Ok, in Sonic the Hedgehog 1 He's just another antagonist kinda like Bowser in Mario Bros.

It Sonic & Knuckles however, Sega turned up the heat and somewhat increased the
quality and depth of the Sonic series. What with the hidden palace and Knuckles being betrayed
and all. Gotto love Mecha Sonic.

In Sonic Adventure 2 however, Dr. Robotnik has a new awesome theme song, is bent
on World Domination, and has gained a more complete backstory, that somewhat connects him and Shadow.

He has a grandfather, you know his name, General Gerald Robotnik, along with a mysterious cousin.
Maria.

The United Federation, told General Gerald to shut down and evacuate space colony ARK.
But if I recall correctly, he would not give up his studies on imortallity.

But the United Federation meant business and then Identified Gerald and ARKs inhabitants
as rebels and enemies. So they killed anyone left on the ARK when they invaded it to shut it down.

Perhaps Dr Robotnik wants justice done to the leaders of the United Federation for killing his
cousin, grandfather, and who knows who else was related to him that might have been killed.
Maybe that's why we mostly see the mad scientist threaten the UF.

Could Dr, Robotnik have lived on ARK as a child?