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
Previously shell mode required cellcount=1 along at least one axis. This CL
adds support for cellcount > 1 in all three axes by pinning interior grid nodes
to the parent body and reconstructing their positions from boundary nodes via
Transfinite Interpolation (TFI).
PiperOrigin-RevId: 924314800
Change-Id: I8c2438f4866dd4133feed65f535a1ab69f0c9188
Warp is not a true stretch mode but a parasitic shear mode so it should be scaled like bending (~thickness^3) rather than stretching (~thickness). The thickness parameter can therefore be used to set the stretch to warp stiffness ratio of the strain constraints.
PiperOrigin-RevId: 916900311
Change-Id: I52e54210fbb2a6d309abc1f084934830adce3423
Standard flex (flex_interp=0) with thin-plate bending treated bending forces purely explicitly. This caused contact-induced vertex vibrations and non-physical energy injection for flat resting sheets, because the solver treated each vertex as an independent mass during contact and contact normals are orthogonal to stretch constraints.
Fix: extend the existing preconditioned CG solver to include the constant bending stiffness K_bend in the implicit operator via matrix-free mat-vec.
PiperOrigin-RevId: 914774020
Change-Id: I45e0d6749abb6f873566203bccae956514b2576b
with a preconditioned Conjugate Gradient (CG) solver that operates
on the full system matrix.
The previous approach extracted flex DOFs into a reduced banded system,
factored it separately, and overwrote the global solve. This required
precomputed bandwidth (makeFlexBandwidth), parent-joint detection,
coupling corrections, and a FlexInterpContext struct — and only worked
for standalone flex trees without parent joints.
The new CG solver uses the already-factored global system (M - h*qDeriv)
as a preconditioner and adds the flex stiffness contribution via
matrix-free products (mjd_flexInterp_mulKD/mulK). This handles any
kinematic configuration — including flexes attached to articulated
chains or with parent joints — without sparsity pattern restrictions.
Before (`bunny_multicell`):
```
Simulation time : 50.80 s
Steps per second : 197
Realtime factor : 0.20 x
Time per step : 5080.3 µs
CG iters / step : 3.16
Contacts / step : 31.04
Constraints / step : 124.15
Degrees of freedom : 178
Dynamic memory usage : 0.4% of 100M
```
After:
```
Simulation time : 9.52 s
Steps per second : 1051
Realtime factor : 1.05 x
Time per step : 951.7 µs
CG iters / step : 3.21
Contacts / step : 30.90
Constraints / step : 123.61
Degrees of freedom : 178
Dynamic memory usage : 0.3% of 100M
```
PiperOrigin-RevId: 913758038
Change-Id: If5aa617b2d535c86aec9bd71c9e0003a2b38bdd7
This change adds a new passive force computation for flexes with elastic2d="bend" and dof="trilinear". The bending energy is based on the squared difference of normals between adjacent face elements at their shared edge midpoint. The edge data is precomputed during model compilation and stored in flex_bending.
PiperOrigin-RevId: 910772638
Change-Id: I3b12c7b7f1ba6ac1875df495d89e8cfec921ca80
Modify EigendecomposeStiffness to project out rigid body translations and rotations from the stiffness matrix eigenvectors. This prevents "ghost damping" from rigid body modes being incorrectly constrained. Update hollow_vs_solid.xml with solimp parameters for edge constraints. Adjust engine_core_constraint_test.cc to reflect the reduced number of equality constraints due to the projection.
PiperOrigin-RevId: 910631207
Change-Id: Ibaaa59bc030cfc6ae657d8f0d1b2a51002cc8d4e
When elastic2d="stretch" is set on an interpolated flexcomp, treat the bounding box boundary as membrane elements rather than volumetric cells. This computes plane-stress stiffness over the boundary faces and updates the runtime force/derivative kernels accordingly.
Interior vertex tracking (moving vertices that follow the deforming shell) is not yet implemented so all mesh vertices need to be on the bounding box surface or the background grid should have no interior nodes (i.e. cellcount should be 1 on at least one axis).
PiperOrigin-RevId: 907654080
Change-Id: I51b90e2f6a1d1b036f9604e42de20e377dc5d3f9
Do not allow a mix of `elastic2d != none` with `dof = trilinear` since the latter assumes 3d elasticity.
Also, do not assume that `flex_interp > 0` in the engine. This will enable to use, e.g., `flex_interp = -1` to mean a linear surface finite element instead of a 3d finite element which is currently identified with `flex_interp = 1`.
PiperOrigin-RevId: 903852035
Change-Id: Ia6290b4a05e9e510ffb7f36d141cd525b40d3110
This change introduces a `flex_cellcount` field to `mjModel` to specify the number of cells in each dimension for interpolated flexes. The stiffness computation, passive force calculation, and Jacobian derivatives are updated to operate on a per-cell basis, significantly improving performance by localizing computations to the nodes within each cell.
PiperOrigin-RevId: 901216393
Change-Id: Ic23132e609de11e71bb7fef8d1f139daad2ec264
The `vertcollide` attribute in flex and flexcomp contact specifications has been removed since the next mjWarp release will support flex collisions. This attribute was previously used to enable vertex-based collisions by adding sphere geoms at flex vertices. The functionality associated with this attribute has been deprecated and removed from the XML parser, documentation, and internal data structures. Affected example XML files have also been updated.
PiperOrigin-RevId: 885595503
Change-Id: I6a78975f1bc540c09ea8b5306ff3be0962b7ab24
The flex-SDF algorithm uses the same logic as mesh-SDF. Previous to this change, the flex was instead colliding with the convex hull of the mesh generated automatically with marching cubes from the SDF.
PiperOrigin-RevId: 876420302
Change-Id: I3bf6552b6b8e108ba4c4209bbcf10fe5f2b2fd90
These flexes use only 24 DOFs (3 per vertex of the bounding box), while colliding with the full high resolution mesh.
On an 8x8x8 cube, the performance using DOFs at all vertices is
```
Simulation time : 18.74 s
Steps per second : 533
Realtime factor : 0.53 x
Time per step : 1874.4 µs
Contacts per step : 114.88
Constraints per step : 3322.51
Degrees of freedom : 1536
```
With the new implementation, it is the following:
```
Simulation time : 1.82 s
Steps per second : 5507
Realtime factor : 5.51 x
Time per step : 181.6 µs
Contacts per step : 38.84
Constraints per step : 155.36
Degrees of freedom : 24
```
PiperOrigin-RevId: 721008829
Change-Id: I833df027527db578d86667cc4b24295bcf6f7d22
Add pulley example to show a circle use case.
Switch on flex edge rendering by default (no effect when flex skin is rendered).
PiperOrigin-RevId: 700738379
Change-Id: I8469bbf194de01c8dab66c9a51c49879013df141
Alessio Quaglino