Eggman Empire

The Eggman Empire (エッグマン帝国) is a political body that appears in the anime series Sonic X and its comic series published by Archie Comics. It refers to the totalitarian regime ruled by the infamous Dr. Eggman, and it is the doctor's ultimate goal to have it encompass his entire planet in his quest for global dominance. So far, the Eggman Empire has never actually been built due to Sonic the Hedgehog and his allies, and merely refers to the territories Eggman has claimed and plans to claim.

Initially started on Sonic's world, Eggman tried building the Eggman Empire on Earth after he got stranded there. When he got back to Sonic's world, Eggman resumed his original plans with the Eggman Empire there.

Past
While in Sonic's dimension, Dr. Eggman sought to spread the Eggman Empire on Sonic's world, but was constantly thwarted in his efforts by Sonic the Hedgehog and his friends.

New World Saga and Chaos Emerald Saga
After being transported to Earth due to a large-scale Chaos Control incident, Eggman decided to try and re-establish the Eggman Empire there.

As the starting point for his conquest, Eggman tried destroying Station Square with E-23 Missile Wrist, but was stopped by Sonic and his allies who had come to Earth with him. From there, a myriad of schemes, robots and technology ensued in Eggman's constant quest to establish the Eggman Empire, such as unleashing robots to built new bases, attempting to brainwash the next generation into adoring him, and trying to trick his enemies into destroying each other. Regardless, Eggman's goal always remained to collect the all-powerful Chaos Emeralds for the Eggman Empire. At every step though, he was stopped by Sonic, his friends and their new allies, and the government who had declared war with Eggman Empire. Things came to a head when Eggman competed with Sonic and GUN over the last Chaos Emerald after acquiring the other six. In the ensuring battle, Eggman was defeated and he went underground to make new plans to build the Eggman Empire.

Chaos Saga
Six months later, Eggman attempted to build the Eggman Empire with the aid of Chaos, a water beast he released from the Master Emerald. However, the creature was beyond Eggman's control and destroyed his second Egg Carrier during its rampage, forcing Eggman to have Sonic to stop Chaos for him.

Shadow Saga
After the failure with Chaos, Eggman, with the aid of Shadow the Hedgehog, gained control of the Eclipse Cannon, a weapon capable of destroying planets. With it, Eggman held the world hostage and demanded the population surrendered to the Eggman Empire. However, Eggman's plan failed when it lead to the activation of a doomsday program set up by his grandfather Gerald Robotnik which would destroy the Earth, forcing him to help Sonic save the world. Afterwards, Eggman snuck away to plot his next move for the Eggman Empire.

Egg Moon Saga
Dr. Eggman's next big move for the Eggman Empire involved deceiving the Earth into believing he had turned over a new leaf by having his Eggman Company provide the population with Sunshine Balls for light sources during a permanent eclipse caused by the Egg Moon (which he had staged). Using hypnotic messages emitted by his Sunshine Balls, Eggman planned to brainwash humanity into electing him as the world's new leader. Though he came close, his plot was discovered, leading to his temporary arrest.

Homebound Saga
For one of his last schemes on Earth, Eggman invaded the lost kingdom of Murasia in an attempt to conquer the world by triggering an eruption like that which had destroyed the Murasians, but was thwarted by Sonic and his allies. When Eggman and lackeys later on returned to Sonic's dimension, the doctor went back to his original plans of spreading the Eggman Empire on Sonic's world.

Metarex Saga
Six months later, Eggman put building the Eggman Empire on hold to deal with the alien Metarex and the Chaos Emeralds' dispersion across the galaxy. After that, he resumed his plans to build the Eggman Empire.

Archie Comics
Following his arrival on Earth, Dr. Eggman made numerous schemes to built the Eggman Empire on this new world, only to have them thwarted by Sonic the Hedgehog and his friends. This included setting a horde of ravenous Dark Chao loose and turning Perfect Chaos into his personal weapon.

Trivia

 * The decal of the Eggman Empire varies, from black and yellow designs similar to those seen from Sonic Adventure 2, to more "evil" designs, such as a red and black variant that has much harder lines.