K_stretch was the Gauss-Newton Hessian of the stretch force, not its Jacobian.
With elongation e_a = L_a^2 - L0_a^2 and force f = -sum_ab M_ab e_a grad(e_b)/2,
K = 2 sum_ab M_ab (s_a d_a)(s_b d_b)^T + sum_a Me_a (Laplacian_a (x) I3)
and only the first term was there. The second is proportional to the edge
tension Me_a = sum_b M_ab e_b, so it vanishes at rest and grows with strain:
the operator was first-order correct and no more. Finite-differencing it
against -d(qfrc_passive)/dq on a mesh dilated by 5% gives 7.8% of the force
scale; with the term it is exact to roundoff.
Add only the tensile part. The geometric block is Me_a*[[I,-I],[-I,I]] over the
edge's two vertices, which is positive semi-definite exactly when Me_a >= 0; a
compressed edge would make K indefinite, and both consumers -- the CG
constraint solver and the PCG in mjd_effSolve -- require SPD. The clamp is
structural, so no eigendecomposition is needed, and it is confined to the
operator: mj_flexPassiveStretch keeps the full Me_a, so no force changes.
Both the matrix-free operator and the CSR assembly the effective metric builds
from are updated, since they must agree.
This changes how flexes with elastic2d="stretch" integrate under the implicit
integrators and the effective metric -- bag.xml moves, poncho.xml is
bit-identical because bending energy is quadratic and has no geometric term.
The interpolated-flex path still uses its Gauss-Newton approximation, which
FlexInterpDerivativesDeformed asserts.
Every step, the flex block of the implicit effective metric M + K was
factorized by sparse Cholesky, because K depends on the configuration. On
model/flex/bag.xml, added here, that is roughly half the step, against a
comparable share for the constraint solve it exists to accelerate.
Keep only the metric's per-vertex 3x3 diagonal blocks, prefactored. Neither
consumer needs the exact inverse: the CG constraint solver only wants a
preconditioner, and qacc_smooth can come from an iterative solve using those
blocks. They are O(n) to build and to apply, but weaker, so CG runs about twice
the iterations and qacc_smooth becomes an iteration rather than a direct solve.
Net, the bag model steps roughly twice as fast.
The preconditioner, by metric state. Inactive, meaning no flex elasticity or an
explicit integrator: M^-1, unchanged. Bending only (nefmK == 0): M^-1 plus the
exact constant bending factor from mj_setConst on the dofs it covers,
unchanged; that factor is built at model compile time and costs nothing per
step. Per-step stiffness: M^-1 plus the 3x3 blocks, where before it was a
per-step sparse Cholesky, or, when M couples across the flex block, an inner
PCG of up to 50 iterations run once per outer CG iteration.
Only models carrying per-step stretch stiffness change in wall-clock. Both
ponchos hold their timing and take slightly fewer CG iterations than before,
because the preconditioner is now symmetric: it applies M^-1 and the covered
blocks to disjoint sets of dofs, where previously the two overlapped and the
operator was not symmetric, which PCG requires.
mjd_effSolve is the accurate solve of (M + K)x = b; what used to carry that
name only preconditions and is now mjd_effPrec. Its CG guarded the division by
pAp with mjMINVAL, an absolute floor on a quantity that scales with the square
of the right-hand side, so a small b aborted the solve while the curvature was
healthy: four flex models were quietly left short of tolerance. For an SPD
metric the guard is positivity, and with that the same solves converge. The qacc_smooth call site in
mj_fwdAcceleration is textually unchanged but now reaches the iterative solve,
which converges on opt.tolerance rather than a hardcoded threshold, floored in
mjUSESINGLE builds where the squared target is unreachable in float. Reaching
the iteration cap names the ill-conditioned flex stiffness and then reports it
through mjWARN_INERTIA, rather than returning an under-converged result.
Covered dofs are located by walking the covered rows of the stiffness matrix,
as they need not be 3-aligned from dof 0: any joint declared before a flexcomp
shifts them.
mjData.efm_L_rownnz, efm_L_rowadr and efm_L_colind described the sparsity of
the deleted factorization and are removed: left NULL with nonzero mjxmacro
extents they made the Python bindings hand back uninitialized arrays.
efm_active loses the value 2 for the same reason, nothing selects a solve path
on preconditioner exactness any more. Both are recorded under breaking changes.
model/flex/bag.xml is added because no shipped model carried per-step stretch
stiffness. The ponchos are bending-only and trampoline.xml uses an explicit
integrator, so the metric never activates there. It is excluded from
WriteReadCompareTest: stretch stiffness amplifies rest geometry that XML rounds
on save.
