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Mujoco_WASM/src/engine/engine_forward.h
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Alessio Quaglino ea230a950c Implicit flex elasticity in the CG constraint solver via an effective metric
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
2026-07-15 14:57:42 -07:00

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3.4 KiB
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// Copyright 2021 DeepMind Technologies Limited
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#ifndef MUJOCO_SRC_ENGINE_ENGINE_FORWARD_H_
#define MUJOCO_SRC_ENGINE_ENGINE_FORWARD_H_
#include <mujoco/mjdata.h>
#include <mujoco/mjexport.h>
#include <mujoco/mjmodel.h>
#include <mujoco/mjtype.h>
#ifdef __cplusplus
extern "C" {
#endif
// check positions, velocities, accelerations; reset if bad
MJAPI void mj_checkPos(const mjModel* m, mjData* d);
MJAPI void mj_checkVel(const mjModel* m, mjData* d);
MJAPI void mj_checkAcc(const mjModel* m, mjData* d);
//-------------------------------- top-level API ---------------------------------------------------
// advance simulation: use control callback, no external force, RK4 available
MJAPI void mj_step(const mjModel* m, mjData* d);
// advance simulation in two steps: before external force/control is set by user
MJAPI void mj_step1(const mjModel* m, mjData* d);
// advance simulation in two steps: after external force/control is set by user
MJAPI void mj_step2(const mjModel* m, mjData* d);
// forward dynamics
MJAPI void mj_forward(const mjModel* m, mjData* d);
// forward dynamics with skip; skipstage is mjtStage
MJAPI void mj_forwardSkip(const mjModel* m, mjData* d, int skipstage, int skipsensor);
//-------------------------------- integrators -----------------------------------------------------
// Runge Kutta explicit order-N integrator
MJAPI void mj_RungeKutta(const mjModel* m, mjData* d, int N);
// Euler integrator, semi-implicit in velocity
MJAPI void mj_Euler(const mjModel* m, mjData* d);
// Euler integrator, semi-implicit in velocity, possibly skipping factorisation
MJAPI void mj_EulerSkip(const mjModel* m, mjData* d, int skipfactor);
// fully implicit in velocity
MJAPI void mj_implicit(const mjModel *m, mjData *d);
// fully implicit in velocity, possibly skipping factorization
MJAPI void mj_implicitSkip(const mjModel *m, mjData *d, int skipfactor);
// implicit-flex solve gate: with solver=CG, an implicit integrator and flex stiffness present,
// the constraint solve is dispatched to the flex-augmented primal solver (monolithic,
// pyramidal cones only); solver=Newton keeps its exact-factorization semantics
int mj_flexCG(const mjModel* m);
//-------------------------------- solver components -----------------------------------------------
// all kinematics-like computations
MJAPI void mj_fwdKinematics(const mjModel* m, mjData* d);
// computations that depend only on qpos
MJAPI void mj_fwdPosition(const mjModel* m, mjData* d);
// computations that depend only on qpos and qvel
MJAPI void mj_fwdVelocity(const mjModel* m, mjData* d);
// compute actuator force
MJAPI void mj_fwdActuation(const mjModel* m, mjData* d);
// add up all non-constraint forces, compute qacc_smooth
MJAPI void mj_fwdAcceleration(const mjModel* m, mjData* d);
// forward constraint
MJAPI void mj_fwdConstraint(const mjModel* m, mjData* d);
#ifdef __cplusplus
}
#endif
#endif // MUJOCO_SRC_ENGINE_ENGINE_FORWARD_H_