What are the power options for intelligent humanoid robots?

In my future setting on Earth (or an Earth-like planet; haven't decided), the fields of robotics and AI have taken off and we have intelligent, ambulatory robots. (They were initially thought of as machines, but, as is common in such settings, they have advanced and they are considered "human-equivalent" by many, with the courts slowly catching up.) My question is about power.

I want my robots to be able to move freely around the world (no tethers). It seems like my options are either batteries (plug yourself in each night to recharge) or something passive that keeps enough juice coming in.

For the battery option, how much battery are we talking about? Imagine a human-sized, human-shaped robot that is capable of movement, fine motor control, and "thought"; how big and heavy would a battery to support that for, say, 24 hours need to be? Can I physically fit that somewhere on-board?

For the passive-energy option, do I have options other than solar (which would still require a smaller battery for night/indoors)? If I covered the robot's exterior with the best solar panels that we might be able to build in the next 200 years, would that be anywhere close to what I need? Is there some other way to achieve that end?

How do I realistically power my robots? I am looking for answers that are technically feasible within a couple hundred years; I'm not interested in alien technology or magic.

• Does Mr. Fusion from back to the future count as alien technology or magic? – Culyx Oct 8 '14 at 20:03
• @Culyx I don't know enough about fusion to say. Can you imagine a path from "today" to its existence? (Naturally I don't mean the flux capacitor here, only its power source.) – Monica Cellio Oct 8 '14 at 20:59
• Batteries are one of those fields that has horribly fell behind in terms of miniaturization...we are on a cusp of some breakthroughs. Carbon nano-fibres have the potential of rapid charging a battery so recharge times can be near instant (still a bit aways on that one, more than feasible in 200 years). We are also on the cusp of the energy age...if we could break a proton down into it's components and rearrange those components into electrons (electricity), then you have hydrogen as your fuel source that would generate energy for a considerably large amount of time between refuelings – Twelfth Oct 8 '14 at 21:07
• What about a en.wikipedia.org/wiki/Fuel_cell ? They convert ethanol into electricity. Just like bender in Futurama where he lives off of beers. – Esben Skov Pedersen Oct 9 '14 at 6:50
• @JamesRyan, nvoigt, I realize that technology can be inconceivable to people from just 50-100 years earlier. On the other hand, we've all seen fictional tech where you say "yeah, I can sorta see that" and other future tech where you say "no way; you canna bend the laws of physics". I'm trying to do the former and avoid the latter if at all possible. – Monica Cellio Oct 10 '14 at 0:25

This is a complicated answer since every piece of technology you mention is going to be improving over those 200 years. That said I think the answer will actually be a blend of several renewable resources.

Take a look at this solar efficiency chart from NREL (National Renewable Energy Laboratory): http://www.nrel.gov/ncpv/images/efficiency_chart.jpg

The gist of the chart is that energy conversion efficiency has been rising steadily over the last 40 years.

Computers and other electric devices continue to improve by increasing or maintaining performance at reduced energy requirements.

However, solar only covers your robots for half the day (give or take) but other advances such as the biobattery (http://en.wikipedia.org/wiki/Biobattery) could help make up for the differences in lighting levels.

Biobatteries convert something like glucose into energy via enzymes; very similar to how plants and animals break down food for energy. These batteries could be designed with different enzymatic components allowing your robots to "eat" different materials to power a selection of batteries in the absence of good sunlight. Not too different from Futurama's robots which run off of alchohol.

This gives them the human like trait of sitting down to a meal (or chugging a sugary beverage) to get them through the part of the day.

• Interesting -- didn't know about biobatteries, and the effect of having the robot sit down with others for a meal could be quite handy for socialization. Thanks. – Monica Cellio Oct 8 '14 at 21:01
• And makes for some very interesting scenes. I'm picturing "Dogs Playing Poker", with Bender-like robots instead, chewing on cigars and munching food. – Lou Oct 9 '14 at 16:19
• So they consume beer and belch fire. Would they steal your wallet while they are at it? – Sonvar Jan 9 at 7:22

The power requirements are going to be highly variable. Just think about today's electronics -- you could put a set of AA batteries into your TV remote and have it work for years, but an identical set of batteries from the exact same package in your stereo remote dies in 6 months.

More to the point of robots, you're going to have so many different options for how to implement movement -- servos, stepper motors, "muscle wire", just to name a few -- that it's really impossible to say with any certainty how much battery you'd need, let alone whether it would fit.

