Randomizing inertia

67 · Domain randomization

Five balanced paddles on vertical hinges, held at zero by a torsional drive and released from 57 degrees. At 1 s the script scales each world's body_inertia by a sampled factor at fixed mass. The oscillation period grows with the square root of the inertia, matching 2 pi sqrt(I / ke). The second run uses update_mass_matrix_interval=10000, longer than the whole run, and skips the notification: the mass matrix keeps the old inertia, and all five paddles swing with the unrandomized period.

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0.00 s

What to look at

With notify: the measured periods spread from 0.76 s to 1.41 s, as predicted.
With interval 10000 and no notify: all five swing together with the unrandomized 0.89 s period.

Key parameter

update_mass_matrix_interval

With an interval above 1 the mass matrix is rebuilt only every few steps; a BODY_INERTIAL_PROPERTIES notification forces a rebuild on the next step.

Try changing

Scale only the hinge-axis component of body_inertia.
Add the notify call to the second run and confirm it matches the first.

Concept

When Steel sees a randomized value

What it is

Notify with the matching flags after changing these model arrays so Steel refreshes all derived data consistently. Some inputs are cached until notification; mass, inertia and drive gains can also be picked up by periodic mass-matrix rebuilds, so their behavior without notification depends on update_mass_matrix_interval.

In this scene

With interval 10000 and no notify: all five swing together with the unrandomized 0.89 s period.

Considerations

Cost: Call only, default solver, six-link chain and four boxes per world, 1024 worlds (1.12 ms per collide + step): BODY_INERTIAL_PROPERTIES 31 µs (17 µs captured). Flags measured one at a time; combined calls and feature validation can cost more. Body-inertial and joint-DOF notifications also request a mass-matrix refresh.
Graph capture: These flags can be captured in a reset graph. Kinematic-flag changes, sleeping, and shape flags with sparse factors plus restitution run eagerly; captured calls skip some value checks.
Interactions: world_mask limits which worlds lose their warm start; cached data is refreshed for every world.
Use it when: Rotational dynamics that matter more than mass, such as wheels or paddles.

The script

cd tutorials && python dr_inertia.py prints each variant's final metric; --record out.json also writes the replay. Every tutorial imports replay.py from the same folder.

dr_inertia.py
replay.py

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Inertia randomization: per-world body_inertia at fixed mass changes the natural frequency."""

import math

import newton
import numpy as np
import warp as wp
from newton.solvers import SolverSteel

from replay import Recorder

DT = 1.0 / 240.0
SUBSTEPS = 8
WORLDS = 5
KE = 0.5  # torsional spring (a drive to 0): omega = sqrt(KE / I)


def tf(x, y, z):
    return wp.transform((x, y, z), wp.quat_identity())


def build():
    paddle = newton.ModelBuilder()
    link = paddle.add_link(xform=tf(0.0, 0.0, 0.5))
    paddle.add_shape_box(
        link, hx=0.12, hy=0.02, hz=0.02
    )  # hinged at its center, so no gravity torque
    paddle.add_shape_sphere(link, xform=tf(0.12, 0.0, 0.0), radius=0.04)
    paddle.add_shape_sphere(link, xform=tf(-0.12, 0.0, 0.0), radius=0.04)
    j = paddle.add_joint_revolute(
        -1, link, axis=newton.Axis.Z, parent_xform=tf(0.0, 0.0, 0.5), target_ke=KE
    )
    paddle.add_articulation([j])
    paddle.joint_q[-1] = 1.0
    builder = newton.ModelBuilder()
    builder.replicate(paddle, WORLDS, spacing=(0.0, 0.4, 0.0))
    return builder.finalize()


def simulate(rec, label, scale, notify, **options):
    model = build()
    solver = SolverSteel(model, **options)
    state_0, state_1, control = model.state(), model.state(), model.control()
    newton.eval_fk(model, model.joint_q, model.joint_qd, state_0)

