The actual algorithms used for autopilots are really simple.
A simple autopilot will do nothing more than hold the wings level so the pilot doesn't need to continually keep their hands on the controls. From there, more functionality is added as layers.
Heading mode makes the autopilot always point towards a compass heading. Nav mode is a computer that changes requested compass heading every time it reaches a Nav point.
A more advanced autopilot will add modes for speed-hold and altitude-hold that trade between altitude and speed. When combined with the auto-throttle, the autopilot can implement constant rate climbs and decent.
The autoland mode simply updates to heading mode and constant rate decent to follow the glide slope.
While it's true that a modern autopilot can takeoff, fly to a destination and land without the pilots touching the flight controls, the pilot is required to constantly switch between the various modes, feed nav points, and adjust the autopilots mode. At the same time, the pilots are doing a bunch of other tasks to keep the plane flying and safe.
The simplicity is very intentional. Pilots are expected to know what the autopilot is doing at any point and understand why the autopilot is doing that. They are expected to spot when it's doing something weird very quickly and disconnect it.
Constant adjustment based on density altitude changes, waypoint changes, ATC inputs, depending on turbulence - disable or alter inputs, it is required to be constantly monitored (I am a low hour pilot, but have had one need to be disconnected due to malfunction).
It’s basically a glorified cruise control for airplanes. It will fly a general route, but anything beyond that requires manual input (at least for small plane autopilots).
A good example might be a cop rerouting traffic. This would be an ATC route change in the airplane world necessitating you to reprogram waypoints. I’m afraid of what Tesla’s “autopilot” does in this situation.
One last addition edit - in the airplane world, the PIC has ultimate control and responsibility over the airplane. There are a ton of disclaimers and training that goes along with a real autopilot that makes sure you know what its limitations are. Tesla also has failed here IMO.
A simple autopilot will do nothing more than hold the wings level so the pilot doesn't need to continually keep their hands on the controls. From there, more functionality is added as layers.
Heading mode makes the autopilot always point towards a compass heading. Nav mode is a computer that changes requested compass heading every time it reaches a Nav point.
A more advanced autopilot will add modes for speed-hold and altitude-hold that trade between altitude and speed. When combined with the auto-throttle, the autopilot can implement constant rate climbs and decent.
The autoland mode simply updates to heading mode and constant rate decent to follow the glide slope.
While it's true that a modern autopilot can takeoff, fly to a destination and land without the pilots touching the flight controls, the pilot is required to constantly switch between the various modes, feed nav points, and adjust the autopilots mode. At the same time, the pilots are doing a bunch of other tasks to keep the plane flying and safe.
The simplicity is very intentional. Pilots are expected to know what the autopilot is doing at any point and understand why the autopilot is doing that. They are expected to spot when it's doing something weird very quickly and disconnect it.