Convert the four remaining mju_mulMat{,T}{Vec,Mat}3 call sites in this
file to their inlined mji_ equivalents, so the file is consistent after
the review change to the stretch paths. Aliasing is unaffected: the
inlined variants mark the result restrict, and every call already
required a distinct result (the public versions overwrite res while
reading vec).
Per review on #3437: add the missing blank line above the new comment
block, and use the internal inlined mji_mulMat{,T}{Vec,Mat}3 helpers
rather than the public mju_ ones, matching fe9dc584. Six call sites in
the two stretch paths; pre-existing mju_ calls elsewhere in the file are
left alone.
The implicit effective metric assembles the stretch stiffness from
world-space edge vectors, but a flex vertex body's slide dofs are
expressed in its parent body's frame. When that frame is rotated the
assembled operator is therefore not the Jacobian of the passive stretch
force, which mj_flexPassiveStretch already maps into the dof frame with
xmat^T. The metric is then inconsistent with the force it linearizes:
implicit integration loses its stability guarantee, and models that the
same flex handles comfortably in an unrotated frame diverge.
Apply the matching change of basis in both places that build or apply the
stretch stiffness: mjd_flexStretch_mul rotates the input dof vector into
world and the scattered result back, and mjd_flexStiff_assemble sandwiches
each 3x3 block as R_bi^T * blk * R_bj. Both are no-ops when the parent is
unrotated. Bending needs no change: its blocks are isotropic, and
R^T (q I) R = q I.
This completes the fix in fe9dc584, which covered the passive force paths
and the interp (trilinear) derivative but not the standard stretch one.
On a mesh flex inside a body with a 90-degree rotation, the metric's
directional agreement with the force Jacobian goes from cos = 0.57 to
cos = 1.0, and a hanging sheet that previously reached 176% strain
settles at 0.87%.
Fast path in mj_flexPassiveInterp, mj_flexPassiveBendInterp, and
mj_flexPassiveStretch assumed body slide joints are world-aligned
(J = I). When parent body has a non-identity quaternion, joint axes
are rotated (J = R_body), causing wrong force mapping and instability
(NaN/Inf in QACC).
Fix: project world-frame forces onto body local frame via
mju_mulMatTVec3(R_body^T, force) before adding to qfrc_spring/damper.
Also fix the derivative paths:
- mjd_flexInterp_kernel fast path: R^T * K_rot * R * vec
- mjd_flexStiff_assemble (CSR): R_bi^T * K_rot_block * R_bj
The CSR-assembled stiffness matrix is the actual path used by the
implicit CG solver (mj_flexCG gate). The test uses solver="CG" to
activate this path; without it, flex stiffness is integrated
explicitly and no derivative fix can help.
Ported from GitHub PR https://github.com/google-deepmind/mujoco/pull/3379
Original author: Devansh (https://github.com/devansh0703)
Fixes https://github.com/google-deepmind/mujoco/issues/3364
PiperOrigin-RevId: 952789284
Change-Id: If924f7160dd16c0cc88170d80e6e605da0fe2e04
https://youtu.be/17XpwnqyCXs
New transmission type mjTRN_SO3: a relative orientation, targeting a ball
joint or a site+refsite pair. It is the first transmission with more than
one force output: its length is the norm of the expmap vector of the
relative rotation and its moment axes are the 3 rows of the
relative rotational Jacobian, without projecting onto per-actuator gears.
New force law mjGAIN_SO3/mjBIAS_SO3: a geodesic PD servo, force =
kp * log(q_current^-1 * q_target) - kv * velocity, exact for arbitrary axis
combinations with a unique equilibrium at every commanded orientation.
Error, moment rows and velocity all live in the child frame (joint or
site): the right-difference error is the gradient of the geodesic
potential in that frame. The parent-frame (left) error is not: driving
child-frame torques with it pumps energy at large angles, settling into
steady-spinning limit cycles (the SO3LargeAngleConvergence test). The
integrator variant stores the 3D orientation setpoint in act (actnum = 3,
re-anchored to a bounded representative at integration time). Exposed in
MJCF as <orientation joint=|site=+refsite= kp kv|dampratio>, or via
<general gaintype="so3" biastype="so3">.
