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This does not generally require action on the FMS. After the emergency has been dealt with (and say, the engine has been shut down) a diversion or a return to the departure airport may be required. After training it's easy to program a return to the departure airport, or find out where the nearest airports are and program a diversion into the FMS. More information For more information about FMS trainers, please get in touch. We'll be happy to assist you.
These are fairly complicate things that are typically not done by one person. A single person can do a level 1 autopilot by themselves with a raspberry pi/arduino controller-I did one in college. All that's required is a knowledge of PIDs, the equations of flight mentioned in the books below, and XPlane (wasn't difficult with a serial connection, but that might be depreciated now). This stuff doesn't require things like an RTOS and deep knowledge of an embed device to do. Could make it work for an actual Drone if you want-tho it doesn't scale with the implementation most undergrad/grad people are able to accomplish. Now there are open source FMS for drones that you can look at. Ardupilot covers fixed wing and rotorary craft RC and drones. The RTOS and software used is open source. It's very accurate to the FMS that you would see on a commercial aircraft and drone. Not an easy thing to take on, but worth having as a reference if you want to see how they tackled some of the larger problems when you start trying to incorporate your FMS with bells and whistles.
Good luck.