That said, though, this is of course set in the future, and we are seeing pretty slick advancements in both miniaturization and output of batteries -- as just one example, my Samsung Galaxy S5, despite using more power for its larger screen and faster processor, lasts much longer on a single charge than my old S3 ever did, despite the batteries being roughly the same form factor. So I think it's quite reasonable to say that yes, you absolutely could produce a battery that is powerful enough to run your robot through the day, and small enough to live somewhere within the robot's chassis.

Then again: Why? Using a day-long battery still tethers your robots, albeit the physical tether only lasts overnight (or whatever) -- they still have to remain close enough to be able to plug in at night. That means they can't join their human friends on a weekend camping trip, or hang out at the (power-less) lake cabin for a week. That's going to cause a lot of unnecessary grief.

Why not give them an RTG instead? They sound scary, but when you get down to it they're primarily releasing nigh-harmless alpha particles easily shielded by the robot's own "skin" (or even your own!), let alone the shielding of the device itself. These things can easily provide power for many years, and when they need to be replaced a simple battery backup could keep the robot "alive" while the old RTG is unplugged and a new on plugged in.

Of course, this would have an impact on things like radioactive waste when spent fuel is removed, and the luddites of the era might never get over the "radioactive" bit of the RTG and thus naturally (but quite wrongly) assume that they're walking atomic bombs. All kinds of fun social problems you could run with from this, in addition to the whole "robots aren't humans" aspect.

Safety: RTGs are significantly safer the fission reactors. With an RTG, the only reaction is a steady and unchangeable (albeit decreasing) radioactive decay of the fuel; with fission, it's a controlled fission reaction that at all times has the potential for control to be lost, result in Very Bad Things(R).

RTG fuels are chosen for emitting alpha particles, which won't even penetrate your skin, and for a high production rate of those. While this makes them far more dangerous should you ingest them (don't do that!), it means that any environmental contamination is far less worrying because it will lose its radioactivity in decades rather than centuries. (That's assuming we don't clean up the fuel, which of course we would!) RTGs are further designed with nigh-indestructable containers to further reduce the chance of environmental contamination. When Russia's failed Mars-96 probe re-entered the atmosphere, its two RTGs were believed to have survived re-entry and impact on the ground without damaging the shielding; thus while they've not been recovered, practically no one's worried about any contamination from them.

So to sum up: Yes, you absolutely could have a battery powerful enough and compact enough to power your robot, especially 200 years from now. You could even slap some solar cells on them so they could recharge their batteries (or at least conserve battery power) while outdoors in the sun. Or, you could go space-age and put the same thing we use to power many of our space probes into your robots, and add the "anti-nuclear" luddite social aspect to your world.

And that's all without assuming any new scientific breakthroughs: Remember, according to Back to the Future, we should have Mr. Fusion by next year -- if it can provide the 1.21 gigawatts necessary for time travel, certainly it can run a measly ol' robot!

• Thanks for this thorough answer. I'd much rather my robots be able to go on that camping trip (and was imagining that, if they had to plug in, they'd bring a portable charging station along with the tent and sleeping bags -- but hardly ideal). I know RTGs are shielded but are also used in (mainly) human-free environments; any ideas about the risk to humans who spend lots of time with these robots? Is complete shielding possible? (I like the sociological effect you mentioned.) – Monica Cellio Oct 8 '14 at 21:07
• @MonicaCellio I've edited in a section about the safety of RTGs. The short version is that they're a lot safer than putting miniature fission reactors into your robots! – Kromey Oct 8 '14 at 21:49

If we assumed massive increases in computer power efficiency in the future, the Fujitsu K (http://www.fujitsu.com/global/about/businesspolicy/tech/k/qa/index.html#qa12), which is good for a bunch of things, but not, unfortunately, thinking for itself, uses 12.66 Megawatts per hour. Even if we can compact the necessary hardware down and get an entire thinking robot out of the same power as a modern supercomputer, you'd have to produce a -huge- amount of power to get it all working.

