Electric motor scaling laws and inertia in robot actuators

(robot-daycare.com)

111 points | by o4c 3 days ago

5 comments

  • hinkley 7 hours ago
    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.

    • num42 5 hours ago
      Sorry for going off topic. "Electric Motor Scaling Laws and Inertia in Robot Actuators" by Ben Katz who designed the MIT Mini Cheetah in 2018 is very well known in the legged robotics community. His master’s thesis on actuator design is also widely referenced.

      During the COVID period, some Chinese companies even sold variants of actuators inspired by the Mini Cheetah design.

      Aaed Musa has also mentioned in some of his videos that his actuator designs were inspired by the Mini Cheetah actuator. Yes, His capstan drive video is especially impressive.

      For example, in Aaed Musa’s video "I Built a Rubik's Cube Solving Robot" (https://www.youtube.com/watch?v=m0bMMALYMYk), he states in the description that the design was inspired by Ben Katz’s work.

      Ben Katz master thesis, is worth reading: "A low cost modular actuator for dynamic robots" 2018 https://dspace.mit.edu/handle/1721.1/118671 and also has a good post https://robot-daycare.com/posts/2019-12-16-the-mini-cheetah-...

      And also, The Rubik's Contraption (2018), 297 points, the work done by same author https://news.ycombinator.com/item?id=16561049

      • jcims 1 hour ago
        I did a bit of a deep dive into motor control and actuators in building a two axis gimbal for tracking satellites with an RF antenna (with the eventual goal of building a mount for optical tracking).

        Ben's vids were kind of mind-blowing for me at that time. I couldn't believe some of the control that was possible with relatively pedestrian electronics. Aaed's vids do a wonderful job of making it accessible in an applied way.

        It's something I think a lot of the folks on HN would find interesting to tinker with. Nice mix of software and hardware that actually does work in physical reality. It also gives me a level of appreciation for the advances in humanoid robots that I don't think I would have had otherwise. (If you *do* get into it, I'd highly recommend getting into field oriented control with brushless motors and encoders. Small hobby servos are fun but they encapsulate a lot of the interesting parts and tend to have limited options available for things like the capstan vid linked above)

    • keeda 6 hours ago
      Thanks for this. I almost never have the patience for any videos, but this one hooked me and kept me engaged throughout. Worth it for that random "yo mama" joke alone.
  • Animats 6 hours ago
    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

    • blueblisters 6 hours ago
      Reflected inertia does scale as the square of the gear ratio but it's a bit misleading unless you also consider the change in rotor inertia, which scales as a cube of the rotor radius (as the article points out).

      The other side of the scaling laws say that motor torque scales as a square of air gap radius (roughly rotor radius), and output torque scales as linearly with gearing ratio.

      When you balance these out, the reflected inertia depends on the inverse of power dissipated for a fixed output torque.

      In an ideal world, your total reflected inertia is independent of the gearbox and largely depends on the motor fill factor and how hot you can run it.

  • numpad0 4 hours ago
    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?
    • tlb 49 minutes ago
      Heat goes up with the square of current, so putting 10x the current to get 10x the force means 100x the heat.

      Still, I think this idea is under-explored. There are probably applications for robots that move really fast, but only for a second before having to cool down.

    • moffkalast 4 hours ago
      Cause it'll run three minutes on battery power.
      • numpad0 4 hours ago
        Just put a chainsaw power pack in the back. That'll be massively cool anyway.
    • cyberax 4 hours ago
      You can play around with a solenoid calculator like this one: https://www.getzenquery.com/tools/solenoid-force-calculator/

      TLDR; is that you need high current, meaning a lot of ohmic heating. With non-negligible back-EMF resulting in even more losses. Rotating motors essentially "lengthen" the travel of the "plunger" compared to linear motors.

  • pfdietz 8 hours ago
    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.
    • blueblisters 6 hours ago
      You would hit electrical steel saturation limits way before you need to pump in enough current to justify super-conductance.

      Cooling in general is not a bad idea to allow you dissipate heat as you push motors to their saturation limits.

    • PowerElectronix 4 hours ago
      Power disipation in the motor is not the limiting factor. Moving a robot requires work and the motor provides that work with a high eficiency already.

      Plus, cryo temps require a lot of power to keep thing cool and coper and iron embrittle so the forces acting on the winding could shatter them.

      • hrmtst93837 1 hour ago
        People gloss over peak torque versus thermal limits in robot actuators because stall torque even for a short burst will cook the motor long before copper embrittlement matters.

        At cryo nobody sane is building robots unless the budget is a joke.

    • Robotbeat 8 hours ago
      Even copper has vastly lower resistance when cryogenically cooled. It's not a bad idea for some applications, and water cooling is already a good way to increase power density.
      • hinkley 7 hours ago
        I learned recently that the inductive heating coils used for metallurgy (smithing) are copper tubing with coolant flushing through them. The copper tries to heat up along with the bar you’re heating in the coil. Both from resistance and from radiative heating.
  • brcmthrowaway 6 hours ago
    The real innovation will be in soft robotics and compliant mechanisms. You read it here first.
    • pedro_caetano 2 hours ago
      No, compliant mechanisms are important but the real gap in Robotics is perception (and no perception is not just Computer Vision).

      There is such an insane amount of information richness in mammals and sensor specialization:

      - Merkel discs

      - Ruffini corpuscles

      - Meissner corpuscles

      - Pacinian corpuscles

      - Muscle spindles

      - Golgi tendon organs

      - Nociceptors

      And it's not the biology 101 types of sensors (in terms of variety of sources) but also the information density per square millimetre. It is orders of magnitude above anything that has ever been created with technology.

      Once we leap above just Visual Servoing and start reaching sensory density and feature parity with human skin, joints, muscle, feet/hands, then we may start to see real breakthroughs.