Engineering · Measurement

You cannot control
what you cannot measure.

Direct drive removes the mechanism between the motor and the load. That only helps if the controller knows where the shaft is to a finer degree than the motion you are trying to produce. Every leg of the PDK carries a 21-bit absolute encoder, and the drive reads it on every cycle.

Two encoder rings side by side: a 14-bit ring with 16,384 positions per revolution and a 21-bit ring with 2,097,152, joined by an arrow marked 128×.

The number

2,097,152 positions,
one revolution.

Twenty-one bits gives 2 to the 21st distinct absolute positions per turn — 2,097,152 of them. Divide a full revolution by that and each step is 0.0001716 of a degree. The arithmetic is the whole claim; there is nothing to take on trust.


For scale

What would a coarser encoder give you?

A 14-bit encoder is a common and perfectly reasonable part. Setting the two side by side is the clearest way to show what the extra bits are for — each bit doubles the count.

21-bit and 14-bit absolute encoders compared by divisions per revolution
EncoderDivisions per revolutionAngular step
21-bit (PDK)2,097,1520.0001716°
14-bit (baseline)16,3840.022°
Ratio128×128× finer
How we know this
  • 21-bit figures and the 14-bit baseline ARK engineering record · arithmetic shown on this page
  • Both rows are pure arithmetic from the bit depth and can be recomputed 2^21 and 2^14 divided into 360°

The 14-bit row is a comparison baseline, not a competitor's specification. We are not naming a product or claiming anyone ships one.

Absolute, not incremental

Why absolute encoders and not incremental?

An incremental encoder counts steps from wherever it happened to be switched on. An absolute encoder reports a position. On a six-legged platform carrying a person, that difference is a safety property, not a convenience.

No homing sequence

There is no start-up routine that drives each leg to a limit to find zero. The pose is known at power-on, which means the machine can refuse to move if the pose it reads is not one it should be in.

Position survives a fault

Lose power mid-motion and an incremental system loses its reference entirely. An absolute encoder gives you the same answer when it comes back, so recovery starts from a known state rather than a search.

The part, named

Each motor shaft carries an MT6835 magnetic rotary encoder, sampled once per 125 µs drive cycle over SPI — the same cycle that closes the current and position loops. We name the part because a specification you cannot look up is not really a specification.

The boundary

Resolution is not accuracy, and neither is precision.

Twenty-one bits describes how finely the encoder can divide a revolution. It does not describe how well that division corresponds to the true angle, which is a different property with its own error sources — mounting eccentricity, magnetic field distortion, thermal drift in the sensing element. A very high-resolution encoder mounted badly reports a very precise wrong answer.

Nor does encoder resolution propagate to the platform on its own. It reaches the platform only if nothing mechanical sits in between to absorb it, which is the argument on the direct drive page, and only if the control loop is fast enough to act on it, which is the argument on field-oriented control. The three claims only mean anything together.

You may see a figure of more than 100 kHz attached to encoder sampling for this platform. That is a capability figure for the sensing element, not the rate this system reads it at. This system reads it 8,000 times a second, once per drive cycle — an internal drive-loop rate, not a telemetry rate — and that is the number that describes the machine.

Questions

What people ask about the encoder.

How many positions does a 21-bit encoder have?

Twenty-one bits gives 2,097,152 distinct absolute positions in one revolution. Divide a full turn by that and each step is 0.0001716 of a degree. Both figures are arithmetic from the bit depth — 2 to the 21st, then 360 divided by the result — so there is nothing in either of them to take on trust.

Does higher resolution mean higher accuracy?

No, and precision is a third thing again. Resolution is how finely the encoder divides a revolution. Accuracy is how closely that division corresponds to the true angle, and it has its own error sources — mounting eccentricity, magnetic field distortion, thermal drift in the sensing element. Precision is whether you get the same answer twice. A very high-resolution encoder mounted badly reports a very precise wrong answer, which is why we publish the resolution and the rate it is read at, and do not dress either one up as accuracy.

Do I have to home it every time I power it on?

No. There is no start-up routine that drives each leg to a limit to find zero, so nothing has to move before the platform is usable. It reads its pose at power-on, and that is also what lets it refuse to move when the pose it reads is not one it should be in. On a machine that carries a person, a start-up hunt for zero is a movement nobody asked for.

Can a person feel two million positions?

Not as two million of anything. What the resolution sets is the floor: a movement finer than one encoder step is one the drive cannot measure, so it is not a movement the loop can hold, and it never reaches the platform at all. Whether what does reach the platform reaches the driver depends on two further things — nothing mechanical sitting in between to absorb it, which is the argument on the direct drive page, and a control loop fast enough to act on it, which is the argument on field-oriented control. Those three together are the reason the number is worth publishing. What any one person notices in any one title is not something we can measure for them.

Keep reading

Field-oriented control

What the drive does with the encoder reading, 8,000 times a second (internal drive loop), on every motor.

Backlash

Why fine measurement at the shaft is wasted if there is a mechanism after it.

Direct drive

The architecture that lets the encoder's resolution reach the platform at all.

Every build starts with this platform. The PDK + ARK Ecosystem finishes it — racing chassis, wheelbase, wheel, load-cell pedals and button box, $8,499.99.

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