The Settlement of 2051 was made possible to a great extent by the existence of RCRs, which give humans the ability to experience non-human 'bodies', stretched or altered states of mind and senses without genetically or bionically altering themselves. With such a universe of alternative life-states available to them vicariously, it was easier to agree not to tamper too much with the basic human genome.
Sentient robots made their appearance in 2012, although they were prohibitively expensive until the rapid development of bio-electronics in the 2020s, which allowed robotic brain tissue to be 'grown' in a way that is analogous to the growth of a human or animal brain. Remote control of robots or other electronic devices by the human brain had been demonstrated in 2014, but was something of a solution without a use until robots themselves could be cheaply equipped with brains on a par with those of humans. By 2030 the various components for this were in place, and the following decade saw an explosion of human-controlled non-human forms in all walks of life. The population of RCRs soared above the 1 billion level by 2035, and reached 5 billion by 2040 – although that was still only one RCR for each two humans.
By the time that the (terrestrial) human population stabilized at 20 billion in 2080, there were several times as many RCRs as humans.
Only early robots took on human appearance. Science fiction novels and movies have typically given human form to robots, but in reality it was agreed soon after the first sentient robots emerged in the 2020s that it was better for them to look different from humans.
A catalogue of different types of RCR (they were no longer called robots after 2020) would be immense. Initially they had human-like sentience, but by 2035, when the genomes of most major animal species had been decoded, they came with a wide variety of psyches. People didn't want dogs with human temperaments, it was immediately clear, and when canine RCRs replaced the 'real' variety (they excrete shrink-wrapped, non-smelly disposable packets, once a day, don't get lost in shopping centres or attack children, and bark much more harmoniously) they were equipped with slightly modified canine brains and alternative, genetically-encoded human control circuits. You want to be your dog for a day and suckle her puppies? Go ahead - the smells are awesome!