PYTHON · NUMPY

The contact limit is a published field

Read ISO/TS 15066:2016 Annex A as an instrument rather than as an adjective, and turn its energy limits into an admissible approach speed for a 1 kg and a 20 kg effective robot mass.

01Challenge

Convert the 0.11 J face limit into a speed a policy could act on, then check your model against the standard's own published speed pair for the chest.

Predict firstThe face limit is 0.11 J and the pelvis limit is 2.6 J, a 23.6x span in joules. How wide is that span in admissible approach speed?

02Model

Safety in robot learning is usually carried by an adjective. Gentle contact. Soft policies. Compliant behaviour. ISO/TS 15066:2016 Annex A is what that adjective looks like after somebody measured it. Table A.2 states maximum permissible peak pressure at quasi-static contact for 29 body localisations, from 110 N/cm2 at the temple to 300 N/cm2 at the dominant index-finger pad, and quasi-static force for twelve body regions, from 65 N at the face to 220 N at thigh and knee, with a transient multiplier of 2 everywhere except head and face, where transient contact is not permitted at all. Table A.3 gives the body a spring-mass model, with effective spring constants running from 10 N/mm at the abdomen to 150 N/mm at the skull. Table A.4 states maximum transferable energy per region, 0.11 J at the face to 2.6 J at the pelvis. The protocol travels with the numbers: 100 subjects, pain-onset threshold, third quartile, a 1.4 by 1.4 cm metal stamp with a 2 mm edge radius, pressure averaged at 1 mm2 resolution. Once the limit is stated in joules an approach speed follows, because the energy a moving robot transfers into a body region is half the reduced mass of the pair times the square of the relative speed. Table A.5 runs that arithmetic and publishes the result for the chest: 1500 mm/s at 1 kg of effective robot mass falling to 400 mm/s at 20 kg, a 3.75x contraction over a twenty-fold mass range. The certified action set is therefore a function of the robot's own configuration, and this review located no action representation in any of the five regions that encodes it. All of this is in English, freely retrievable, and ten years old. What it lacks is readers. This review located no policy-learning paper in any of the five regions treating the 0.11 J face limit as a constraint on a learned contact policy, having searched all five in the native language. That is why gap 11 closes from the standards regime rather than from the robotics literature, why it stands at 78 degrees of ninety, and why its binding constraint is regulatory.

03Guided practice

1. Read the field as a table. Twenty-nine pressure localisations, twelve force regions, a spring-mass body model and an energy limit per region. Print the spans. The energy field runs 23.6x from face to pelvis, and the pressure field only 2.73x from temple to index-finger pad, so the regions disagree far more about energy than about pressure.

2. Turn joules into millimetres per second. The model is E = 0.5 mu v squared, with mu the reduced mass of the pair, 1/mu = 1/m_body + 1/m_robot. Solve for v.

3. Take the honest bound. You do not need a per-region body mass to get a usable answer. Because mu is always smaller than the robot's effective mass, sqrt(2E/m_robot) is admissible whatever the body region's effective mass turns out to be. Compute it at 1 kg and at 20 kg for the face and the pelvis.

4. Check the model against the standard. ISO/TS 15066 Table A.5 publishes two chest speeds, 1500 mm/s at 1 kg and 400 mm/s at 20 kg. Two published points, two unknowns in the model. Solve for the effective body mass and the energy limit and see whether the two points agree with each other. They do, to floating-point noise, which tells you the model in step 2 is the one the standard used.

5. Write the constraint. Clip a commanded Cartesian speed to the cap for the body region being approached. It is four lines. Then note what this review looked for and did not locate: any policy-learning paper in any of the five regions treating that 0.11 J face limit as a constraint on a learned contact policy.

04Feedback

PASS WHEN PASS when the second cell prints a face speed cap of 469.0 mm/s at 1 kg of effective robot mass and 104.9 mm/s at 20 kg, and the third cell recovers an effective body mass of 44.0 kg with both published chest points returning the same energy limit of 1.100 J at a residual below 1e-9 J.

If your run fails, check:

If the recovered body mass comes out negative, check the sign of the solve. With a = r squared times m_lo, the algebra is m_body = m_hi (m_lo - a) / (a - m_hi), and both factors are negative at these numbers.
If the two chest points disagree on the energy limit by more than floating-point noise, you are probably using m_robot in place of the reduced mass. The reduced mass is what makes 1500 and 400 mm/s consistent with one number.
The 1.10 J chest limit and the 44.0 kg body mass are derived here, not quoted. Report them as recovered from the two published speeds, which is a different grade from the 0.11 J and 2.6 J endpoints the standard states directly.

05Retrieve & space

How many body localisations carry a peak-pressure limit in ISO/TS 15066 Table A.2, and how many body regions carry a force limit?
What is the maximum transferable energy at the face, and at the pelvis?
Which two body regions are excluded from the transient multiplier of 2, and what applies to them instead?
Why is a 23.6x span in the energy field only a 4.86x span in admissible approach speed?
What did this review look for, in five languages, and not locate regarding the 0.11 J face limit?

06Mastery & project

You can state a contact limit as a number with its protocol, convert an energy limit into an admissible approach speed through the reduced mass, and say what the same limit costs a 1 kg arm against a 20 kg one. You can also say why the certified action set is a function of robot state, and report the absence honestly: this review located no policy-learning paper in any of the five regions treating the face limit as a constraint on a learned contact policy.

Take a policy you have trained or can run and add the four-line clip to its action path, with the body-region energy limit and the arm's effective mass as arguments. Log how often the clip binds over a rollout. If it never binds, your commanded speeds were already inside the limit and you have a number to report. If it binds constantly, you have located the gap between what your policy asks for and what the certification field allows.

GO FURTHER · THE LIVE PLAYGROUND

TR-2026-35, section 6 ↗ · Contact, friction and deformables, with every figure in this lesson carried beside the grade it holds and the region it came from.
ISO/TS 15066:2016, Annex A ↗ · Tables A.2 to A.5 in full: the pressure field, the force field, the spring-mass body model and the worked transient speed limits the third lab cell checks against.
DGUV FB HM-080 ↗ · The German planning document that renders Annex A and adds the buildable phantom: damping material, thickness and spring constant per body region, and a 1 kHz measurement chain with a 100 Hz Butterworth filter.
ISO/PAS 5672:2023 ↗ · Test methods for measuring forces and pressures in human-robot contacts, which is the measurement side of the same field.
Contact impedance sim ↗ · Play with stiffness and mass on the contact directly, so the 10 to 150 N/mm range in Table A.3 stops being an abstraction.

← Three bands, one real number Friction, assumed everywhere and estimated nowhere →

PYTHON · NUMPY

The contact limit is a published field

Read the field, convert its energy limits into admissible approach speeds, and check your model against the standard's own published speed pair.

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