Is the time-optimal carry's speed-limited advantage just the min-jerk profile's shape?

What it found

A follow-up to robofab-jointspeed (stylised, preliminary): the min-jerk comparator is replaced by a trapezoidal-velocity move with a tuned ramp fraction, under the same torque, jaw-force and joint-speed limits. Over three arm sizes, three jaw caps and speed limits of 6 to 1 rad/s, the time-optimal profile beats the best trapezoid by only 0.4 to 2.9% at 2 and 1 rad/s (0.4 to 0.8% at 1 rad/s), against 46% over min-jerk, so the earlier ceiling was mostly the comparator. Without a speed limit it still wins by 8.7 to 22.5%. The smallest ramp fraction tried (0.01) binds in most tight-limit rows, so the small gap is bounded by the grid. All parameters are assumed; the speed limits are round numbers, not an actuator rating.

A figure from its own output

Paper, code and results

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

More in Robot manufacturing loops

• How much of the time-optimal carry's edge survives a jerk-limited (S-curve) profile?Does rounding the trapezoid's corners (a jerk-limited S-curve) change the time-optimal carry's edge? An S-curve is never faster than the trapezoid and costs 0.0 to 2.0% (half-jerk) or 0.0 to 7.0% (full-jerk) at speed limits of 2 and 1 rad/s, but 1.4 to 33.7% with no speed limit (stylised, assumed parameters).
• 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.

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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.