Papers

They used a Parrot AR.Drone 2
The last paragraph of the paper says "Further open issues are the lack of general obstacle avoidance solution, which is crucial of for UAV navigation...". This seems to be what Dr Gonzales wants us to investigate. While it's--by nature--not very specific, I think progress towards general obstacle avoidance is the key deliverable. I think some people don't like that it's too general.
Mathe mentioned that developing trajectories for object avoidance was what they were currently investigating when they wrote this paper, but it looks like he hasn't published anything since this paper. He seemed to have finished his PhD in September last year and focused specifically on drones for railway maintenance. I think he choose railroads because they form easy lines to follow. I think tracking objects isn't part of general drone navigation, but just a simplification to follow people, railroads, etc.
He listed a couple classic planning algorithms: Model Predictive Control (MPC), Rapidly-exploring random tree (RRT). I know D* is another commonly used one, but I don't know how it works. If we wanted to handle more general object avoidance, I think we'd actually want to learn trajectory heuristics to be responsive to work within probabilisitic guarantees in unknown environments tractably.