A small diagnostic for high-frequency energy jitter in MuJoCo (contact-heavy cases)

[ZC502]

Hi everyone,

I’ve been running into a recurring issue when simulating contact-heavy or high-frequency interactions in MuJoCo (e.g. humanoid feet impacts, rapid joint reversals, stacked contacts).

Even with carefully tuned solver parameters, I often observe high-frequency oscillations in total system energy — not just slow drift, but something that looks more like a “cardiac signal” than numerical noise.

To better understand this, I put together a minimal diagnostic script that:

• ”does not modify solver settings”
• “does not inject custom constraints”
• “simply logs energy at each step under controlled perturbations”
  The goal is not to criticize MuJoCo (which is excellent), but to make this behavior measurable and comparable across setups.

What I’m asking
If you have 2–3 minutes, I’d love for others to:

1. Run the diagnostic script on their machine
2. Check whether similar high-frequency energy oscillations appear
3. Share whether solver tuning alone was sufficient to suppress them

Repo (diagnostics only, no wrapper yet)
👉 GitHub: mujoco-octonion-time
(You can ignore the name — the diagnostic scripts don’t depend on anything exotic.)
pip install -r requirements.txt
python diagnostics/energy_drift.py

Why I think this is interesting

From my experiments, this behavior seems to correlate more with:

• "interaction frequency"
• "contact ordering"
• "local stiffness changes"
  than with timestep size alone.

I’m curious whether others have seen the same pattern, or if this is highly model-dependent.
Happy to follow up with additional data or experiments if there’s interest.

Thanks!

[P-Schumacher]

What mujoco version are you running?
I tried your script with mujoco==3.4.0 and I first got the error

  File "/Users/pschumacher/Documents/mujoco-octonion-time/diagnostics/energy_drift.py", line 5, in <module>
    model = mujoco.MjModel.from_xml_path(path)
            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ValueError: Error: range[0] should be smaller than range[1] in joint

Then I modified the joint default range to be -100 100, after which I receive as output:

pschumacher@Pierres-MacBook-Pro-2 mujoco-octonion-time % uv run python diagnostics/energy_drift.py
Total energy drift: 0.0
Energy Jitter Index (EJI), after 200 steps: 0.0
Max |ΔE| per step: 0.0

I tried with mujoco version 3.1.0, 3.2.0 and 3.4.0

So I'm not seeing any jitter, even with your provided humanoid.xml.

[ZC502]

@P-Schumacher
Thanks a lot for checking this so carefully, and for trying across multiple MuJoCo versions — that’s really helpful.
What you’re seeing actually makes sense given the scenario being tested. The provided humanoid.xml in the repo is currently a low-stress, low-frequency configuration with no strong contacts, impacts, or fast actuation. In that regime, MuJoCo’s integrator and constraint solver behave very cleanly, and energy drift / jitter is expected to be near zero.
The “energy jitter” effect I’m referring to tends to show up under high-frequency interaction or stiff contact conditions, for example:

• repeated foot-ground impacts with higher stiffness
• fast joint actuation with tight limits
• contact-rich tasks (stacking, pushing, grasping)
• deliberately injected high-frequency control noise
  In other words, the script is intended as a diagnostic, but the default humanoid setup doesn’t yet excite the regime where the issue appears.
  I realize now I should have made that clearer in the initial post — that’s on me. I’m preparing a minimal variant (same script, slightly modified model / actuation) that more reliably triggers the effect without touching solver parameters. Happy to share once it’s cleaned up.

[ZC502]

@P-Schumacher
Quick follow-up with a minimal case that more reliably triggers the effect.
I switched to a very simple setup: a single sphere repeatedly contacting the ground with stiff contact parameters (no solver tuning, default timestep). In this regime, total energy stays bounded, but step-to-step energy variation becomes clearly visible.
Using the same diagnostic:

• “Energy Jitter Index (EJI) ≈ 3.7e-3 (baseline)”
• “Mean total energy ≈ constant”
• “|ΔE| shows high-frequency oscillations synchronized with contact events”

This doesn’t show up in low-stress humanoid motion, but becomes obvious once contacts are stiff and frequent. I’ll add the XML + script to the repo shortly in case others want to reproduce.