Digestion

I think the easiest way to do an internal solution would simply be to have them break down items into an easily stored fuel, which they would carry around. Essentially, the robots would "digest" materials and foods (with the byproduct that they appear more human if they eat), grind it up into a concentrated, energy rich slurry, and burn that as necessary in an internal engine. Anything that can't be used in the fuel is simply disposed of cleanly, as we might do. Unfortunately, the order of power we're looking at is.. unfathomable. 1 kcal is 1.163 watt hours (and one w/h is 0.86 kcal, so this robot would need to eat

12.66Mw/h = 12,660,000w/h

12,660,000w/h = 10,887,600 kcal

and the average adult male should eat about 2,500 kcal. You see the problem?

http://www.unitjuggler.com/convert-energy-from-kcal-to-Wh.html

Nuclear

Apparently one gramme of the uranium we use in our nuclear power stations creates about 1MW of energy per day, or 0.04 MW/h (http://www2.lbl.gov/abc/wallchart/chapters/14/1.html), so potentially a teeny tiny fission reactor, which, aside from the scale, is being used to produce a lot of the world's energy right now, could produce enough power from 24 grammes of uranium to power it for one day. This is definitely possible. I couldn't find the size of a gramme of uranium, but I can tell you that you could fit enough uranium to power this robot for a month at least, from a glob the size of a tennis ball.

Solar

Externally, I'm not sure they could operate on sunlight alone. I think we're definitely looking at an internal fuel source, unless there's vastly more energy in the sunlight of whatever world they happen to be living on. Here on Earth, the sun produces 1120 watts per square metre on average, so it's likely that generally they'll get even less than this most of the time, even if they have a full square metre of solar panel showing on their humanoid form (how big is your head?) and the solar panels convert energy at 100% efficiency or close enough.

Summation

So, in summary, go nuclear. I don't think i'm mucked up any of my calculations, but if you spot an error, feel free to point it out. All of this assumes no radical change in architecture that makes thinking really energy-cheap to perform (clearly we've got a secret, because we manage it). If something came along to eliminate the need for all that hardware, then both solar and digestion become valid sources of energy.

• In the time it took me to research and post this (I saw this question when it was just a minute old), the question was answered 3 times :D – Rowanas Oct 8 '14 at 20:54
• I can't help but question the energy consupmtion figure. My metric tells me that "watts per hour" are not actually a unit of either energy or power (and further are distinct from watthours). Power consumption of an actual articulated robot might give you a more relevant figure, seeing as supercomputers are also wildly inefficient and do not make a good benchmark. – Mike L. Oct 8 '14 at 21:01
• I thought I had converted the watts per hour, megawatts per hour and kcal required to provide that power correctly, but it's entirely possible that I haven't. I understood that w/h and Mw/h were units of energy per unit time, and the actual relations between the various units were calculated using figures present online. If i'm wrong, can you show me how it should look? I'd be very grateful :D I also thought that a supercomputer is the closest thing we have to a proper robot brain, and as our brains are the things that use the most juice in a human, that would be the best palce to start. – Rowanas Oct 8 '14 at 22:07
• Well, your problem starts right at the beginning - Joule (J) is a unit of energy, while Joule per second (J/s aka Watt) is a unit of power. Watt hours (meaning Watt times one hour, or 3600J) are sometimes used for convenience in calculating electric bills, but Watts per hour are nonsense, or more accurately, probably a mistake by someone being sloppy with their units. Because a Watt is a measure of energy per time, it can be used to express power consumption and consumption of eg. appliances is indeed commonly expressed in watts. – Mike L. Oct 8 '14 at 22:14
• (contd) Saying that a supercomputer consumes some number of Watts per hour is complete gibberish - it can either consume some number of Joules per hour (which could be instead expressed in Watts), or some number of Watt hours per hour, which is also equivalent to Watts. My guess is that the figure in the FAQ comes from a marketing person with no idea about physics, and you should probably not be basing your estimate off of that. Also keep in mind that 126 MW is a ridiculous amount of power - it's approximately the engine power of a Kirov-class nuclear battlecruiser. – Mike L. Oct 8 '14 at 22:18

Energy Storage: Nanocapacitors

A Capacitor is two layers of conductive material separated by a layer of insulator. They contain no moving parts, have no chemical reactions, and charge extremely quickly. Their power storage increases with the surface area of the two conducting layers, and how close together they are.

In a society with nano-fabrication, or at least the ability to efficiently lay extremely thin wafers and use them in a circuit, capacitors become quite powerful, and might be viable for proper energy storage.

We're currently orders of magnitude away from the power your robots would need, but Volvo had a concept car that ran off of capacitors built into the panels of the car body. http://www.21stcentech.com/transportation-update-volvo-e-car-concept-runs-super-capacitor/

As a bonus, you could justify your robots to have a body cavity filled with layers of high-surface area material, that fulfills the same functions of a human's lungs and digestive tract.

