paper: Let's Do Robot Math


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Let’s Do Robot Math
by: Mike Schreiber

Covers some physics and equations that are used in JVNs calculator and some commonly used design concepts / principles related to motors, drivetrains, and arms.

I put this presentation together since I got a lot of feedback that there was interest in this type of material from our students. Target audience is high school students - some math may be over younger students’ heads. Thought this might be useful for people that use JVN calculator all the time but don’t really understand what it’s doing. Covers some physics and equations that are used and some common design concepts / principles related to motors, drivetrains, and arms. Feedback welcome.

2018_12_02_Robot_Math_rev2.pptx (608 KB)


Thanks for helping save the world. :slight_smile:


Good stuff! I do have a few suggestions:

OK, quite a few
[spoiler]Slide 2: In my experience, geometry as a prereq means juniors and seniors - with a few exceptions.
Slide 3:

  • Use of “linear” in first bullet: I know what you mean, but wouldn’t have in high school, or IIRC even the first couple of years of physics in college.
  • I’d also define “free” and “stall” here.
  • Last bullet: has anyone tested this? I’m working on this, but I’ve never seen anyone else do so.
    Slide 4:
  • I had never heard of EMF until college. Either use “voltage”, or otherwise make it clear that EMF is voltage.
  • 2a: suggest that you capitalize or bold “a lot”
    Slide 4: alumni is a plural - JVN is an alumnus - though “alum” or “graduate” might work as well.
    Slide 7: Perhaps a matter of different experiences, but 8.86 ft/s is not a “very slow” top speed to me - in games with short sprints (e.g. Power Up), I’ve had numbers near this be the “fastest” sprint speed for a full weight robot with a four-CIM non-shifting drivetrain. I suggest “somewhat” or “rather” or <simply> slow.
    Slide 8:
    Bullet 1.3: Again, your speeds seem high, especially for such an elementary presentation.
    Bullet 1.3: Traction limited drive trains are a no-compromise necessity? In any case, I suggest adding the phrase “traction limited” here to define the term as you use it later without a definition.
    Bullet 1.4.x: Should also note that higher geared robots require more current to accelerate linearly, most notably at low speeds.
    Bullet 1.5.3(push around): you should follow this statement up with some why. Is it because you designed a traction-limited drive train, or they’re fast enough to run away, or something else?
    Bullet 2.1(shifting): I don’t know exactly what you mean here gearing down to help make a turn. Your target audience will likely not why a robot would be unable to turn.
    Bullet 3 (wheel Size): I would move first bullet (“we mostly use”) to the end, after you have described he factors. I would also state all factors in bullets 2, 3, 4 in positive terms, or all negative: “Larger wheels wear slower; Larger wheels give better ground clearance…; Smaller wheels do not require as much gear reduction” or “Smaller wheels wear faster ; Smaller wheels provide less ground clearance…; larger wheels require more gear reduction”.
    Slide 9, bullet 1: breaking traction does not always ensure that you won’t trip breakers. You still gotta do the math. Check the “Peak Power Test” for the 775pro here: Personally, I prefer designing for the wheels to slip at a specified current draw (e.g. 50A per motor for CIM). I see you mention this on slide 11.
    Slide 14: Not as difficult as you make out - you have to do the optimization side manually, but you can do this iteratively using linear approximations. The excel sheet at will help you do the calculation.
    Slide 19, bullet 5 (current draw) should specify SRX; teams still have SRs about. Also, you don’t need a specific motor controller - the PDP will measure current for you as well.[/spoiler]

Thanks for the feedback. Will definitely tweak a few things.

The presentation should probably be prefaced with an “I don’t expect you to understand all this math and that’s okay”. I didn’t plan to cover EMF in great detail other than to show an equation for how motor curves are formed and expose students to the topic so they can go do more research if they want. Many of the details that are missing are talking points that would be addressed when presenting this material - I’m still working on populating the notes sections. I also haven’t actually presented this yet and it’s been a while since I was in high school so I forget what people know.

With regard to speeds, the KOP chassis is geared 10.71:1 with 6" wheels for a free speed of 13 fps. 9 fps free speed (not adjusted) is slow in the context of our teams typical drive setup.

With regard to optimizing sprint distance, I agree it’s not THAT complicated and have a setup in Python that does the optimization with a numerical method very quickly, but the friction parameters you specify have such a large impact on your results that I don’t want to confuse students until there is more correlation work with friction and battery parameters like the data 5406 posted to match their own data and 234s.


RE: optimizing sprint distance

Last year was the first time 254 put a lot of energy into modeling the dynamics of our drivetrain based on empirical data. What we found was pretty interesting (and seemed to agree with general findings that 971 - longtime drivetrain modelers - have found). We had generally been dramatically overestimating the torque efficiency of our drivetrain (by 30%+ compared to motor specs).

So I think teaching the theory is important and useful, but I am increasingly of the belief that teaching students (1) which parameters tend to be most uncertain and (2) how to design good experiments from which parameters can be estimated is just as important.


Yes!!! And please teach some of my co-workers too.


Was motor performance reduction at higher-than-ambient internal temperatures accounted for in your earlier over-estimates of drivetrain torque efficiency? Hot armatures make a difference, and we can’t cool them fast enough during FRC match play.

^Emphasis mine. I agree wholeheartedly, but must caution that this is MUCH harder than many people seem to think. Good experiment design requires much more than learning a method. Correctly identifying and ranging significant factors for study often requires a deep understanding of first principles (also called physics, or theory) that can only be acquired through a combination of training and experience. Well designed experiments complement and enhance the value of theoretical perspectives; they cannot substitute for them.

Back to the original topic: the OP’s presentation is very good. I concur with Gus’s suggestions.

Generally, I expect that a lot of this material will roll right past nine out of ten FRC students. I want to hire the one that gets it. Experimental learning is (IMO) the best way to reinforce theory, but theory is the only real basis for thinking about techniques that have not been tried before.