Robot arms in factories: repeatability vs accuracy

TL;DR:

• Accuracy is how close the arm gets to the point you commanded. Repeatability is how close it gets to the same point each time.

• An arm can be very repeatable and still inaccurate, because a steady offset is a bias, not scatter.

• Calibration can remove bias, but it cannot remove random scatter, which is why repeatability is the spec that matters most for taught points.

A robot arm on an assembly line puts a small part into a hole thousands of times a day. Two questions decide whether that works. Does the arm go where it is told? And does it go to the same place every time? They sound like one question, but they are not.

Definitions

Accuracy (pose accuracy) is the difference between the commanded position and the average position the arm actually reaches. Repeatability is how tightly the actual positions cluster when the arm is sent to the same target again and again. The standard test methods for both are set out in an international standard for industrial robots, ISO 9283.

A dartboard picture helps. Darts all landing close together but far from the bullseye are repeatable and inaccurate. Darts spread all around the bullseye are accurate on average and not repeatable. You want both, but they have different causes.

Worked example: an arm returning to the same spot

Command an arm to x = 500.00 mm along one axis, five times. Each time, move it away and back, and measure where the tool tip actually ends up with a dial gauge or a measuring system. The readings are 500.12, 500.08, 500.10, 500.14 and 500.11 mm.

1. Mean: (500.12 + 500.08 + 500.10 + 500.14 + 500.11) / 5 = 2500.55 / 5 = 500.11 mm.

2. Accuracy error (bias): 500.11 − 500.00 = 0.11 mm too far.

3. Deviations from the mean: +0.01, −0.03, −0.01, +0.03, 0.00.

4. Sample standard deviation: squares sum to 0.0001 + 0.0009 + 0.0001 + 0.0009 + 0 = 0.0020; divide by n − 1 = 4 to get 0.0005; the square root is 0.022 mm.

5. Range of the scatter: 500.14 − 500.08 = 0.06 mm.

So this arm is off by 0.11 mm on average (its accuracy error), but its scatter is only about 0.02 mm to 0.06 mm (its repeatability). The bias is five times bigger than the standard deviation (0.11 / 0.022 = 5). Real specs are usually given as a worst-case band such as plus or minus some number of millimeters, so check how the manufacturer defines theirs.

Calibration

Accuracy errors come from things that are the same each time: link lengths slightly different from the design, joint zero positions set a little off, a tool mounted slightly crooked, a base that sags. Calibration measures the arm at many positions and adjusts the robot's kinematic model so these systematic errors are corrected.

In our example, subtracting the 0.11 mm offset would bring the mean to 500.00 mm. The scatter of about 0.02 mm stays. After calibration the accuracy is limited by the repeatability, because random error is what is left.

Why repeatability matters most

Most factory arms are taught their points. A person guides the arm to the hole, saves the position, and the arm goes back there. Any steady offset between the model and reality is built into the taught point itself, because the arm was moved by hand to the correct spot as seen. Only the scatter shows up later. So for taught points, repeatability is the number that decides if the part fits.

Accuracy matters more when positions are calculated rather than taught: for instance, when a camera finds a part and the arm computes where to go, or when a program written offline is loaded onto a different robot. Then calibration, including the camera and the tool, is essential.

Where it goes wrong

• Speed and payload. Specs are measured under stated conditions. Faster moves and heavier loads increase scatter.

• Warm-up. Motors and gearboxes expand as they heat up, which shifts positions through the day.

• Approach direction. Backlash in gears means the arm may land differently coming from the left than from the right.

• Reach. Errors usually grow when the arm is stretched far out.

• Confusing the terms. A brochure's single number may be one or the other. Read the definition.

Working around arms: An industrial arm moves quickly and with enough force to crush. Stay outside the guarded area while it runs, use the lockout and stop procedures for your site, and never reach into a cell without making the robot safe first.

How real robots use it

Factories pair robots with fixtures that guide parts to within a known tolerance, and choose arms whose repeatability is several times tighter than the tolerance they need. Sensors such as cameras add a correction on top. Because people may share the area, safety is a separate topic, covered in collaborative robots and working safely near people.

Try it yourself

Use a small hobby arm or even a pencil on a jig. Move to a marked point ten times, from different directions, and mark the landing spot each time on tape. Measure the cluster's size (repeatability) and the distance from its centre to the target (accuracy). Then shift your reference by that distance and see the error disappear while the cluster stays the same size.

Frequently asked questions

Can software improve repeatability?

Only a little. Repeatability is mostly set by the mechanics: gears, bearings, stiffness. Software can reduce the effects of known causes such as temperature.

Is accuracy always worse than repeatability?

For typical industrial arms, yes. Uncalibrated, they can miss by much more than their scatter, which is why calibration is a real step.