does anyone know how these types of follow-me drones do with obstacle avoidance? do you just tell them to fly high enough that they avoid things by going over them?
Obstacle avoidance is coming though! The research world is converging on a solution!
To answer the initial question, the latest versions of ArduPilot implement terrain following (based on terrain data loaded into the flight computer before-hand). Additionally, there is also now support for range-finding instruments like Lidar Lite [0], although I don't believe those are currently being used in the terrain following mode. Such instruments could conceivably be used to implement "look-ahead" functionality to more accurately avoid obstacles.