As a drawback, this introduces all of the other societal implications of industrial-scale nano-fabrication, which are hard to enumerate and predict. Don't know if you want to open that can of nanoworms.

Energy Transfer: Magnetic Resonance Coupling

Electric circuits in an oscillating magnetic field can be made to resonate, like a pane of glass in a room with the proverbial opera singer. This principle can be used to wirelessly and directionlessly transmit energy to a receiver, with relatively low power lost to the environment.

There are currently several competing standards, but the Alliance for Wireless Power has a device that can charge at a range of several centimeters. http://www.rezence.com/technology/meet-rezence

This might also be the principle behind come of Tesla's unpublished party tricks, which are said to have extended through the room or into his backyard.

200 years might be enough to scale that up to a field the size of a room, or a building, or a space-station, as appropriate to your needs.

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[2]. 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

The numbers

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[4] (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 kWh per 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[8] 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 inputs, from 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.

Converted to kWs, we get 300e3 kJ = 300e3 kWs or 300 MWs. Converted to 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 be 903 kWh. Divided by 30 to get the daily average, we get 903/30 = 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 number.

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 Mtoe is Megatons 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 is 4e6 t which is 4e9 kg. Ten percent of that is 4e8 kg.

The global energy consumption converted to kWh is 1.474e14 kWh 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 4e8 / 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 mg.

To get the total boron needed per day for our calculated 84 kWh we multiply by 2.71 mg/kWh: 84 * 2.71 = 227.64 - the result is in mg.

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.

• Explain the downvote – mechalynx Oct 8 '14 at 21:41
• Thanks for this analysis. As someone not equipped to independently validate or challenge this, I'd really appreciate an explanation for the downvote. Is there some flaw in either the assumptions or the math here? – Monica Cellio Oct 8 '14 at 21:41
• @MonicaCellio I'm assuming the downvoter thinks this is some pseudoscience mumbo jumbo, but apparently didn't even do a google search to examine the details. It doesn't have to revolutionize the world overnight to be quantifiable and it's well-documented and researched. Also, this is fiction - I'm not advocating some new age tripe, it's a suggestion for futuristic fiction. – mechalynx Oct 8 '14 at 21:45
• I didn't think it's psuedoscience, your math is bad and you are inconsistent with your units. This makes me somewhat distrustful of everything else, but not enough so to say that it's definitely wrong. Will come back and give fixed version of math in a few hours. – Saidoro Oct 8 '14 at 21:48
• Looks good now. The linked calculator is giving me a significantly different values for the same inputs than you're reporting(also different ones from the ones I got at a different computer earlier), but it's close enough to not change the outcome. Downvote removed. – Saidoro Oct 9 '14 at 3:18

Assumptions: A typical human has a mass around 70 kg. They consume about 1.1 W/kg continuously(I'm approximating) throughout the day or about 96 kJ/kg daily. This together with the average mass gives about 80W continuously or 7MJ daily(rounded). They have a total surface area of about 1.75m and a volume of about 66L. A robot will need an amount of power equal to some multiple of what a human needs which varies based on efficiency. Probably a very large multiple.

Batteries: Our best rechargeable batteries have an energy density of about 2.6 MJ/L and .875 MJ/kg, meaning it would take about 3 liters and 8 kgs of battery if robots take as much power as humans. That's a large component, but not impossibly so. However, it doesn't scale very well if the robots take more power than humans, if it takes 5 times as much energy to run a robot as a human(Which is a very, very small estimate) it's up to 15 liters, almost a quarter of your volume. And you need that volume for other components. There's also the issue of cost, high end batteries cost \$300 per MJ and have to be replaced biannually with continuous charges and discharges. This cost stays constant regardless of how you subdivide the charges, batteries wear out when charged and discharged, not by time.

Solar: Just isn't going to work. A human has a surface area of 1.75 square meters. They can keep maybe .75 square meters of that pointed at the sun continuously. When the sun is out. And it isn't cloudy. And there aren't any buildings in the way(No city-dwelling robots here). Current solar cells can produce 150 watts per meter. So you're looking at just barely exceeding the energy requirements of a human for half the day. Robots are likely to require far more energy than humans. This isn't going to fly. Or even walk.