    run = rec.variant(label, model)
    for frame in range(rec.frames(5.0)):
        if frame == rec.fps:  # randomize at 1 s, as an episode reset would
            s = scale[model.body_world.numpy()][:, None, None]
            model.body_inertia.assign(model.body_inertia.numpy() * s)
            model.body_inv_inertia.assign(model.body_inv_inertia.numpy() / s)
            if notify:
                solver.notify_model_changed(newton.ModelFlags.BODY_INERTIAL_PROPERTIES)
        q = np.degrees(state_0.joint_q.numpy())
        run.frame(state_0, **{f"inertia x{v:.2f}": a for v, a in zip(scale, q)})
        for _ in range(SUBSTEPS):
            solver.step(state_0, state_1, control, None, DT)
            state_0, state_1 = state_1, state_0
    run.check(solver)


if __name__ == "__main__":
    rng = np.random.default_rng(2)
    scale = np.sort(rng.uniform(0.5, 3.0, WORLDS))
    rec = Recorder()
    simulate(rec, "inertia scaled per world + notify", scale, True)
    # the run is shorter than the interval, so without notify the mass matrix keeps the old inertia
    simulate(
        rec,
        "update_mass_matrix_interval=10000, no notify",
        scale,
        False,
        update_mass_matrix_interval=10000,
    )
    rec.save()
    i_z = build().body_inertia.numpy()[0, 2, 2]
    print("expected period, s:", np.round(2.0 * math.pi * np.sqrt(scale * i_z / KE), 2))

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Record Steel tutorial runs as replay JSON for the tutorials page, or print a summary.

Every tutorial imports this module. ``python NN_name.py`` runs the variants and prints
the final metric of each; ``--record out.json`` also writes body poses, shapes and metric
series that the page replays in 3D.
"""

import argparse
import base64
import json
import os
import subprocess
import sys
import time

import newton
import numpy as np
import warp as wp

from source_hash import source_sha256

_RENDERED_TYPES = {
    newton.GeoType.PLANE,
    newton.GeoType.SPHERE,
    newton.GeoType.CAPSULE,
    newton.GeoType.ELLIPSOID,
    newton.GeoType.CYLINDER,
    newton.GeoType.BOX,
    newton.GeoType.MESH,
    newton.GeoType.CONE,
    newton.GeoType.CONVEX_MESH,
}


class Recorder:
    """Collect the variants of one tutorial; ``fps`` is the replay frame rate."""

    def __init__(self, fps: int = 30):
        parser = argparse.ArgumentParser()
        parser.add_argument(
            "--record", metavar="OUT.json", help="write a replay file for the tutorials page"
        )
        parser.add_argument("--device", default=None, help="Warp device, for example cuda:0")
        self.args = parser.parse_args()
        if self.args.device:
            wp.set_device(self.args.device)
        self.fps = fps
        self.script = os.path.abspath(sys.argv[0])
        self.variants: list[Variant] = []

    def frames(self, seconds: float) -> int:
        """Number of replay frames in ``seconds``, including the first."""
        return int(round(seconds * self.fps)) + 1

    def variant(
        self,
        label: str,
        model: newton.Model,
        *,
        ghost: bool = False,
        slot: int | None = None,
        scene: str | None = None,
    ) -> "Variant":
        """Start one run; ``ghost`` overlays run ``slot``, ``scene`` groups runs for charts."""
        variant = Variant(label, model, self.fps, ghost, slot, scene)
        self.variants.append(variant)
        return variant

    def save(self) -> None:
        """Print a summary and, with ``--record``, write the replay file."""
        for variant in self.variants:
            last = variant.metrics[-1] if variant.metrics else {}
            flag = "  (rows dropped)" if variant.overflow else ""
            print(f"{variant.label:<48} {json.dumps(last)}  {variant.wall:.2f} s{flag}")
        if not self.args.record:
            return
        source_sha = source_sha256(self.script)
        doc = {
            "script": os.path.basename(self.script),
            "script_sha256": source_sha,
            "newton_commit": _newton_commit(),
            "newton_version": newton.__version__,
            "warp_version": wp.config.version,
            "gpu": wp.get_device().name,
            "fps": self.fps,
            "variants": [v.to_json() for v in self.variants],
        }
        with open(self.args.record, "w") as f:
            json.dump(doc, f, separators=(",", ":"))
        print(f"wrote {self.args.record}")


class Variant:
    """One recorded run: a pose per frame for every body, plus named metric values."""

