Three calibrations, not one

“Calibrating a joint” covers three different jobs, done at different times with different tools. Mixing them up is the most common source of confusion when a robot comes back from repair and walks badly.

• Commutation offset. A brushless joint motor is driven by field-oriented control, which needs to know where the rotor magnets sit relative to the stator windings. The drive learns the angle between the motor encoder’s zero and the rotor’s electrical zero. Wrong offset: less torque per amp, more heat, or a motor that will not turn at all.
• Joint zero. The controller needs to know which encoder reading corresponds to, say, a straight knee. This is the offset between the sensor and the mechanical reference of the link. Wrong offset: every posture the policy commands is shifted by that angle.
• Kinematic (geometric) calibration. Even with perfect joint zeros, link lengths and axis directions differ slightly from the CAD model. Whole-body calibration fits those parameters, plus residual joint offsets, from measured poses. Wrong model: the hand or foot ends up somewhere other than where the robot believes it is.

The commutation offset: the drive’s first job

The servo drive cannot know how the encoder magnet was glued to the rotor. Open-source drives make the measurement explicit. On the ODrive, the offset calibration first energises one phase to pull the rotor to a known electrical angle, then turns the motor open-loop forwards and backwards while summing encoder positions, and stores the average as the offset. Scanning in both directions averages out friction. The motor has to turn during this step, which is why a robot that runs it at power-up twitches every joint.

Because the offset is a property of how the parts were assembled, it only has to be measured once if the drive can trust its encoder after a power cycle. With an absolute motor encoder the saved offset applies immediately. With an incremental encoder and an index pin, the drive must turn the motor until it finds the index before it can apply the stored value. Production humanoid actuators generally do this step at the factory and store the result in the joint.

Joint zero and the gear-ratio ambiguity

The harder problem is the joint’s own zero, and the reducer is what makes it hard. A motor-side encoder turns N times for every turn of the joint. A single-turn reading, or an index pulse, therefore matches N different joint angles. The Open Dynamic Robot Initiative’s Solo actuator shows the effect plainly: with a 9:1 reduction and an incremental motor encoder, “the encoder will see 9 index pulses per joint revolution”. Its calibration routine expects the operator to place the legs near the zero pose by hand; the software then snaps to the closest index.

There are three ways out. The first is to move the joint to something known at every start: a hard stop, a limit switch or a hand-placed pose. Industrial arms and many research robots do this, but a humanoid lying on a pallet or hanging from a gantry cannot always sweep its joints safely. The second is a battery-backed multi-turn encoder that keeps counting while the robot is off. Harmonic Drive’s multi-turn ABS option works this way and needs a battery for it.

The third, now common in humanoid actuators, is a second absolute encoder on the output. Harmonic Drive’s dual-absolute FHA-Mini carries a 14-bit single-turn encoder on each side of the gear. At 100:1 the motor encoder resolves 1,638,400 counts per output turn while the output encoder’s 16,384 counts settle which turn the motor is on, and the company says no battery is needed within 360° of output rotation. A teardown of the Unitree G1 knee actuator also reports dual encoders. A related trick, the nonius or vernier track, puts two magnetic tracks with one pole pair difference on one ring; the phase difference between them gives absolute position, and Hutchinson pairs such rings with iC-Haus iC-MU sensors.

An absolute sensor removes homing, but not the zero itself. Someone still has to tell the joint which reading means “straight”, and that offset has to follow the joint through every repair. One Unitree G1 owner who fitted a replacement wrist reported joint angles about 90° off the expected range: the new part was apparently built for the other side of the robot. Swapping an actuator without updating its zero is a quick way to give a robot a new and wrong posture.

What a small offset costs at the hand and foot

A zero error of θ at a joint moves anything a distance L from its axis by about L·θ, with θ in radians. That makes small angles expensive. A 0.1° offset at the shoulder of a 0.6 m arm puts the hand about 1 mm off; 1° puts it 10.5 mm off. Errors in several joints of a chain add or cancel depending on posture, which is why the result often looks like a robot that is accurate in one pose and sloppy in another.

Whole-body calibration: measured results

Humanoids cannot easily be bolted into a metrology rig, so researchers use constraints the robot can create itself. Katsu Yamane at Disney Research proposed in 2011 estimating joint-sensor offsets from the constraint that both feet lie flat on the floor, using only joint angles and link orientation sensors. PAL Robotics’ TALOS, a 32-joint, 95 kg humanoid, was calibrated in 2025 by pressing its gripper onto a single table plane with force control: 31 recorded postures, about two minutes each, cut the mean vertical error from 9.19 mm to 2.88 mm and roll and pitch errors from about 1° to about 0.3°. On unseen postures the improvement was about 2.3 times. The identified rotational parameters fell within ±1.5°, the largest being joint offsets, mainly in the arms.

A September 2026 paper goes further and uses nothing but the robot’s joint encoders and pelvis IMU in static double-support stance, fitting a 12-value leg offset vector so that the transform between the feet stays constant across postures. On two humanoids it reduced held-out foot-height residuals from 4.26 to 2.20 mm and from 8.03 to 1.43 mm. The authors are frank about the limits: offsets along the chain of parallel pitch axes are weakly observable and depend on a prior.

What to ask about calibration

• Start-up motion. Does the robot need to move its joints, or be placed in a pose, before it knows where they are? That decides whether it can start safely on a stand, on the floor or in a crowded cell.
• Encoder layout. Motor only, motor plus output, or multi-turn with battery. Dual absolute encoders also let the drive measure reducer wind-up, which links calibration to torsional stiffness.
• Where offsets live. In the actuator, in the robot computer, or both. Offsets stored in the joint travel with it; offsets stored centrally must be updated when a joint is replaced.
• Field self-check. Whether the robot can re-estimate offsets from its own sensors, as in the stance-based method above, or needs a technician and a fixture.

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