Timed takeoff and landing

Is it possible to program a quadcopter with Arducopter to tell it when to takeoff, land, shut down, takeoff again to fly a preprogrammed waypoint mission, and then land again at a new destination? Has this been done?

Synchronize to the world time? or after power ON?

shutdown?? I believe you mean to disarm the drone.

Potentially a proprietary LUA scripting.

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Shut down how?