vibrations on the frame- whip up a small battery powered, WiFi enabled high-frequency accelerometer logger to dig deeper into it.