I’ve been wanting to build a dynamometer for a while to better characterize the performance of the direct drive and geared versions of the moteus controller. I have now started down that path with a torque transducer, which I calibrated with the below fixture:
I got a what ended up being a low quality load cell amplifier to use with it from the same supplier, although discovered it was total garbage and am now using a SparkFun OpenScale board which seems to be working much better. Soon I’ll hopefully have something wired up that actually has a controller or two on it.
I’ve started some development on higher speed gaits for the quad A1! No real details to report now, just a video showing the first time I tested it not in simulation. I will admit these clips were cherry-picked, as there are problems still, but it is a start!
When I first posted the qdd100 beta on mjbots.com, I performed a simple “continuous torque” test where I measured the torque that could be applied indefinitely without thermal limiting in a lab environment. It has come to my attention that other servos rate their “continuous torque” for a much lower value of “continuous”, sometimes only 30s. To make the situation clearer, I measured the time to thermal limiting at a range of torques and updated the product page.
For this test, at each torque value I started with the qdd100 in thermal equilibrium with an ambient 20C lab environment, then applied the given torque and waited until thermal throttling set in. No forced airflow was present and no conductive or radiative cooling enhancements were used.
I’ve worked through a number of different iterations of the stand-up sequence for the quad A1 (2019-05, 2019-09). The version I’ve been using for the last 6 months or so works pretty well, but because it drags the legs along the ground to get them into position, it can have problems when operating on surfaces with a lot of traction, like EVA foam, besides being uselessly noisy.
To make things just a bit more robust, I’ve now tweaked the startup routine so that the shoulders lift legs clear off the ground before positioning the legs, then lowers them back down into place. This makes the stand up routine much more likely to succeed on just about any surface:
In my previous experiments demonstrating torque feedback (full rate inverse dynamics, ground truth torque testing), I’ve glossed over the fact that as the stator approaches magnetic saturation, the linear relationship between torque and current breaks down. Now finally I’ll take at least one step towards allowing moteus to accurately work in the torque domain as motors reach saturation.
The stator in a rotor consists of windings wrapped around usually an iron core. The iron in the core consists of lots of little sub-domains of magnetized material, that normally are randomly oriented resulting in a net zero magnetic field. As current is applied to the windings, those domains line up, greatly magnifying the resulting magnetic field. Eventually most of the sub-domains are aligned, at which point you don’t get any more magnifying effect from the iron core. In this region, the stator is said to be “saturated”. You can read about it in much more depth on wikipedia or with even more detail here. The end result is a curve of magnetic field versus applied current that looks something like this:
To date, moteus assumes that you are operating completely in the “Linear” region, where the torque and current are linearly related.
Operating in the Rotation Region
To operate in the “rotation” region I ended up using the following formula:
Where is the input current, is the motor torque constant, , and are three constants that I fit to measured torque data. With some approximations, this can be calculated relatively efficiently on the STM32G4 that drives the moteus controller, adding only a microsecond to the overall loop time to go in both directions.
I then ran a torque sweep with my load-cell fixture from before, and sure enough, the input and output torque match much better now across the entire range of operation, despite the fact that the phase current needs to start growing very rapidly near the top end:
My initial design torque for the qdd100 was a little over 17 Nm. However, when I did my first ground truth torque testing, I found that some servos had a lower maximum torque than I had specified. While working to diagnose those, I built a qdd100 that used an alternate stator winding of 105Kv instead of the 135Kv that are in all the beta units. The Kv rating of a stator describes how fast the motor will spin for a given applied voltage. If you assume the same amount of copper mass of wiring, a lower Kv will mean that there are thinner wires that wrap around the stator more turns (or fewer wires in parallel). A higher Kv will have thicker wires with fewer overall turns.
On paper, if you assume a perfect controller, this shouldn’t make much of a difference. The same input power should be required for the same output torque. The only differences should come into play once you have a controller with either a limited maximum voltage or a limited maximum current. The higher Kv motor will be able to go faster given a fixed maximum voltage, and the lower Kv motor will have more torque for a given maximum current.
I wanted to verify that this was true as part of my evaluation to identify the cause of my decreased torque, so I used a slightly upgraded torque testing fixture:
For now, I rigged up the world’s cheapest load cell from amazon to a Nucleo configured to report the load in grams over the serial port. I also wired up my Chroma power supply over USB using the linux USBTMC driver. With those two things hooked up, I was able to run tests that sweeped across torque commands, while recording output torque, phase current, and input power.
At higher torques, the input power was pretty sensitive to the temperature of the windings — hotter windings increased the resistance, which increased the power required to achieve a given phase current, thus my plot isn’t perfect as it was grabbed over several different runs. For the highest power samples I couldn’t use my Chroma, as it is limited to around 600W. Thus those samples don’t record the input power.
Plotting the input power vs output torque on the same chart shows that indeed, modulo some measurement error, they are the same for the two stators:
So, this experiment reaffirmed my understanding of stator magnetics and confirmed that the stator winding was not the cause of my decreased torque.
Note, both of those methods involve being tethered to a computer, which makes it hard to be mobile. As a possibly short term solution to this problem, I went ahead and got a bluetooth “gaming” controller for my phone (non-affiliate amazon link):
I first wrote about the very very simple web UI for the quad A1 some time ago. That UI served its purpose, although it was largely inscrutable to anyone but myself, as the primary data display was a giant wall of unformatted JSON which filled most of the page. It was also pretty easy to accidentally pick the wrong mode, cause the robot to jump instead of walk, or cut power to everything.
Clearly I’m not going to win any design awards… but since all the styling is done with CSS, it should be not too hard to make something that looks arbitrarily nice without a whole lot of effort. As a bonus, I also added some minimal keyboard bindings for movement, so the joystick isn’t required if you don’t care about precise or aggressive maneuvers.