The setpoint input has two charts: an expmap target (3 controls, default)
or a quaternion target (4 controls) -- <orientation input="quat">, the
first actuator with different input and output widths. The signature is
recorded in a new per-actuator field actuator_ctrlspec (mjtCtrlChart),
whose meaning is scoped by the gain type the way gain/bias parameters are;
ctrlnum is derived from it at compile time and remains the layout
authority. An explicit field rather than width inference or a prm slot:
width-as-chart cannot express same-width signatures (upcoming servo input
subsets), and prm slots are the input_mode pattern this stack retires.
The force law normalizes the commanded quaternion, making it scale- and
antipodally-invariant. The all-zero ctrl still maps to the identity via
mju_normalize4, but it is a degenerate point (a nudge of any component
commands a half-turn), so quat inputs reset to the identity quaternion:
new mj_resetCtrl sets neutral ctrl values (zero, except qw = 1), called
by mj_resetData and the viewers' Clear All. The quat chart is
restricted to dyntype 'none': integrating a quaternion setpoint linearly
is not meaningful on the manifold. New mjsActuator.ctrlspec field carries
the signature through the spec and XML round-trip.
Actuator sensors (actuatorpos/vel/frc) now report one value per force
output; dim = 3 on an SO3 actuator.
As the first actuator with nu != nactuator, this commit also makes the
viewers multi-input aware: the control sliders in simulate and studio,
which indexed per-actuator arrays by control index (out of bounds on
this model class), are generated per control and labeled with the
actuator name plus an input suffix ("orient/qw"), via the new
introspection helper mj_actuatorInputName -- the single source of truth
for input names, extended by each new multi-input type (quaternion
components are w-first: qw, qx, qy, qz). Slider ranges now honor a
defined ctrlrange even when ctrllimited is false: range is the UI hint,
limited is the clamp -- wrapped and expmap setpoints are unbounded but
still want finite sliders, while quat components are truly bounded.
The rotational demo model is orientation.xml under
test/engine/testdata/actuation/, upgraded to a three-way contrast:
per-axis wrapped servos vs an expmap-commanded vs a quat-commanded
orientation actuator, on identical checker-textured boxes. It is loaded
by the mixed-axis contrast and input-name tests, and doubles as the
viewer test model (slider groups of 3 independent, 3 grouped, 4 grouped).
PiperOrigin-RevId: 951607063
Change-Id: If235dba8e2f2ca72672e7c62531a27e967c6a373
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
The gyroscopic (bias) derivatives applied to standalone free bodies by the
implicitfast integrator provide comparable stability for spinning bodies,
with none of midpoint's restrictions: they apply under contacts, fluid
forces and constraints, and preserve the linear force-velocity relation
required by discrete-time inverse dynamics. The invdiscrete flag reverts to
its original single meaning and no longer affects forward dynamics.
Restore implicitfast coverage in the DiscreteInverseMatch test, removed
when midpoint made discrete inverse dynamics untestable.
Add implicit gyroscopic (bias) derivatives for free bodies in implicitfast.
The implicitfast integrator drops the RNE (bias) derivative to stay on the
symmetric Cholesky path, so fast-spinning free bodies integrate gyroscopic
forces explicitly and can gain energy. Symmetrizing the gyroscopic Jacobian
is not an option: its stabilizing content is the antisymmetric part, and
adding only the symmetric part is destabilizing.
Instead, exploit the fact that for a standalone free body the 6x6 block of
M - h*D is decoupled from the rest of the system (qDeriv sparsity is
tree-local): after the global solve, rebuild the block with the exact bias
derivative in closed form (mjd_freeBias_vel) and re-solve it with dense
unsymmetric LU, overwriting the block's rows of qacc. For lone spinning
bodies this makes implicitfast match implicit to rounding, at ~150ns per
eligible body: cheaper than the midpoint machinery it will replace.
Eligibility is structural only; contacts, fluid and constraints need no
gating. The same block is mirrored in discrete inverse dynamics
(mj_discreteAcc), making invdiscrete exact for spinning free bodies.
