Electric motor scaling laws and inertia in robot actuators

Aaed Musa blew my mind about 18 months ago with his capstan drive video:

https://youtube.com/watch?v=MwIBTbumd1Q

Eight months ago he built a quadrupedal robot that could step sideways using three of them per leg. I’m not going to link that, you’ll have to find it from his YouTube page because you should look around.

Same issue covered on HN a few weeks ago.[1] This one has more motor theory but less machine learning theory.

Too much gear reduction, and you can't back-drive or sense forces from the motor end. Too little gear reduction, and your motors are too bulky or too weak. Reflected inertia goes up as the square of the gear ratio, as the article points out, because the gear ratio gets you both coming and going. So high gear ratios really hurt.

Robots, like drones, need custom motors sized for the specific requirements of the joint. For a long time, the robotics industry was too tiny to get such custom motors engineered, and had to use motors designed for other purposes. This will become a non-problem as volume increases. Especially since 3-phase servomotor controllers, which drones need, are now small and cheap. They used to be the size of a paperback book or larger.

(I've been out of this for years. I've used hydraulic robots and R/C servo powered robots. The newer machinery sucks a lot less.)

[1] https://news.ycombinator.com/item?id=47184744

I think electric motors are just barely suitable for mobile / humanoid robots. Compared to human muscles, they're heavy and they overheat quickly. Current humanoid robots are spending most of their energy in carrying around just themselves, which is a huge amount of dead weight, while being unsafe for anyone to be around.

If someone invents a new type of 'artificial muscle' which has low inertia, high force/torque density, and can work without overheating, that would instantly kill all other robotics companies.

I'm used to approaching these problems from a slightly different angle. There are two simple cases that can be used to establish guide points.

If you have a load that is purely inertial, the optimum gear ratio (to minimize I-squared-R motor loss) is found by picking a gear ratio which matches the reflected inertia of load and motor. At this point, on every acceleration you put just as much energy into the rotor inertia as into the load inertia.

In contrast, for a steady-state load which is all friction (e.g. a mixer such as for paint or food), a gear ratio which balances friction loss in the motor with the load friction will minimize the armature loss.

Most applications have live between these points, and these optimizations ignore gearing losses and expense and noise, but they can serve as guide posts.

There's also the issue of separating winding choice from gearing choice. For each candidate motor there exists an optimum gear ratio which will minimize the heat produced when driving a given load (friction and inertia) over a given velocity profile. That gearing can be found by trial and error in a simulation. These aren't crazy difficult simulations (can be done in a spreadsheet) but do need to take temperature dissipation and change of motor performance with temperature into account. Once that gearing is found, the V-I requirements of the motor at that gearing will be known and then winding adjusted to fit requirements of driver circuitry (i.e. trade current for voltage).

What is the "ELI5" summary of the practical limits & scaling laws that govern robotics?

The current "futurist" vision is one of humanoid robots taking over many/most jobs done by humans today, but - as someone that routinely hires human welders & assemblers - the dexterity required for most ad-hoc tasks seems many many decades (if not more?) away from what I see robots do--yes, even the fancy chinese jumping ones.

This has led me to think one of two things:

1. The robotics revolution will not come. It's predicated on the idea that advances in robotics will follow a curve of the same shape as advances in compute/ai, which will not happen. OR...

2. There has been some paradigm-shift or some breakthrough that has put robotics improvement on a new curve.

To an outsider, what I see in robots is not categorically different than like, the sony AIBO dog in 1999. It's significantly better of course, but is it really that different? (Whereas what we can do in compute-land today is categorically diffrent because of the transformer model breakthrough).

So:

1. Have there been any breakthroughs that would lead us to believe that a robot will be able to like, look under a table to adjust a screw?

2. What are the scaling laws & practical limits to present-day robotic dexterity? Is it materials? Energy density? What?

3. What is the real rate of improvement along these key dimensions? Are robots improving linearly? Geometrically? Exponentially?

4.Or should I keep discounting robotics until we get our first robots that are made of meat? That I'd believe would result in exponential change!

Why can't we just dump massive currents into spring returning solenoids with ~5mm or ~1/4" range of motion, and amplify that motion through tendon systems for whole joint motion ranges?

I wonder if robots could be made to work better at cryogenic temperature, so superconductors could be used. The figure of merit would be much higher if resistance was zero. Or maybe this is another reason to want room temperature superconductors.

The real innovation will be in soft robotics and compliant mechanisms. You read it here first.