PYTHON · NUMPY

Sim-to-Real by Domain Randomization

Choose a controller that survives the reality gap by optimizing worst-case behavior across a randomized ensemble of robot models, the recipe behind 84-93% zero-shot transfer.

01Challenge

A gain tuned on one nominal model looks great in that simulation and falls over on the real robot, whose mass and friction are different. Instead, pick the gain with the best worst-case error across a randomized ensemble, and it holds across all of them.

Predict firstYou train a walking policy in one perfectly-tuned simulator, then deploy it to the real robot. It most often…

02Model

The magical result in modern locomotion, in Tedrake's words, is that a policy trained across randomized simulations walks over almost anything in the real world. The reason a controller tuned on a single model fails is that the real robot is never exactly the model: its mass is off, the floor's friction varies, the actuators lag. Domain randomization trains and validates across a spread of these parameters and keeps what works in the worst case, not the average. It is why 2025 humanoid pipelines report 84 to 93 percent zero-shot sim-to-real transfer. You are choosing the design that is robust, not the one that is merely optimal on paper.

03Guided practice

1. See the failure. k_nominal = 1.0 is tuned for m=1, f=0 and has a large worst-case error over the ensemble. 2. Optimize worst-case. For each candidate k in ks, compute the MAX error over the ensemble; pick the k with the smallest max. 3. Set k_robust to that argmin. 4. Compare. The robust gain's worst-case error must beat the nominal one and stay under 0.5.

04Feedback

PASS WHEN PASS when your robust gain has a smaller worst-case error than the nominal gain and stays under 0.5: robustness by design.

If your run fails, check:

No improvement: `k_robust` is still `k_nominal`. Search `ks` and pick the one minimizing the max ensemble error.
Worst-case still high: make sure you take the MAX error over the ensemble for each k, then the MIN of those.
Close but above 0.5: the argmin over the given `ks` range does clear 0.5; check you evaluate the full ensemble.

05Retrieve & space

Why does a controller tuned on one model fail to transfer to the real robot? (the real robot differs; the gap).
What does domain randomization optimize, and why worst-case over average? (robustness across the spread).
What sim-to-real transfer rates do 2025 humanoid pipelines report? (roughly 84-93% zero-shot).

06Mastery & project

Select a controller by worst-case performance across a randomized ensemble: the design move that crosses the reality gap.

The transfer discipline that makes the Forge learn-to-walk policy survive outside its training simulation.

GO FURTHER · THE LIVE PLAYGROUND

Run a learned policy in Forge ↗ — the on-device learned walker you would want to transfer to hardware

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PYTHON · NUMPY

Sim-to-Real by Domain Randomization

A toy plant with randomized mass and friction. Pick the gain that minimizes worst-case error across the ensemble.

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