Alessio Quaglino
ea230a950c
This CL replaces the post-hoc implicit flex correction (`flexInterp_cgsolve`) with a **linearly-implicit effective metric** `M̃ = M + (h² + h·damping)·K` carried by the CG constraint solver itself. Contact/friction forces and implicit flex elasticity are now computed against one consistent metric, instead of the solver seeing `M` and a post-solve correction changing `qacc` behind its back. Gate (unchanged semantics): `solver="CG"` + implicit/implicitfast integrator + pyramidal cones + flex stiffness present. Newton and PGS are untouched. `solver="CG"` remains the user-facing contract — the factorization is an implementation detail of the preconditioner. ### What's in the metric - **mjData `efm_*`** (arena, efc-like lifetime/skip semantics; built in `mj_fwdPosition`, value-refreshed in `mj_fwdVelocity`): the per-step stiffness CSR `efm_B_*`, its reverse-Cholesky factor `efm_dofid` + `efm_L_*` (nested-dissection ordered, separators-first for the reverse factorization), and the smooth-force shift `efm_c = h·K·qvel`. - **`mjd_flexStiff_assemble`** now assembles stretch (Gauss–Newton), standard dim-2 bending, and — via the cached corotated stiffness `d->flexelem_krot` — interp stiffness (all node bodies on simple sliders: point Jacobian is I₃, `flex_centered` not required; fixed nodes drop like pins) into one dof-level CSR. `mjd_effMulAdd`/`mjd_effSolve` apply the metric, with matrix-free operator fallbacks where assembly does not apply. - **mjModel `efm0_*`** (`nefm0dof`/`nefm0L`): the constant part of the metric factor — currently the dim-2 bending factor, computed once in `mj_setConst` — so bending-only models pay zero per-step factorization cost. Naming mirrors mjData's `efm_*` with the standard `0`-suffix (reference/constant) idiom, and is deliberately not bending-specific: future constant contributors extend it without renames. - The solver consumes the metric through pre-shifted `qfrc_smooth` and the metric products `Ma`/`Mv`/`Mgrad`; `qacc_smooth` becomes the unconstrained minimizer of the implicit dynamics, which makes the no-constraint shortcut and the warmstart choice consistent by construction. - **`mj_inverse` adds `B·qacc − c`**, making inverse dynamics discrete-consistent with the gated forward dynamics — exact, since the gated path has no qDeriv term (new test `ForwardTest.GatedFlexInverseConsistency`). ### Performance All numbers: ms/step over the same 2000-step window, models as shipped on each side (old code with the old model settings vs this CL with the new ones). The new solver path activates on exactly two shipped models — the ponchos, the only flex models that need an implicit integrator (poncho on Euler degenerates to >200 ms/step). For them, this CL trades speed for consistency: the implicit bending solve now runs inside every solver iteration, where the contact solve can see the stiffness, instead of once after the solve. Solver iterations drop because the curvature is visible, but each iteration pays for the implicit solve: | model | before | after | solver iters/step | |---|---|---|---| | poncho | 2.47 | 3.30 (1.33×) | 16.8 → 11.8 | | poncho_edgeequality | 1.96 | 2.72 (1.39×) | 13.2 → 10.0 | What that price buys: contact forces consistent with the implicit elasticity (previously the post-hoc correction changed `qacc` after the constraint solve), discrete-consistent inverse dynamics, and the removal of the post-hoc special case from the integration path. Raising poncho's timestep from 2 to 5 ms leaves its per-step cost nearly flat, so the consistency price can be recovered by taking fewer steps where accuracy allows. Every other flex model was measured stable on Euler at its shipped timestep and switches to it (these models predate the post-hoc integrator; implicit was never load-bearing for them). They end up equal or faster than before: bunny_multicell 0.47 → 0.40, trampoline 0.28 → 0.25, plate 1.02 → 0.99, pancake 0.34 → 0.33. Finally, the per-step factorization makes configurations practical that the old code could only integrate explicitly: implicit stretch elasticity (`elastic2d="stretch"`/`"both"`, dim-3 solids) and factorized interp stiffness. No before/after exists for these — stock has no implicit treatment of stretch at all. ### Behavior changes - With the post-hoc correction deleted, interp/bending models running `solver="Newton"` (or elliptic cones, or islands) now integrate flex elasticity **explicitly** (previously: post-hoc implicit). Affects e.g. `gripper_trilinear` (stable, and faster, but different semantics). Follow-up options: Newton-side metric support, or a documented fallback. - With the gate on, `mj_forward` outputs are timestep-dependent for gated models (they answer the linearly-implicit discrete problem); `qacc_smooth` and `mj_inverse` change accordingly. Non-gated models are bit-identical (full suite green throughout). ### Validation - 1737/1737 tests, including new: `FlexStretchDerivatives` (FD-validated GN operator), `FlexStiffAssemble`/`FlexStiffAssembleInterp` (CSR ≡ operators), `GatedFlexInverseConsistency` (fails pre-change), equivalence tests vs the old post-hoc treatment (bending matches to 2e-11). - Fingerprint discipline throughout: bending-only models bit-exact across every refactor; permutation/kernel changes verified iteration-identical. ### Known follow-ups (not in this CL) 3×3-block sparse Cholesky kernel (the numeric factorization is index-bound; projected ~3× on the factor); mjModel persistence of the factor's symbolic pattern (rest-pose ND makes sizes compile-time); the general effective-metric mode (all solvers, all PSD-safe force classes, behind an enable flag). PiperOrigin-RevId: 948561856 Change-Id: I8b8e32ebd0428042af71647d0470d10773bf6daf
MuJoCo Python Bindings
This package is the canonical Python bindings for the MuJoCo physics engine. These bindings are developed and maintained by Google DeepMind, and is kept up-to-date with the latest developments in MuJoCo itself.
The mujoco package provides direct access to raw MuJoCo C API functions,
structs, constants, and enumerations. Structs are provided as Python classes,
with Pythonic initialization and deletion semantics.
It is not the aim of this package to provide fully fledged
scene/environment/game authoring API, as there are already a number of existing
packages that do this well. However, this package does provide a number of
lower-level components outside of MuJoCo itself that are likely to be useful to
most users who access MuJoCo through Python. For example, the egl, glfw, and
osmesa subpackages contain utilities for setting up OpenGL rendering contexts.
Installation
The recommended way to install this package is via PyPI:
pip install mujoco
A copy of the MuJoCo library is provided as part of the package and does not need to be downloaded or installed separately.
Source
IMPORTANT: Building from source is only necessary if you are modifying the Python bindings (or are trying to run on exceptionally old Linux systems). If that's not the case, then we recommend installing the prebuilt binaries from PyPI.
If you need to build the Python bindings from source, please consult the documentation.
Usage
Once installed, the package can be imported via import mujoco. Please consult
our documentation for
further detail on the package's API.
We recommend going through the tutorial notebook which covers the basics of
MuJoCo using Python:
Versioning
The major.minor.micro portion of the version number matches the version of
MuJoCo that the bindings provide. Optionally, if we release updates to the
Python bindings themselves that target the same version of MuJoCo, a .postN
suffix is added, for example 2.1.2.post2 represents the second update to the
bindings for MuJoCo 2.1.2.
License and Disclaimer
Copyright 2022 DeepMind Technologies Limited
MuJoCo and its Python bindings are licensed under the Apache License, Version 2.0. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0.
This is not an officially supported Google product.