One of the promising forms of energy production that I know of, which isn't yet well developed enough but could take off and is scientifically sound, is focus fusion, as applied with a dense plasma focus. The advantages are that you can make a generator of practically any size and it generates electricity directly, using hydrogen (deuterium) and boron (currently, but other fuels can be used and you can come up with some fictional ideal fuel that gives a higher yield).
This is what the cross section of the dense plasma focus looks like:
This is futuristic enough, can be used for large generators as well as small ones you can fit on your robots and uses a relatively abundant form of fuel. You could even get fancy and have blue tubes for hydrogen and red for boron and create a super-futuristic heart for them :P
Lets see how much energy we need:
Using this calculator, I calculated that, at the maximum (hard work is why we have robots anyway), you'd need about
300e3 kJ per day, if the robot was doing hard work all day for 24hrs, assuming it weighs 200kg, is 1.8m tall and has the efficiency of human muscle of course (the calculator includes metabolism etc. but lets just overestimate things to be of the safe side). Given the daily energy need of
300e3 kJ which is equal to about
84 kWh, and comparing with what US households use on average per day (again going for the highest margin here), which is about
30 kWh per day, that's almost 3 times as much. Nobody said this would be cheap!
How much fuel for the needed output?
Going by this 2011 article (and its claim of how much of the total boron production would be needed to cover worldwide energy needs in 2011) and the relevant Wikipedia articles, it seems we can get a
2.71 mg of boron, or
227.64 mg for our daily use. That's tiny and it means we can deal with a very inefficient conversion rate.
It's already hard to get numbers on the amount of fuel needed, but what's for sure is that this process requires energy to be put in, so if the robot runs completely out of fuel, it would need a safety feature to keep enough energy stored to restart the process, much like how we have batteries for motherboards (this could be a great plot device but the energy is probably not much and it's easy to just plug it in and give it enough to restart the fusion process).
This may not be mature technology yet, but it's being actively worked on and is realistic, so it makes a convincing feature for science fiction and there's lots of articles around for more information, which can help flesh it out. It gives a lot of space for energy, allowing your robots to exert themselves a lot and even consume a lot more than I've estimated here. One problem is how much it heats up, but you can probably use the extra heat to increase the body temperature of your robots to human-like or use some fancy peltier device to either get rid of it or transfer it to wall-mounted heat-sinks or something like that. Using this, there's no need for solar panels, or wall sockets - they can probably store a kilogram of boron and as much deuterium (I think it's a 1:1 reaction) and run for days on end.
Since this answer was downvoted for it's math, I'm adding this
addendum showing exactly how the above numbers are computed and where
they come from.
Calculation of energy required for robot
I start my estimate from how much energy a human being requires per
day, since the robot is humanoid and thus designed to do a human's
work. I used the largest estimate I could reasonably make, to give an
upper margin - the logic is, if our energy source can meet this
threshold, it should be ok in any case. I used this calculator,
with age at
7yrs (since lower ages increase metabolic rate and give
a higher estimate),
200kg of weight,
1.8m of height and
24 hrs of
heavy exercise. I sum both the energy cost of metabolism and energy
output and round to
300e3 kJ (using metric on the calculator).
Keep in mind that this calculator apparently is inaccurate or varies
a lot in its output - Saidoro reports that it gave him, with the same
274e3 kJ to as as low as
144e3 kJ for the total
energy, which is less than half the value I used here. Using that
value, we'd require half the boron etc. - the point of the
calculations is to primarily establish an upper bound, so they hold
and the outcome doesn't effectively change, despite the significant
change in the values.
kWs, we get
300e3 kJ = 300e3 kWs or
kWh so that it's comparable to the other numbers,
300e3 kWs = 83,333 kWh. I rounded this number to
84 kWh. Over a
period of 24hrs this is a total of
3,5 kW per hour.
The average household consumption is taken from here which
provides annual and monthly averages. The monthly average is stated to
903 kWh. Divided by
30 to get the daily average, we get
= 30.1 kWh, which I averaged to
30 kWh per day. Dividing
84 kWh / 30 kWh = 2.8, which I rounded to
3 even though I don't reuse the
I tried to find information on how much fuel the device requires per
unit of output energy. All I could find was a mention, in this
article, that "If all of the world’s power was generated from
boron, it would only use 10% of our current production [of boron]". I
found the total energy consumption worldwide in 2011 from this
source which appears to be
12675 Mtoe, where
oil equivalent. I found the total boron production from the
Wikipedia article on boron, which, as far as I can tell is
post-2011. The article states "Global proven boron mineral mining
reserves exceed one billion metric tonnes, against a yearly production
of about four million tonnes" thus I assumed global yearly production
4e6 t which is
4e9 kg. Ten percent of that is
The global energy consumption converted to
according to the conversions from the Wikipedia article on Tonnes of
oil equivalent which is stated as
1 toe = 11630.0 kWh. To get
how much boron we need per unit of energy, I divided the two
1.474e14 = 2.71e-6 which is in
kg/kWh. Since the number is small, it's beneficial to convert
kg to a smaller unit:
2.71e-6 kg = 2.71
To get the total boron needed per day for our calculated
84 kWh we
84 * 2.71 = 227.64 - the result is in
The original errors where:
- Calculating the energy usage per hour for the robot and stating it in the wrong unit. This number was never used.
- Performing the ratio of boron to Mtoe calculation and then converting to kWh. This was an error due to reusing numbers from
other calculations - should have redone them all at the end - the result was that the boron calculations where backwards.
- Not using 10% of the boron production. This had an effect of the calculation showing the necessary boron being 10 times the actual
amount - the prior error clouded this fact however.
Not multiplying the boron per kWh by the total kWh needed. While the outcome is practically the same in this case, since at even 80+
times the boron needed, it still is very little, it was a serious
mistake that in another calculation could have changed the outcome.
These errors have been corrected in the answer and would have been
solved sooner had the downvoter stated the reason.