Nuclear: Could work. The issue here is shielding, The fuel is easily tiny enough, but you don't want people walking around emitting harmful radiation at all hours. If you can miniaturize the components enough that the robot could be built almost entirely around the power supply instead of needing the power supply to be a smallish component, this might be feasible. On the other hand, this would pretty much make your robots big concrete tubes with limbs bolted on, which may not fit your aesthetic. Kromey's RTG may be better, but I haven't looked at it in detail.

It would be interesting if the technology to wirelessly charge your phone was expanded upon in the next two-hundred years.

Of course the dream is that one day your electronics can wirelessly charge without having to touch anything, or maybe even just always be powered completely wirelessly, no batteries needed. So, the question really is, how do we realistically come as close to that as possible? In my view, there are several generic ideas you can pick and choose from before deciding exactly what technology you want to go with.

Make each electronic device generate its own electricity

Answers which involve eating, or having each robot have its own generator, or using some outside resource like solar energy to generate electricity are all included in this section. It seems more natural because its what plants and animals do. It's also very modular - everything only depends on itself to run. Most current answers seem to be in support of this section.

Have devices capable of storing great amounts of energy in a small space

Batteries for the most part, but could also be considered for fuel-like sources such as gas or hydrogen. We support gas stations for cars, if robots are human-equivalent maybe a new function of gas stations is that they can charge robots as well. The idea is that the energy we use to power our houses or such can be stored for later use and is easily refilled when it needs to be.

Devices which run on electricity provided to them

Most house-hold electrical devices are simply plugged into the wall and don't require a method of storage or generation. These are possibly the most user-friendly. You plug it in, you don't need to worry about refueling or putting it in the right conditions so it can generate its own power. I like the idea of the wirelessly charging phone in the first paragraph because its one of the few ideas (that is actually in use today) I've seen that fits into this category without just being plugged into the wall. You could also say something like bumper cars or electric-ran trolleys (also known as trams) run in this way. Imagine if the mat that can charge your phone could be easily attached to any surface in your home and thus, could run anything touching that surface.

Combine and choose

I feel like I should mention that when you take any one current technology and try to extrapolate it into the future there is a certain... "Cars will all be flying by the year 2000" type of feel to it. Most likely you will want several different technologies which, together, achieve the feel you want, because that will also be what will make it unique for your world.

To offer a third option, robots could be somewhat like humans by needing to regularly consume carriers of energy, such as oil, hydrogen or batteries and then excreting the remnants. The technology for this is available right now; it’s just not feasible as this kind of mobility is not a desired feature for robots for now. Your robots would not be restricted, as the energy source can be widely available and the robots can carry backup energy around with them – just like humans.

There are fuel cells which run on sugars. (Here and here)

The robot may be autonomous and take its own dose of sugar (with some water for the fuel cell) every now and then.

Even if electronics become very efficient, (i.e. quantum computer, optic computer, etc...) the minimum energy requirement for a robot to do physical tasks is the same (Climbing up the stairs, lifting heavy objects, running, etc... would all require a minimum energy output based on physical laws, and figures cannot go below those values).

• Wow, sugar -- so that bottle of Jolt isn't just for the caffeine. Cool! – Monica Cellio Jan 9 at 15:20

Turning my comment into an answer. 200 years is an incredible amount of time given our current rate of discoveries...so it's hard to tell what options we might have...though I would suggest our current ones are harshly limited and probably not feasible in a robot. Right now battery technology lags behind most other tech advances (most phones are 80% battery anymore...we've miniaturized electronic to the nth degree, but have basically failed to come up with a better electricity storage option.)

Some more futuristic style advances:

Lets say we get a much larger particle collider and we discover that ultimately a proton and electron are made of the same thing. A proton is thousands of times more massive than an electron...but if a proton breaks down into the same components as an electron, whats stopping us from rearranging these former proton particles into a much larger number of electrons? A single proton (also known as a hydrogen atom) can easily be taken from water, leaving a simple o2 cloud as it's exhaust and the occasional need to add water to itself.

How far futuristic do you want to go? Our current computing has almost reached the limit as to how far we can miniaturize a computer processor. The 'next' step as some have envisioned is quantum computing. Instead of taking a million 1 bit transactions through the processor, the processor opens up 1 million dimensions containing one processor that does one calculation before collapsing (the scale of this is amazing...1 million calcs by one processor vs 1 million processors doing 1 calc each. It's this level that I envision an AI starts becoming possible). Heh, multi-dimensional parallel processing! Whats stopping us from opening 1 million dimensions and stealing a single electron from each before collapsing?