Does the time-optimal carry's edge over a tuned trapezoid survive a motor torque-speed line?
research/robofab-motorcurve
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.
What it found
Follow-up to robofab-torquebound (stylised, preliminary). The same nine torque- and jaw-bound rows are re-solved with each joint's torque limit falling linearly with speed, 5 N m × (1 − |speed|/w0), for no-load speeds w0 of 20, 10, 6 and 4 rad/s. The time-optimal carry stays faster than the tuned trapezoid in every one of the 45 cells, but its edge is no longer one number: 3.5% to 28.6%, against 9.0% to 22.9% under a constant limit. Where a jaw cap binds on the smaller arms the edge shrinks as w0 falls (22.9% to 5.0% for the 0.08 m arm, k = 2); where only torque binds it grows (9.0% to 28.6% for the 0.2 m arm). The constant-limit profiles reach joint speeds up to 139 rad/s, which no motor does. One planar arm, assumed parameters, a linear motor model, not checked in MuJoCo; simulated only.
A figure from its own output
Paper, code and results
More in Robot manufacturing loops
- 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). - 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-scurvefineat 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. - How hard must the jaws squeeze while the arm moves?How hard must the jaws squeeze while the arm moves? Simulated minimum force matches the m·sqrt((g+a)²)/(2μ) bound within 7% over 77 cases and is at most 0.3 N at 40 m/s²; a contact time constant that passes the static test reports slip at any force once the jaws accelerate (stylised).
- Does the jaw-force bound still hold at arm accelerations of 100 to 800 m/s²?Does the jaw-force bound still hold at arm accelerations of 100 to 800 m/s²? With fine MuJoCo contact settings the minimum force is 0.89–1.02× the bound over 39 cases; the earlier settings fail above 200 m/s² (stylised, prescribed acceleration, no arm).
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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.