At tight joint-speed limits, is the time-optimal carry's edge over a trapezoid real or an artefact of the ramp grid?
research/robofab-scurvefine
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).
What it found
A check on robofab-scurve (stylised, negative on its old figure). Refining the ramp-fraction grid alone makes the trapezoid beat the time-optimal solver by up to 1.8%, because the 201-point torque check misses the acceleration peak of a 0.2% ramp. With extra samples inside each ramp the time-optimal edge at 2 and 1 rad/s is −0.3 to +0.9% (old figure 1.3 to 1.5%), and raising the solver from 400 to 6400 nodes moves one row by 0.5%, as large as the whole edge. Jerk-limited profiles are still never faster than the trapezoid. Only the speed-limited rows were re-run, and every parameter is assumed.
Paper, code and results
More in Robot manufacturing loops
- 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-motorcurvemotor-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 missingcoverprofile 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-torqueboundrows 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-torqueboundrows 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-torqueboundrows 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).
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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.