Minimizing Energy Loss in High-Impact Simulations with Joint Limits in MuJoCo

[caba0404]

Intro

Hello everyone,

I’m using MuJoCo for high-energy impact simulations with tensegrity robots

My setup

My current setup is:
• solver: Newton
• integrator: RK4
• cone: elliptic
• solimp.d: 0.999
• codim: 1

My question

For contacts and joint limits, I’ve been tuning the solref parameter to reduce energy loss. Specifically, I’m using:
solref="-1/dt^2 0"

where dt is my simulation timestep. While this helps reduce energy dissipation, I still observe significant energy loss during joint limit engagement and ground impacts.

Has anyone found a robust configuration for \texttt{solref} that minimizes energy loss, especially during impacts and joint limit collisions? Are there additional parameters---such as increasing \texttt{solimp.mindist}, tuning \texttt{imp_ratio}, or increasing solver iterations---that can help achieve near-conservative behavior?

The following plot illustrates the energy behavior during simulation. As shown, energy losses become evident when the joint limits are active. Moreover, there is a noticeable drop in energy at around \textbf{0.7 seconds}, which corresponds to the moment the robot impacts the ground.

Total_Energy.pdf

In addition, I am wondering if there is a way to explicitly define the stiffness to prevent energy loss. I noticed that using lower stiffness values (\texttt{k}) results in higher energy dissipation, particularly during joint limit activation. However, when \texttt{k} is set too high, I observe an unphysical increase in total energy, especially at the moment of ground impact. This suggests a numerical instability or energy injection caused by an overly stiff contact model. It appears there is a delicate trade-off when selecting the appropriate stiffness value: too low leads to damping-like energy loss, and too high can result in energy gain. Any recommendations on how to balance this stiffness setting effectively to achieve near-conservative dynamics would be greatly appreciated.

Any insights or recommendations would be greatly appreciated!

Thanks in advance,
Agustin

XLM Code

• I searched the latest documentation thoroughly before posting.
• I searched previous Issues and Discussions, I am certain this has not been raised before.

[v-r-a]

Hi,
I am a MuJoCo user. The following might help you.

You could get better help if you shared the model you are working with. Here are some suggestions (mostly regarding contact parameters, which might be useful for the constraint model in general)

1. You are right to use the direct format for defining solref. I would suggest you to take a look at the contact settings from the Newton's cradle example.
2. Set priority to 1 in the geometry where you are experimenting with contact parameters. (So that you have complete control over what you're experimenting.)
3. Penetrations (/joint overshoot) during impact may not go far beyond $d_{width}$. The constraint model may not work as intended for penetrations beyond that (it becomes too soft).
4. I have a half-baked notebook to experiment and understand the effects of various contact parameters quickly. See if it helps you.

[caba0404]

Hello,

I’m working with a very simple MuJoCo model that reproduces the issue I’m studying. It consists of three masses connected by tendons. All masses are constrained to move only along the z-axis. The main goal is to evaluate how contact events (particularly when one mass hits the floor) affect the system’s energy.

I’ve noticed that for certain values of K in solref="-K 0" (where K is large and negative), the energy before and after the contact is nearly conserved. However, when K is too small or too large in magnitude, the energy after impact becomes significantly different, indicating either damping-like loss or numerical instability.

I also observed that decreasing the timestep helps improve energy conservation. In particular, there seems to be a sweet spot where the combination of solref stiffness and timestep leads to nearly perfect conservation during contacts.

My question is:
How can I estimate a suitable value of K in solref="-K 0" and the appropriate timestep dt for a general system to ensure energy is conserved across impacts?

I’m including the current XML below for reference (excerpted for clarity). Any insight into the interplay between solref, timestep, and energy stability would be greatly appreciated.

energy_evolution_k1e+05.pdf
energy_evolution_k1e+09.pdf
energy_evolution_k1e+12.pdf

z_positions_k1e+05.pdf
z_positions_k1e+09.pdf
z_positions_k1e+12.pdf

XLM code:

[caba0404]

[caba0404]

[caba0404]

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[v-r-a]

I guess something is wrong with the formatting in the XML. You can use ``` (backtick) to start and end code.

So, do I assume that the simulations corresponding to all three plots are done at a fair value of timestep? Trying to understand how you chose the simulation timestep. I would choose a suitable value below (one order or half order) which the quantities of interest don't change much, i.e., look for convergence in numerical simulation. But you chose it based on the simulation that had the best energy conservation (for given solref)?

I would also check the maximum penetration, say fraction of dwidth.