Achieving Stable and Elastic Jumps in MuJoCo Simulations

[caba0404]

Intro

Hi!

I am a graduate student, I use MuJoCo for my research on Tensegrity robots.

My setup

I am utilizing Python to generate XML files and execute MuJoCo simulations seamlessly.

My question

Hi everyone,

I’m a graduate student conducting research on Tensegrity robots, and I’ve been using MuJoCo extensively for my simulations. Recently, I observed some unexpected behavior in my simulations and wanted to seek advice from the community.

When my Tensegrity robot structure interacts with the ground (specifically during jumps), I noticed that the solref parameters in the floor geom have a significant impact on the behavior of the structure. While I understand that this makes sense given the dynamics of the system, I’ve encountered an issue that’s puzzling me.

When plotting the total energy of the system over time, I see that it first decreases and then it increases at certain moments. This energy behavior sometimes leads to numerical instabilities in the simulation, forcing me to opt for non-elastic jumps to stabilize the system. However, my goal is to simulate jumps that are as elastic as possible without causing these instabilities.

Here are the steps I’ve tried so far:

1. Adjusting the solref parameters to balance softness and restitution.
2. Refining the timestep in the simulation.
3. Exploring different solimp settings to improve contact stability.
4. Modifying damping properties of my structure. I understand that this can cause non-elastic jumps, but I would like to achieve an elastic response from the ground, or as stiff as possible.
5. Changing the size of the body that interacts with the ground, which I have noted tends to mitigate the issues with jumps.

I have also noted that when I change the size of the body that interact with the ground issue in the jumps tend to be mitigated

Despite these efforts, the energy behavior remains inconsistent, and I’m unsure how to proceed to achieve stable, elastic jumps.

I’d greatly appreciate it if anyone could provide insights or recommendations on how to fine-tune the simulation to address this issue. Specifically:

• Are there particular solref or solimp configurations that work well for similar scenarios?
• Is there a known method to ensure energy consistency in MuJoCo simulations during high-impact events?
• Could there be other parameters (e.g., solver settings or friction coefficients) that I should focus on?

Thank you in advance for your help!

Here are some example figures to illustrate my point. After contact with the floor, the energy decreases and then increases. This phenomenon is observed in a case where I used a solref value of [4e-2, 1] to make the effect more noticeable.

In the second figure, the displacements are shown in millimeters.

[yuvaltassa]

To clarify, you want perfect elasticity? I.e. no energy loss at contact?

[caba0404]

I am using the command data.energy.copy() in my simulations.

[yuvaltassa]

Okay, this is the problem. Currently MuJoCo doesn't add elastic energy in contacts to those values. So what you are seeing is not energy dropping, but rather energy being converted to elastic energy within the contact which is invisible to you, and then you see it come back as kinetic energy after the bounce. I've never thought about this too deeply, but this "dark energy" (😜) should be something like

sum(efc_KBIP[:, 0] * efc_pos[:])

I.e. the contact's spring constant times the penetration. Maybe I'm missing a minus sign. I'll need to think about it more, but why don't you try that and let me know what you see?

For reference, this is all that is being computed at the moment.

[caba0404]

Thanks! I suspected that something like this might be happening. How could I minimize this displacement? When my structure receives this energy back, especially during high-impact events, it causes numerical issues and the simulation diverges.

[yuvaltassa]

Minimize what displacement? The change in energy? I just told you.

energy[0] ± sum(efc_KBIP[:, 0] * efc_pos[:])

[caba0404]

Yes, I want the floor to be as stiff as (floor penetration = 0 meters) possible because the displacement you mentioned directly affects the behavior of my tensegrity robot. I followed your advice, and here are the energy results I obtained during an impact of the robot with the ground. I also noticed that the robot penetrates the floor by about 1 meter for a solref value of [4e-2, 1]. I understand that by adjusting these values, the penetration will decrease. However, at some point, I end up with the graph presented in the third figure.

energy[0] ± sum(efc_KBIP[:, 0] * efc_pos[:])

Floor penetration

solref value of [4e-4, 1]
Floor penetration is about 0.2 m

Energy

[yuvaltassa]

Sorry, that's obviously wrong. I meant

energy[0] += 0.5 * sum(efc_KBIP[:, 0] * efc_pos[:]**2)

[yuvaltassa]

Tried my own recommendation, it's almost right, but not quite. I need to think about it more.
In any case, for this to work make sure you use elliptic cones.
Here's my attempt below, you can see that it improves thing quite a bit, but not to the point of correct energy conservation.

xml = """
<mujoco>
  <option integrator="RK4" cone="elliptic">
    <flag energy="enable"/>
  </option>

  <worldbody>
    <light pos="0 0 2"/>
    <geom type="plane" size="5 5 .1"/>
    <body pos="0 0 1">
      <geom size=".2" mass="1" priority="1" solref="-1000 0" solimp="0.99 0.99 0.01"/>
      <freejoint/>
    </body>
  </worldbody>
</mujoco>
"""
model = mujoco.MjModel.from_xml_string(xml)
data = mujoco.MjData(model)

TIME = []
POTENTIAL = []
KINETIC = []

while data.time < 2.25:
  mujoco.mj_step(model, data)
  TIME.append(data.time)
  p = data.energy[0]
  # elastic energy in contact
  p += 0.5 * np.sum(data.efc_KBIP[:, 0] * data.efc_pos ** 2)
  POTENTIAL.append(p)

  KINETIC.append(data.energy[1])


POTENTIAL = np.asarray(POTENTIAL)
KINETIC = np.asarray(KINETIC)
ENERGY = np.vstack((POTENTIAL, KINETIC, POTENTIAL+KINETIC)).T


plt.plot(np.asarray(TIME), ENERGY)
plt.legend(['potential', 'kinetic', 'total'])