Sadly i've never gotten around to designing any, so am posting here wondering what take on robots others have and any designs people have worked up, specifically regarding Imperium uses, in government or militaries. Say an auto-loading missile navy bot, as an example, or the rumored X-boat autopilot "experimental" bot.
When necessary, I tend to use the simplified system from JTAS instead of Book 8, but the two are roughly compatible overall. Book 8 simply goes into more mechanical detail and allows (much) greater brainpower.
IMTU, there is a strong tendency to avoid "expert" robotic systems (such as pilotbots with Pilot-4, for example), but ironically, all vehicles above about TL9 have some form of simple preset course-following autopilot which can also accept instructions from some external source (if not manually overridden), typically a traffic control computer on the ground. Indeed, it is generally illegal IMTU to operate a flying vehicle on manual, rather than under traffic-control commanded autopilot, over any world of TL9+ and LL3+.
There's also a strong "full employment" political principle which puts automation cost-savings secondary to gainful employment for sophonts, as well as a general prohibition on warbots (cf. the Imperial Rules of War) as such weapons are perceived as the hallmark of cowardice and moral inferiority. People field armies of robots only when their cause isn't Just-enough to motivate sentient beings to join in it.
All that said, "dumbots" are prevalent, and even moreso, remote-controlled "drones" (some with simple brains of their own to avoid immediate pitfalls, cf. NASA's Mars Rovers) are utilized extensively in hazardous situations (even in combat, so long as they are unarmed -- and yes, that even prohibits laser designators and that ilk).
I used the parameters of Special Supplement 3: Missiles and Striker to develop a whole serious of popular-with-PCs recon and sensor probes which could be launched from standard spacecraft missile racks, and tele-operated via a handheld plugged into the turret's fire control, for example.
Plus, I have from time to time allowed PCs with good character conceptions to design robot bodyguard/valets, so long as such things carry no offensive armaments (except for a really well-thought-out "caddy" one PC designed as a perfectly-loyal dumbot henchman to follow him around toting his massive inventory of gear -- weaponry and otherwise -- in a theft-resistant, yet conveniently-accessible package; that was inspired enough for me to indulge).
In general, robots are "chrome" IMTU: only in the forefront when PCs want them
and have a good justification for them. I simply keep the machines as stupid as possible...