Citizen Robot

Repeatability

Repeatability is not accuracy

An arm quoted at ±0.03 mm will return to the same wrong place all day. The spec sheet measures self-agreement; the world demands something else entirely.

Hands using a dial thickness gauge to measure a small metal piece
Plate 1An arm quoted at ±0.03 mm will return to the same wrong place all day. Repeatability is agreement with itself; accuracy is agreement with the world, and almost every published figure is the first one.Photo: Sandin Redzo / Pexels

§ 1The distinction the brochure skips

Repeatability and accuracy sound like synonyms for the same virtue — both concern how precisely a robot arrives where it is supposed to arrive. But they measure different things, and confusing them costs money in the kind of way that only reveals itself once parts are being assembled.

Repeatability is the arm's ability to return to the same pose when commanded to return to the same pose. Teach it a point, command it back ten thousand times, and measure the scatter of where the tool centre point actually lands. A robot quoted at ±0.03 mm means that scatter is within a 0.06 mm diameter sphere: an impressive figure, and one that says nothing about where that sphere is sitting in space.

Accuracy is agreement with the world — whether the point the controller believes it has reached is the point that genuinely exists at those coordinates in your workshop. A robot arm is a long kinematic chain of joints and links, and every small deviation in the geometry of that chain — a link slightly shorter than nominal, a joint axis not quite perpendicular to where the drawing says it should be, a base not perfectly level — accumulates. The tool tip ends up not where the mathematical model predicts, but somewhere nearby. In a moderately well-calibrated arm, that error might be a millimetre or two. In an uncalibrated arm on a slightly uneven floor plate, it can be several millimetres. The repeatability figure does not move.

Extreme close-up of a metal gear's teeth meshing with a threaded shaft component
Plate 2Lost motion enters here. A gear train stiff enough to be accurate is also stiff enough to transmit every shock the tool takes.Photo: Tima Miroshnichenko / Pexels

This is why the published number is almost always the repeatability figure, not the accuracy figure. Repeatability is stable, testable in a factory, and reproducible across units. Accuracy depends on installation conditions, thermal state, payload, and the quality of the kinematic model loaded into the controller — variables no manufacturer can control once the machine leaves the dock.

§ 2Why the figures diverge

The kinematic model is the controller's internal description of the arm: how long each link is, where each axis sits relative to the last, what the joint angle truly means in terms of physical rotation. Real arms deviate from their nominal geometry at the level of tenths of a millimetre and fractions of a degree. These deviations are small, but a six-axis arm is six sequential transformations; errors compound through each one.

Calibration — measuring the arm against a known external artefact and fitting a corrected kinematic model — can bring accuracy much closer to the repeatability limit. But calibration takes time, requires equipment, and drifts. Thermal expansion alone is a significant source of accuracy error: steel grows as the cell warms over the first hour of a shift, changing the effective length of each link and nudging the tool tip away from where a cold-start calibration placed it. Repeatability is largely unaffected, because the arm is consistently wrong in the same direction.

Payload adds another layer. A mass at the wrist introduces gravity-induced deflection along the links and compliance in the gearboxes. If the arm was calibrated unloaded and then given a heavy gripper, the accuracy degrades accordingly. Repeatability may still be excellent — the deflection is consistent and reproducible — but the tool tip has shifted away from where the model predicts.

The joint resolution of the motor encoders also matters. Each axis is driven through a large gear reduction, which multiplies angular position into linear displacement at the tip. A tiny quantisation error in the encoder, multiplied through the kinematics, places a floor under achievable accuracy that no calibration can get below. Repeatability sits comfortably above this floor; accuracy has to contend with it.

A handheld teach pendant mounted on a factory wall near a yellow robotic arm
Plate 3Teaching by hand hides the accuracy error: the programmer drives the arm to the physical feature, and the taught point carries whatever bias the model has.

§ 3How the figure is actually measured

The ISO 9283 standard defines how repeatability is measured: the arm is commanded to a single reference pose from multiple approach directions, many times, and the cloud of actual arrival positions is characterised. The radius of the sphere that encloses most of those points — with a defined statistical confidence — is the repeatability figure.

What that test does not do is command the arm to a point defined by external coordinates and measure the error against them. It does not check whether the arm's internal model of space matches the physical space around it. It measures scatter, not trueness. A mechanical engineer would recognise this as the difference between precision and accuracy in measurement system terms: a gauge can be repeatable and biased simultaneously, and so can a robot arm.

The test is also run at a single location in the workspace, at rated speed, at a single temperature, without a payload. Each of those conditions is chosen for test convenience, not for production resemblance. What the figure excludes matters here: the number on the data sheet is a best case, and production conditions are rarely best-case conditions.

The taught positions absorb the accuracy error.

§ 4When repeatability is the right measure

For most robot applications, repeatability is exactly what you need to care about. Pick-and-place, welding along a taught path, machine loading, palletising — in all of these, the arm is taught positions by a programmer driving it to the actual physical locations. The taught positions absorb the accuracy error. If the arm is biased by 1.5 mm at a given location, the programmer simply teaches the point 1.5 mm from where a CAD model would place it. The arm then returns to that point with ±0.03 mm consistency, which is the number you actually need.

Accuracy becomes the operative limit when positions are generated from data rather than taught by hand: offline programming from a CAD model, vision-guided correction to a reference frame, or coordinating two arms that need to agree on a shared workspace. In offline programming, the controller receives coordinates it has never physically visited. The arm goes to where its kinematic model says those coordinates are — and if the model is off, the motion is off. There is no human-taught correction to absorb the bias.

Similarly, if a fixture is moved and the offset is applied mathematically rather than re-taught, accuracy determines whether that offset is correctly executed. The arm's kinematic model has to faithfully represent geometry that nobody has physically demonstrated to it.

Yellow industrial robotic arm mounted behind a bolted steel mounting plate on the floor
Plate 4Dowels locate, bolts clamp. Replace an arm without dowels and every taught point moves.

The practical upshot: an arm with excellent repeatability and poor accuracy is a machine that does exactly what it remembers, but only approximates what it is told. For most factory work, that is sufficient, and the teach-pendant workflow is specifically designed to work around the accuracy limitation. Push outside that workflow — into offline programming, into sensor-guided corrections, into tight coordination across multiple arms — and accuracy stops being the overlooked cousin and becomes the binding constraint.

The spec sheet will still quote repeatability.