PYTHON · NUMPY

Four bands and a missing axis

Rebuild the French randomisation ladder from 0 out of 20 to 93 per cent, price the marginal gain of every rung, and audit which physical channels the ladder never varies.

01Challenge

A sim-to-real tax quoted as one number hides the experiment that produced it. Build the ladder underneath, then check whether the tax is bigger than one real episode.

Predict firstThe four rungs run 0.0, 56.5, 70.0 and 93.0 per cent. Which band adds the least?

02Model

The French ladder is one policy family evaluated four times on a UR5, over seven tasks at twenty real episodes each, with one more class of randomisation switched on at every rung. Two-dimensional image augmentation alone scores 0 out of 20 on every task. Adding 1,203 ambientCG textures on robot, table, wall and floor gives 11.3 out of 20, or 56.5 per cent. Adding lighting and object colour gives 14.0 out of 20, or 70.0 per cent. Adding camera parameters gives 18.6 out of 20, or 93.0 per cent. Reading the rungs in order tells you where the transfer was bought. Reading the band definitions tells you what was never varied: every rung is an appearance channel, and mass, friction, latency and actuator terms appear nowhere in the ladder. Against 98.34 per cent for the same policy family over 250 simulation episodes per task, the tax at the top is 5.34 percentage points, and twenty real trials per task resolves to 5 pp per task, which is the size of the quantity being reported. So the ladder is strong evidence about appearance and silent about dynamics, and its headline tax sits at the grain of its own instrument.

03Guided practice

1. Enter the four rungs as the paper states them. Mean successful episodes out of 20, over 7 tasks: 0.0, 11.3, 14.0, 18.6. Convert each to a percentage.

2. Difference the rungs. The marginal gain of a band is its rate minus the rate of the rung below it. Rank the three bands that add anything.

3. Price the tax. Take 98.34 per cent as the simulation figure, over 250 simulation episodes per task, and subtract the top of the ladder.

4. Ask what the instrument can see. One episode out of 20 is 5 pp of a task. Divide the tax by that number and read the ratio.

5. Tag the bands. Write out every quantity each band randomises and label it appearance or dynamics. Count the bands that touch a dynamics channel.

6. Hold the task fixed instead. The same source moves one nuisance variable at a time over 20 trials per cell. Compare the randomisation-trained policy against the real-data-trained one, cell by cell.

04Feedback

PASS WHEN PASS when the ladder prints 0.0, 56.5, 70.0 and 93.0 per cent with marginal gains of +56.5, +13.5 and +23.0 pp, the tax prints as 5.34 pp against a per-task resolution of 5.00 pp for a ratio of 1.07, the dynamics-band count prints as 0 of 4, and the two nuisance-sweep means print as 17.3/20 and 13.2/20.

If your run fails, check:

If a marginal gain comes out negative, you are differencing against the wrong rung. Each band is cumulative: it adds to the one below rather than replacing it.
If the tax does not land on 5.34 pp, check that you are subtracting 93.0 from 98.34 and not from 100.
The ranking is worth pausing on. The middle band adds 13.5 pp and the top band adds 23.0 pp, so the rungs do not fall away in order, and a ladder truncated after three bands would have understated what randomisation can buy.

05Retrieve & space

What real success rate does two-dimensional image augmentation alone reach on the seven UR5 tasks?
Which of the four bands adds the most, and which adds the least?
The tax at the top of the ladder is 5.34 pp. What is one real episode worth, expressed per task, and what does that do to the tax?
Name the physical channels that appear in none of the four bands.
In the nuisance sweep with task, robot and policy held fixed, which single cell separates the two policies most widely?

06Mastery & project

You can take a published transfer number, ask for the ladder underneath it, price each rung, and state which physical channels the randomisation never touched.

Take a randomisation configuration you actually use, or the shipped vendor configuration quoted in the paper, and tag every band as appearance or dynamics. Then write one line saying what your best real success rate is evidence about, and one line saying what it is silent on.

GO FURTHER · THE LIVE PLAYGROUND

Sim to Real: The Road to Physical Agency (TR-2026-35) ↗ · Section 5 carries the randomisation-band table for five regions, with the grade on every row and a note that reward-denominated rows are not commensurable with success-rate rows.
Robust Visual Sim-to-Real Transfer for Robotic Manipulation ↗ · The published form of the ladder. The band definitions travel with it, including the 1,203 texture assets and the light-source distance of 1.0 to 3.0 m from the workspace centre.
Learning Visuomotor Policies for Robotic Manipulation (HAL tel-05535510) ↗ · The thesis behind it. Table 3.3 is the ladder you rebuild in cell 1 and Table 3.4 is the held-fixed nuisance sweep in cell 4.

← Angle is the integral of angular velocity, so say so in the loss Three bands, one real number →

PYTHON · NUMPY

Four bands and a missing axis

Four rungs, one tax, and a channel audit. Standard library only, and every figure is the paper's own.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you