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
- Simplified constraint tree discovery with a unified iterator.
- Filling in a new `efc_tree` array to avoid calling tree discovery again in the constraint phase.
- Implemented dof skipping in the dense case for efficiency.
PiperOrigin-RevId: 875440387
Change-Id: Id44a5a6fe2a80edaaf30935506a023a307e21303
Replace dynamically-sized edge list with a dense ntree×ntree adjacency matrix for deduplication and a flat CSR representation.
PiperOrigin-RevId: 868728432
Change-Id: Iebe97a0870740e5465549b967bbde0c81e658269
The introduction of site specification to connects and welds in 3.2.3 conditionally changed the semantics of `mjData.eq_obj1id` and `mjData.eq_obj2id`. These changes were not properly propagated in several places leading to incorrect computations of constraint inertia, readings of affected force/torque sensors and runtime enabling/disabling of such constraints.
PiperOrigin-RevId: 690670420
Change-Id: I55ee8a013cbee8457f8d6c7f33c2981aedafbab6
Also fix bug in allocation for constraint islands, added allocation for limit constraints.
PiperOrigin-RevId: 561083128
Change-Id: I9e01d5a5b7454ec3cf60bccadaa0f96f2c0d87d1
Required for constraint solver islanding.
Replace linked lists with `island_{dof,efc}_{num,adr,ind}`, corresponding to the standard `{rownnz,rowadr,colind}` sparse matrix representation. By effectively defining two sparse matrix structures of dimensions `nisland x nv` and `nisland x nefc`, respectively, this representation is more conducive to reuse of existing sparse matrix utility functions, while being cache-friendlier by making sequential indices adjacent in memory.
PiperOrigin-RevId: 559704957
Change-Id: I919362cbef0d5fe5acc4aa2bb4ffb17eee8223a2
Alessio Quaglino