PiperOrigin-RevId: 948472495
Change-Id: I813ef3d98c7b399881bc8603b9f9208cfb02eb58
An actuator now owns a block of consecutive controls
(actuator_ctrladr/ctrlnum, width defined by the actuator type) and a block
of consecutive force outputs (actuator_outadr/outnum, width defined by the
transmission type). Force outputs are the scalars of actuation space: one
force, length, velocity and moment row each. nout = dim(actuator_force) is
derived from transmission types; all current types have width 1, so all
three counts coincide for every existing model and behavior is bit-exact.
Array re-keying: ctrlrange/ctrllimited by nu; forcerange/forcelimited/gear/
acc0/length0/lengthrange and the moment row structure by nout; everything
else per actuator. The mjModel actuator block is re-sorted by size key.
Layout-breaking, not behavior-breaking: saved .mjb files are invalidated
(size list changed) and recompilation is required.
PiperOrigin-RevId: 948351772
Change-Id: Icbc196ffa083cb1eaa6f1a3710869c89d8f62540
Introduce a fast path in mj_addFlexDerivatives for centered flexes where all nodes are attached to bodies with only 3 translational DOFs and no DOF-contributing ancestors. This allows for a direct scatter of K*vec, avoiding the overhead of sparse Jacobian construction and multiplication.
PiperOrigin-RevId: 916063477
Change-Id: I824728a5bdc3b975b04b46ecf22994922e307a8c
This gives a 3x speedup in implicitfast.
Also cleanup old code that was used in the dense factorization of the stiffness matrix before we switched to CG.
PiperOrigin-RevId: 915900315
Change-Id: Id6973c4bfd7d371a43ec6db982703969b23a3550
The flex interp stiffness matrix is Negative Semi-Definite (NSD). When forming the RHS for implicit integration, the term involving the velocity and stiffness should be added, not subtracted. A new test is added to ensure energy stability for flex interp stretch stiffness with the implicitfast integrator.
PiperOrigin-RevId: 914845245
Change-Id: Iaaf0914909128e64e195f17cc5f2f344a8a43bc2
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
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 an optimization for flexcomp objects defined by a mesh. It identifies grid cells that do not contain any mesh vertices and marks them as empty. Nodes that are exclusively part of empty cells are pinned, preventing them from moving. Stiffness computations are skipped for empty cells, reducing computational cost. The total mass is now distributed only among the non-pinned nodes.
PiperOrigin-RevId: 902565735
Change-Id: Id0a9a685536d5e18a3e42124a25ab08ff3a918f2
This provides a reduction from 26 to 18 constraints for trilinear and from 162 to 75 for quadratic. The assembly of the constraints becomes trivial. In total the speedup for a trilinear 3x3x3 grid is about 3x.
PiperOrigin-RevId: 902502398
Change-Id: I764772c7adef78da5a644f64701f842d36e4b543
The flex interpolation stiffness matrix within the implicit/implicitfast solvers is now built and factorized in a banded format instead of a dense one. This involves:
- Calculating the bandwidth based on the sparsity of the mass/damping matrix and the connectivity within flex cells.
- Allocating and populating a banded matrix `H`.
- Using `mju_cholFactorBand` and `mju_cholSolveBand` for factorization and solving.
This change improves performance for flexes with many DOFs but local coupling.
PiperOrigin-RevId: 901297952
Change-Id: I3efe06353d1903ea65ab30dc49685cede228bb68
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
This change introduces `nflexstiffness` and `flex_stiffnessadr` to allow flex stiffness matrices to have sizes other than the fixed 21 per element. Higher-order flexes can now store larger stiffness matrices based on their number of nodes. The `flex_stiffnessadr` array provides the starting index for each flex's stiffness data within the `flex_stiffness` array.
PiperOrigin-RevId: 899632263
Change-Id: Ie49182c46c3777acf0c6b492345edfcf62fb5e44
The derivatives of actuator velocity with respect to generalized velocities were incorrectly computed when the actuator force was limited by `forcerange`. This CL adds a check to zero out these derivatives when the actuator force is at its upper or lower limit, as the force is no longer a function of velocity in this clamped state.
PiperOrigin-RevId: 868818281
Change-Id: I89742a3f04989dd11f9cfada107200015b1472a7
The derivative calculation for actuator velocity in implicit integrators now correctly accounts for the `actearly` flag, using the next activation value when `actearly` is true.
PiperOrigin-RevId: 868598722
Change-Id: Ia180afb15b31a718170aeaf9d4ac514bb9e6073b
Alessio