    def __init__(self, label, model, fps, ghost, slot, scene):
        self.label, self.model, self.fps, self.ghost, self.slot = label, model, fps, ghost, slot
        self.scene = scene
        self.poses: list[np.ndarray] = []
        self.metrics: list[dict] = []
        self.awake: list[list[int]] = []
        self.particles: list[np.ndarray] = []
        self.overflow = False
        self.start = time.perf_counter()
        self.wall = 0.0

    def frame(self, state: newton.State, awake=None, particles=None, **metrics) -> None:
        """Record ``state.body_q``, optional awake flags, particle positions and metric values."""
        self.poses.append(state.body_q.numpy().astype(np.float32).copy())
        if particles is not None:
            self.particles.append(particles.numpy().astype(np.float32).copy())
        self.metrics.append({k: _round(v) for k, v in metrics.items()})
        if awake is not None:
            self.awake.append([int(x) for x in awake.numpy()])
        self.wall = time.perf_counter() - self.start

    def check(self, solver) -> None:
        """Note whether the solver dropped rows; call once after the run."""
        try:
            solver.check_constraint_capacity()
        except RuntimeError:
            self.overflow = True

    def to_json(self) -> dict:
        poses = (
            np.stack(self.poses)
            if self.poses
            else np.zeros((0, self.model.body_count, 7), np.float32)
        )
        return {
            "label": self.label,
            "fps": self.fps,
            "ghost": self.ghost,
            "slot": self.slot,
            "scene": self.scene,
            "bodies": int(self.model.body_count),
            "frames": int(poses.shape[0]),
            "poses": base64.b64encode(poses.astype(np.float32).tobytes()).decode(),
            "shapes": _shape_table(self.model),
            "metric": self.metrics,
            "awake": self.awake or None,
            "particles": self._particles_json(),
            "wall_s": round(self.wall, 3),
            "overflow": self.overflow,
        }

    def _particles_json(self):
        if not self.particles:
            return None
        frames = np.stack(self.particles)
        tris = self.model.tri_indices
        radius = self.model.particle_radius.numpy()
        return {
            "count": int(frames.shape[1]),
            "frames": base64.b64encode(frames.astype(np.float32).tobytes()).decode(),
            "radius": round(float(radius.mean()), 5) if radius.size else 0.0,
            "tris": [int(v) for v in tris.numpy().reshape(-1)]
            if tris is not None and tris.shape[0]
            else None,
        }


def _shape_table(model):
    types = model.shape_type.numpy()
    scales = model.shape_scale.numpy()
    xforms = model.shape_transform.numpy()
    bodies = model.shape_body.numpy()
    flags = model.shape_flags.numpy()
    shapes = []
    for i, t in enumerate(types):
        if int(t) not in _RENDERED_TYPES or not flags[i] & int(newton.ShapeFlags.VISIBLE):
            continue
        shape = {
            "b": int(bodies[i]),
            "t": int(t),
            "s": [round(float(v), 5) for v in scales[i]],
            "x": [round(float(v), 6) for v in xforms[i]],
        }
        if int(t) in (newton.GeoType.MESH, newton.GeoType.CONVEX_MESH):
            mesh = model.shape_source[i]
            shape["v"] = [round(float(v), 5) for v in np.asarray(mesh.vertices).reshape(-1)]
            shape["i"] = [int(v) for v in np.asarray(mesh.indices).reshape(-1)]
        shapes.append(shape)
    return shapes


def _round(value):
    value = float(value)
    return round(value, 5) if np.isfinite(value) else None


def _newton_commit():
    if os.environ.get("NEWTON_COMMIT"):
        return os.environ["NEWTON_COMMIT"]
    try:
        root = os.path.dirname(os.path.dirname(newton.__file__))
        return subprocess.check_output(["git", "-C", root, "rev-parse", "HEAD"], text=True).strip()
    except (OSError, subprocess.CalledProcessError):
        return None

Recorded with SolverSteel on Newton 1.9.0.dev0, Warp 1.19.0, NVIDIA RTX PRO 6000 Blackwell Server Edition. Replays read the state back every frame, so they are not a speed benchmark. Script · page text

Steel docs and tutorials are licensed under Apache-2.0. Third-party notices. "Skild", "Skild AI" and the Skild logo are trademarks of Skild AI and are not licensed under Apache-2.0.