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1. digital signal processing (DSP)
2. automatic control theory (TAU)
3. programming of microcontrollers
4. Theoretical foundations of electrical engineering (TOE)
Briefly: gas dynamics, solid state physics, electrostatics, electrical engineering, microcontrollers, the basics of designing automatic systems and control units (+ programming the operation logic).
Matlab has a Stateflow Onramp tutorial . It shows the logic of behavior (cleaning the room (scanning), recharging.
Look at the magazine "Lefty" for 2015. There they collect without any DSP and TOE.
a bit of mechanics :)
body + impeller (even though self-made even from a vacuum cleaner from "all for 50") + wheels.
the simplest vacuum cleaner rushes from wall to wall, turning at a random angle from impacts. Chaotic movement allows you to remove 95% of the floor :)
and if you want to build something more serious, you will need a microcontroller (at least an ardruinka) plus sensors.
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