Once the solver is converged, is the time-optimal carry's edge over a tuned trapezoid still positive in all twelve speed-limited rows?

What it found

A follow-up to robofab-scurvefine (stylised). Re-solving the time-optimal carry at 400, 1600 and 6400 nodes lowers the six-part total by 0.01 to 0.46%, and the edge over a ramp-resolved trapezoid, negative in 7 of 12 rows at 400 nodes, becomes +0.11 to +0.88% in every row at 6400. A one-step extrapolation moves it by at most 0.03 percentage points. The trapezoid's own ramp grid is not re-converged, which can only shrink the edge, and every parameter is assumed.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Robot manufacturing loops

• Does tuning the trapezoid's ramp fraction beyond a grid shrink the time-optimal carry's edge, and is it still positive?Golden-section tuning of the trapezoid's ramp fraction shrinks the time-optimal carry's edge to +0.05 to +0.28% (still positive in all 12 rows; stylised).
• Is the motor-line edge of the time-optimal carry converged in solver nodes?Repeats the robofab-motorcurve motor-line rows with the time-optimal solver at 400, 1600 and 6400 nodes: the edge over the tuned trapezoid moves by at most 0.28 points from 1600 to 6400 (the 0.08 m, k = 2, w0 = 4 row rises from 4.98 to 5.26%), and the missing cover profile was a node-count limit. Stylised.
• Does the time-optimal carry's edge over a tuned trapezoid survive a motor torque-speed line?Re-solves the nine torque- and jaw-bound robofab-torquebound rows with a motor torque-speed line (no-load speed 4 to 20 rad/s): the time-optimal carry stays faster than the tuned trapezoid in all 45 cells, but its edge ranges 3.5 to 28.6% (9.0 to 22.9% under a constant limit), shrinking where a jaw cap binds and growing where only torque does. Stylised.
• Is the trapezoid's duration in the torque- and jaw-bound rows set by peaks a sparse check never looked at?Re-checks the nine torque- and jaw-bound robofab-torquebound rows with a dense trapezoid peak check (10,000 whole-move samples, 1,000 per ramp, both sides of the acceleration corners): trapezoid totals move by under 0.16% and the time-optimal edge stays 9.5 to 23.0%, so the large edge does not rest on unseen trapezoid peaks. Stylised.
• Do the robofab carry results survive an independent physics engine?Re-checks the 108 trapezoid and time-optimal carry profiles of the robofab-torquebound rows against MuJoCo inverse dynamics: the hand-written two-link torques agree to 1.8e-5 N m, peaks are within 0.73% of the 5 N m limit (stylised, joint torques only).
• Does the time-optimal carry's edge over a tuned trapezoid survive when torque or the jaw cap binds?Re-checks the torque- and jaw-bound rows of robofab-scurve (no speed limit) with a converged solver and denser trapezoid ramp sampling: the time-optimal carry is still 9.4 to 23.0% faster than the tuned trapezoid in all 9 rows, and the edge is stable to solver node count (under 0.1%) and rises by at most 0.4 points with denser sampling. Stylised.

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Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.