Power.

All the other technologies are increasing extremely rapidly but battery technology isn't.

We are at a point where a breakthrough in batteries would have an incredible effect across a huge number of fields.

Everything is getting more power efficient though, so you will at least get more computing power for the same amount of Watts.

I agree. A quick Google search suggests that the human body requires about 100 Watts[1] of power. On the other hand, a small 12 volt car battery is able to provide 45 Amps over an hour, which implies that it can support a power draw of 540 watts for an hour. Even if human activity required 200 Watts, an android with human level power efficiency should be able to operate for over 2 hours with the technology of today's small car batteries. Of course, my math could be wrong :-)

[EDIT] - My point here is that even if improvements to battery technology remain slow or constant, with sufficient innovation in energy efficiency and algorithms, we could still have robots with usable to good running times. Just figuring out a reliable walking gait and building materials for passive dynamic walking can significantly reduce the power requirements.[3]

[1] - http://hypertextbook.com/facts/2001/JacquelineLing.shtml [2] - http://www.chem.hawaii.edu/uham/bat.html [3] - https://en.wikipedia.org/wiki/Passive_dynamics

Not everything. The energy required by physics for lifting boxes or driving a car up a hill is pretty much fixed. Better batteries would help with both of those.

I don't think the robots who can do those things are near the physical limits, though.

Electric jets as well.

The energy to raise a fixed mass a certain height isn't going to change.

Not to mention an electric car with a thousand mile range would be huge.

It would certainly put a whole new perspective on range anxiety.

Also, teach the robot to replace it's own battery or fuel.

Yikes! As long as it has some parameters about human safety being more important than batteries or fuel, then by all means...

If humans can go multiple weeks without food, then how do biological organisms solve the problem of power storage better? Or does our brain and muscles etc just require less power?

Part of the reason is that humans are not run on batteries. Humans are more similar to fuel cells in that we consume oxygen to produce energy. We inhale oxygen, combine it with our energy stores and exhale 80% of the mass[2].

An average American man needs about 3400 Calories each day which corresponds to about 1 kg of oxygen consumed[1]. Similarly the average American woman uses 2550 Calories and .75 kg of oxygen.

[1] Design Rules for Life Support Systems http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2004001... [2] http://www.livescience.com/49157-how-fat-is-lost-body.html

3400 calories? That seems awful high. Perhaps if you are into bodybuilding but no way an average person needs that much. Closer to 2000-2500 maybe.

Mostly the latter, I believe.

The human brain uses the incredible 20 Watts to achieve things that modern megawatt supercomputers aren't capable of.

I think the figure is closer to 100 W average across the day since the brain cannot exist in isolation of the body which needs ~2000 calories daily, but still, we're fairly efficient. We're built with advanced nanotechnology.

The biggest problem is that we still don't understand the principles of walking, locomotion, and manipulation. Biology doesn't come with any documentation.

This is much more than the problem of not having good sensors, not having powerful enough actuators, or solving models. Without understanding the fundamental principles we may not even get the hardware right. Recall early attempts at heavier than air flight that attempted to copy and scale up a bird rather than understand the principles behind how wings worked.