How much of the time-optimal carry's edge survives a jerk-limited (S-curve) profile?

What it found

A follow-up to robofab-trapezoid (stylised, preliminary): the trapezoid's acceleration corners are rounded into jerk-limited S-curves (half- and full-jerk ramps) under the same torque, jaw-force and joint-speed limits. In none of 45 speed-limited rows is an S-curve faster than the trapezoid; at speed limits of 2 and 1 rad/s it costs 0.0 to 2.0% (half-jerk) or 0.0 to 7.0% (full-jerk), and the time-optimal profile is 1.3 to 9.2% faster than the full-jerk one. With no speed limit the S-curves cost 1.4 to 33.7% and the time-optimal profile is 22.5 to 36.8% faster than the full-jerk one. Jerk is limited by profile shape, not an absolute bound, and the ramp grid is coarse. Simulated only.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
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More in Robot manufacturing loops

• At tight joint-speed limits, is the time-optimal carry's edge over a trapezoid real or an artefact of the ramp grid?Checks robofab-scurve on a finer ramp grid: sampling a 0.2% ramp is needed or the trapezoid wrongly beats the time-optimal solver; with it the time-optimal edge at 2 and 1 rad/s is −0.3 to +0.9%, below the solver's own ~0.5% node-count error (stylised, negative on the old figure).
• Once the solver is converged, is the time-optimal carry's edge over a tuned trapezoid still positive in all twelve speed-limited rows?Re-solves the time-optimal carry at 400, 1600 and 6400 nodes in all 12 speed-limited rows of robofab-scurvefine: once converged the edge over a tuned trapezoid is positive everywhere, +0.1 to +0.9% (stylised).
• 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.

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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.