Spin and rolling friction

06 · Contact and friction

A ball spinning at 25 rad/s about the vertical and a ball rolling at 1 m/s. A ball touches the ground at one point, so sliding friction alone stops neither. The per-shape attribute steel:condim uses MuJoCo's convention: 3 is sliding only, 4 adds a spin row bounded by μ_torsional times the normal load, and 6 also adds a rolling pair bounded by μ_rolling.

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What to look at

condim 3: both balls keep going.
condim 4: the spinning ball stops in about a second; the rolling ball keeps rolling.
condim 6: both stop.

Key parameter

steel:condim

Per shape, 3, 4 or 6. Applies to free-body contacts; register it with SolverSteel.register_custom_attributes(builder) and fill model.steel.condim.

Try changing

Raise mu_rolling to 0.02 and watch the rolling ball stop sooner.
Give only the ground condim 6: a contact takes the larger coefficient of its two shapes.

Concept

Spin and rolling friction

What it is

Sliding friction acts at the contact point, so it cannot stop a ball spinning about the contact normal or rolling without slip. condim 4 adds a spin row bounded by μ_torsional·N, and condim 6 adds two rolling rows bounded by μ_rolling·N, with N the patch's pooled normal load.

In this scene

With condim 3 the spinning ball still turns at 19.5 rad/s after 5 s; condim 4 stops it in about 0.6 s, and condim 6 also stops the rolling ball in about 2 s.

Considerations

Cost: Up to six rows per contact instead of three; raise free_body_constraint_max if constraint_overflow reports drops.
Interactions: Read only for free bodies; articulated links use steel:min_torsional_patch_radius. Contacts share a patch only if their coefficients match.
Use it when: Balls, wheels and pucks that should come to rest. Keep condim 3 for boxes.

The script

cd tutorials && python 06_spin_rolling_friction.py prints each variant's final metric; --record out.json also writes the replay. Every tutorial imports replay.py from the same folder.

06_spin_rolling_friction.py
replay.py

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

"""Spin and rolling friction on free bodies with the per-shape steel:condim attribute."""

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


def build(condim):
    builder = newton.ModelBuilder()
    SolverSteel.register_custom_attributes(builder)
    cfg = newton.ModelBuilder.ShapeConfig(
        density=800.0, mu=0.6, mu_torsional=0.01, mu_rolling=0.004
    )
    builder.add_ground_plane(cfg=cfg)
    spinner = builder.add_body(xform=wp.transform((0.0, 0.0, 0.08), wp.quat_identity()))
    builder.add_shape_sphere(spinner, radius=0.08, cfg=cfg)
    marker = newton.ModelBuilder.ShapeConfig(density=0.0, has_shape_collision=False)
    builder.add_shape_box(
        spinner,
        xform=wp.transform((0.0, 0.0, 0.08), wp.quat_identity()),
        hx=0.06,
        hy=0.008,
        hz=0.004,
        cfg=marker,
    )
    roller = builder.add_body(xform=wp.transform((-0.6, 0.35, 0.08), wp.quat_identity()))
    builder.add_shape_sphere(roller, radius=0.08, cfg=cfg)
    model = builder.finalize()
    model.steel.condim.fill_(condim)
    # free-joint velocity is (linear, angular): spin one ball, roll the other
    model.joint_qd.assign(np.array([0, 0, 0, 0, 0, 25.0, 1.0, 0, 0, 0, 0, 0], dtype=np.float32))
    return model


def simulate(rec, label, condim):
    model = build(condim)
    solver = SolverSteel(model)
    pipeline = newton.CollisionPipeline(model)
    contacts = pipeline.contacts()
    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 _ in range(rec.frames(5.0)):
        qd = state_0.body_qd.numpy()
        run.frame(state_0, spin=qd[0, 5], roll=np.linalg.norm(qd[1, :3]))
        for _ in range(SUBSTEPS):
            pipeline.collide(state_0, contacts)
            solver.step(state_0, state_1, control, contacts, DT)
            state_0, state_1 = state_1, state_0
    run.check(solver)


if __name__ == "__main__":
    rec = Recorder()
    simulate(rec, "condim 3 (sliding only, default)", 3)
    simulate(rec, "condim 4 (+ spin)", 4)
    simulate(rec, "condim 6 (+ spin + rolling)", 6)
    rec.save()

# 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.