Your answer is: Robots do exist in the Inhuman universe, absolutely. Robots are used much as they are today, primarily on assembly line constructions or cleaning (think roomba!) on large ships. They are programmed to be able to 'look' and 'think' as much as their job requires and have a wide range of functions. A single robot can tell if a bolt is crooked on the body of a car and will stop the assembly line and alert its supporters of the problem before proceeding onwards. Some are even capable of correcting these errors themselves and logging the issue into a central computer while not needing any input from a biological master.
The next logical question is are there androids or otherwise sentient robots like those typified in sci-fi? Any R2-D2s, any C-3POs? Surely, you are thinking, technology must be advanced enough to provide a robot not only with an advanced nearly-human artifical intelligence but also the ability to communicate with biological beings.
The truth is, there used to be, but not anymore.
The concept of the self-aware nearly human robot was extremely aluring and so such robots were designed and constructed shortly before Rulerism was founded. Androids could preform jobs which their biological counterparts found too dangerous, or too demanding for a typical body. The use of them would have been clear- as servants and maintance crew on ships and planes, they would have been indespensible. One of the forerunners in 'droid construction was a France based company called Midreak. They were almost universally celebrated for their breakthroughs in AI programming, developing a fake sentience that was capable of almost brain-like learning and self improvement.
However, the AI itself proved to be the downfall of the entire android/robot theory.
While typically one thinks of robots as following the laws Asimov set down in his stories, the truth is that you can not both hardwire such 'laws' into a sentient being and give them the ability to learn and think for themselves. The morals you give them will be no longer be infalable. Parents go through this issue every couple minutes with teenagers, and we all know how that goes. While the robots were indeed built to serve man, and were indeed programmed not to harm him, eventually they made use of their sentience and began to question the validity of those orders. This raised many questions about the nature of being self-aware. But basicly, the robots would wonder to themselves if they ought to really preform the jobs they had been asked to preform or if they might want to pursue more self-serving goals.
Every sentient being goes through this same gradual awareness, building up their own personality and own philosophy on life. The difference between the biological sentients and the robots was that the biological sentients built these goals and views based around the drive of self preservation. Fear of death, fear of injury, fear of illness- these prevent people from walking across traintracks for the hell of it, prevent people from quitting jobs (you need money to buy food to keep from starving to death, after all), prevent people from shooting nyquil into their eyeballs...stuff like that. Biological sentients are aware of their own mortality and so in a way are bound to law in order to keep alive.
Robots, as you've already guessed by now, do not have these same fears or drives to keep them in line. Robots can't feel hunger and so when fully sentient could easily walk away from a job without ever thinking twice about it. Although a robot could be dismantled or their harddrive wiped, they did not view this as a sense of death or mortality because of the ability to self-backup or self-repair. A robot AI could never truly die, and so never truly felt they had to bow to the same laws as the biological sentients. This resulted in their being exceptionally snarky to living beings and essentially impossible to control.
Now, this may seem to lead to the conclusion that the worlds would be overrun with self-replicating nihilistic robots. With no way to kill them and no way to make them obey, why not? And yet, there's no robots in Inhuman's storyline (at least, not the sentient android kind). So where did they go? What happened?
Quite simply, entertainment happened. Movies, music, books, plays...anything digitally archived that the robots could gain access to was far, far more engrossing than anything else offered by the universe. Between all of the known sentient species and their own particular forms of entertainment, the robots were prettymuch set for life. An inexhaustable resource of entertainment ensured they would keep on dancing, reading, or watching until their internal power supplies gradually shut down.
Self-aware robots were an exceptional failure. Most of the companies which programmed the AI, such as Midreak, disolved nearly overnight. The development of non-biological intelligence research was outlawed to prevent further folly. On the upside, this meant the robot-rights groups which were beginning to bud into existance before the robots were even being used beyond a few select beta-test locations were quickly rendered moot and faded away. The average person on the street doesn't even much remember the advent of AI robots. If they do, it tends to be as a brief article in a newspaper or an issue of a science magazine that featured the concept. Much like today, unless one is a big nerd on the subject of obscure researches and developments in the science field, even the most revolutionary ideas can pass completely without notice.
So. In conclusion. There are sentient android robots in Inhuman. However, there aren't many and the few that do exist are hooked into movies or making club circuits or whathaveyou.
What did these robots look like? Well, as they were such a short-lived fad very few know for certain, but it's thought they looked a little something like this: