Program Arduino Mega Adk on linux for a project my supervisor gave me a Arduino Mega ADK board (https://store.arduino.cc/arduino-mega-adk-rev3) and the usb-cable.

I only programmed a Atmega32 8 bit controller on linux ubuntu. I have no possibility to use windows (i heard it's easy to program the arduino using atmel studio). I can only use ubuntu 16.04. Is there a convient way to program the Arduino like a microcontroller?

I'm not aloud to use the highlevel Arduino libraries. I have to do a cascaded control for a dc-motor and sensor-fusion.

Thanks in advance. 

If it's offtopic, could you transfer me to a suitable board?
You can use Eclipse, along with AVR-GCC and AVRDude and an AVR plug-in for Eclipse. Debugging may be a little painful since you don't have all the tools that Atmel Studio gives you. I'd question your employer if you aren't allowed to use the best (free) tools even if they do run on Windows.

Really all you need is the avr-gcc and avrdude to write software for it, you can use any text editor (although it isn't really convienent).  Seems like they are pigeon-holing you into a difficult job. Good luck.