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CMA-ES Explainer
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Black-box manipulation · grasp verified

Teach a KUKA LBR iiwa 7 R800 to pick, carry, and place

Seven joint target curves plus one gripper-width curve, sampled at sixteen knots: 128 variables optimized against a piecewise physical objective that never leaks a gradient.

8 owner poses · 90 Hz physicsawaiting owner receipt
Orange links connect source-ordered iiwa joint frames. The amber/green flange ring is owner pad force and grasp state; the cyan cones display Coulomb friction boundaries.
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Drag to orbit · pinch to zoom
Tactile Grasp Microscope & Ferrari-Canny GWS HUD
Free-Space Approach
Grip PhasePre-Contact
Ferrari-Canny GWS (ε)0.0%
Normal Pinch Force0.0 N
Friction Cone Capacity0.0 N static
iiwa joint angles · measured owner poses
A1 Base±170°
Unavailable
A2 Shoulder±120°
Unavailable
A3 Arm±170°
Unavailable
A4 Elbow±120°
Unavailable
A5 Wrist 1±170°
Unavailable
A6 Wrist 2±120°
Unavailable
A7 Flange±175°
Unavailable

Frankensim household flagship

Optimize a complete pick-and-place

Seven joint target curves plus one gripper-width curve, each sampled at sixteen knots:(7 joints + 1 gripper) × 16 = 128 variables

CMA-ES receives only a scalar receipt after a full rollout. Compliant contact, stick/slip friction, free object dynamics, release, hard limits, and owner-routed obstacle/self/object separation make the objective piecewise and black-box—there is no browser gradient hiding behind the animation.

At 128 dimensions, all four representations fit the honest browser envelope. Full CMA is pedagogically useful here; it is rightly refused for the 5,040-D walking problem.

Continuous learning12 physical rollouts / generation

The owner keeps the CMA state hot until you press Stop. The best manipulation policy is replayed every 16 generations.

Loading the pinned KUKA model and physical curriculum…
Keep this policyno policy yet

Both are exact. The file is the archival form; the link carries the policy inside the URL fragment, so it is never uploaded anywhere. The link is long — around 50 kB — because anything smaller stopped reproducing the gait that was trained: a rollout this long amplifies rounding, and a lossy link came back walking 0.57 m instead of 0.66 m.

All variants · one physical objective

Which covariance model helps at 128-D?

Run every owner implementation from the identical curriculum, seed, population, and rollout budget. This is a local measurement on one nonsmooth task—not a universal ranking.

Full CMA-ES

Learns every pairwise covariance interaction

O(n²) state · O(n³) decomposition

Separable CMA-ES

Learns one independent scale per coordinate

O(n) state · O(n) update

LM-CMA

Remembers a bounded history of search directions

O(mn) state · O(m²n) worst-case update

LM-MA

Maintains a bounded moving linear transform

O(mn) state · O(mn) update

What the kernel actually does (and doesn't)

tap to expand

Modeled

  • · 7 revolute DoFs (iiwa topology) with hard joint limits
  • · SE(3) FK, inverse-dynamics computed torque
  • · Featherstone articulated-body forward dynamics
  • · Compliant normal pad force + Coulomb friction
  • · Certified convex separation for collision pairs
  • · GJK + EPA query count surfaced in the receipt

Simplified

  • · Collision uses oriented-box envelopes, not triangle meshes
  • · No impulse solver, deformable object, or cable model
  • · Grasp pads are finite, rigid, parallel-jaw style
  • · Object dynamics are rigid-body only
  • · No joint belt-elasticity, backlash, or stiction
  • · No multi-arm coordination, bimanual, or human input

Not modeled

  • · No slip detection, regrasp, or recovery reflex
  • · No inertial measurement, encoder, or actuator lag
  • · No environment lighting, occlusion, or camera noise
  • · No learned policy beyond the periodic basis
  • · No sim-to-real transfer or hardware validation
  • · No reachability planner, grasp planner, or motion planner

A placement the kernel approves can still fail on a real KUKA. The page deliberately stops at a deterministic explainer benchmark; treating it as a controller validation would be a category error.

A parametric model with a paper trail

The procedural shell is intentionally mesh-free. Segment endpoints come from owner poses; the table records the pinned source joint-offset magnitude and mass used by dynamics. Orange housings are display geometry; the collision owner independently builds conservative oriented boxes from those source frames.

source linkjoint offset magnitude (m)mass (kg)
iiwa_link_0base5.0000
iiwa_link_10.15003.4525
iiwa_link_20.19003.4821
iiwa_link_30.21004.0562
iiwa_link_40.19003.4822
iiwa_link_50.21002.1633
iiwa_link_60.19952.3466
iiwa_link_70.10123.1290

Pinned community-reference source: iiwa7.xacro at revision 44f9d13. It is not a KUKA certification artifact.

Why this is a useful black-box flagship

1 · Reach and close

The seven joint splines must align both finite pads with the object while the finger spline is actually closing.

2 · Earn the grasp

Frankensim integrates compliant normal force, friction, object translation, and object rotation. Nothing is latched or teleported.

3 · Lift, route, release

The object must clear 9 cm, reach the goal tolerance, finish released on support, and avoid owner-reported obstacle, self, and proximal-object collision risk.

The source-feasible curriculum makes the demo inspectable from first paint, while live CMA-ES still searches every coordinate. If a sampled policy drops the object or misses the station, the receipt says so; the renderer cannot substitute a canned success animation.

Why 128 dimensions is the honest sweet spot

Seven joint target curves and one gripper-width curve are sampled at sixteen knots — 128 CMA-ES variables. The objective is assembled from a full LBR iiwa 7 R800 rollout with contact activation, static-slip friction capacity, free-space dynamics, release timing, hard limits, and an owner-routed obstacle/self/object separation — piecewise and black-box by construction. There is no browser-side gradient to hide behind, and the grasp is only claimed when the receipt verifies it.

At 128 dimensions all four scalable representations (Full, Separable, LM-CMA, LM-MA) fit the honest browser envelope, so this section is where the family race is physically meaningful — Full CMA is pedagogically useful here and rightly refused for the 5,040-D humanoid walking problem.