Rate of progress of computational power
Moore's law: over the history of computing hardware, the density of transistors on an integrated circuit doubles approximately every two years.
How long will that take until we have human-equivalent processing power (HEPP) ?
As Martin pointed out, Ray Kurzweil and those who listen to him say things like:
"By some estimates, we already have supercomputers that have the raw processing power
necessary to produce HEPP -- we just don't know how yet to program them to act intelligently."
"By 2030, the hardware for a HEPP will cost one dollar." (a b)
Nielsen's Law: network connection speeds double approximately every 21 months.
Rate of progress of electrical energy storage density
unnamed law: electric vehicle batteries double in miles/dollar every 10 years. (b)
The power consumed by a integrated circuit running at full speed remains roughly constant.
The power consumed by a integrated circuit to do any fixed amount of processing halves approximately every two years.
Other trends relevant to robotics
Hendy's Law: digital camera pixels per dollar doubles approximately every 18 months.
Haitz's law: the light output of an LED doubles approximately every 36 months.
Johnny Ryan is gathering data that may lead to a similar law for 3d printing.
(Robots are sometimes built using such 3D printed parts,
and 3D printers themselves are technically a kind of "robot" under most definitions).
[unnamed law]: the power-to-weight ratio of electric motors and their control electronics doubles every [FIXME] years.
(This trend is most obvious in electric aircraft). ( a b )
These trends in the low-level quantitative measures of what people build are surprisingly "linear" (in a log-linear graph) and therefore easy to predict.
However, historically people have made terrible predictions of exactly how much quantity of such low-level hardware was necessary to achieve some qualitative features in AI and other areas of robotics.
Usually people woefully underestimate what is needed to automate things we find "easy" like riding a bike or driving a car.
Occasionally people find it disturbing how easy it is to automate some things ( ELIZA effect ).