Does tuning the trapezoid's ramp fraction beyond a grid shrink the time-optimal carry's edge, and is it still positive?

What it found

A follow-up to robofab-edgeconv (stylised). Golden-section refinement of the trapezoid's ramp fraction lowers its six-part total by 0.00 to 0.60% across the twelve speed-limited rows. With the solver at 6400 nodes the time-optimal edge, +0.11 to +0.88% over the grid-tuned trapezoid, falls to +0.05 to +0.28% over the refined one, still positive in every row. The smallest edges are comparable to the solver's residual discretisation error, so their sign is not firmly established. One planar arm, assumed parameters, no motor dynamics; simulated only.

A figure from its own output

Paper, code and results

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

More in Robot manufacturing loops

• 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.
• Once the time-optimal solver's node count is converged, how big is its edge over a tuned trapezoid?Re-solves the time-optimal carry of robofab-scurvefine at 400 to 25600 nodes in all 12 rows: converged to 0.02% by 6400 nodes, the 400-node answer was up to 0.5% pessimistic, and the converged edge over a ramp-resolved trapezoid is 0.11 to 0.88% in every row; stylised, preliminary.

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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.