how to simulate ball bouncing with (0 < restitution < 1) in mjx/generalized pipeline? #657

zzhixin · 2026-01-05T11:27:50Z

zzhixin
Jan 5, 2026

In the official brax basics tutorial, a ball bouncing with 0.8 restitution is illustrated, where the pipeline is set as positional. However in generalized or mjx pipeline, the same code can't reproduce the bouncing effect, it just not bounce at all.

I understand the behaviour is expected as in mjx(generalized) pipeline, the elasticity paramters is not respected. Instead, the mujoco docs points out that resitution should be simulated by parameters solref. For example, resitution 1.0 can be achieve by solref="-1000 0". But how about a medium resitution like 0.8?

I tried some combs but none of it behaviour well. The "best" one is below (from chatgpt) with extra parameters like solimp. But the result divergence in the third bounce.

Click to expand

import numpy as np 
import jax
from jax import numpy as jnp, random
import brax
from brax.io import mjcf
import matplotlib.pyplot as plt
import matplotlib as mpl
import pprint


ball = mjcf.loads("""
<mujoco>
    <option timestep="0.005" integrator="RK4" cone="elliptic"/>
    <default>
        <geom solref="-10000 -2190" />
    </default>
    <worldbody>
        <geom size="40 40 40" type="plane"/>
        <body pos="0 0 3">
            <joint type="free"/>
            <geom size="0.5" type="sphere"/>
        </body>
    </worldbody>
</mujoco>
""")


def visualize(ax, pos, alpha=1.):
    for p, pn in zip(pos, list(pos[1:]) + [None]):
        ax.add_patch(mpl.patches.Circle(xy=(p[0], p[2]), radius=0.5, fill=False, color=(0, 0, 0, alpha)))
        if pn is not None:
            ax.add_line(mpl.patches.Line2D([p[0], p[2]], [pn[0], pn[2]], color=(0, 1, 0, alpha)))
        ax.set_aspect(1.)


# from brax.positional import pipeline
from brax.mjx import pipeline

elasticity = 0.1
ball_velocity = 0.7

ball = ball.replace(elasticity=jnp.array([elasticity]*ball.ngeom))

qd = jnp.array([ball_velocity, 0, 0, 0, 0, 0,])
state = jax.jit(pipeline.init)(ball, ball.init_q, qd)

fig, ax = plt.subplots()
ax.set_xlim([-5., 5.])
ax.set_ylim([0., 4.])

for t in range(1000):
    if t % 10 == 0:
        visualize(ax, state.x.pos, t / 1000.)
    state = jax.jit(pipeline.step)(ball, state, None)

plt.title("tossing a ball")

zzhixin · 2026-01-05T13:19:38Z

zzhixin
Jan 5, 2026
Author

Finally, I found this parameters combination resembling restitution 0.85 well
<geom solref="-10000 -5"/> with mjx:

elasticity=0.85 with positional:

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