Once the time-optimal solver's node count is converged, how big is its edge over a tuned trapezoid?

What it found

Follow-up to robofab-scurvefine: all 12 rows (three arm sizes, jaw cap 5× or none, joint speed limit 2 or 1 rad/s, six printed parts each) are re-solved at 400, 1600, 6400 and 25600 nodes. The totals change by at most 0.02% between 6400 and 25600 nodes, while 400 nodes is up to 0.5% pessimistic, which explains the negative “edges” there (7 of 12 rows). At 25600 nodes the time-optimal profile is faster than the ramp-resolved trapezoid in every row, by 0.11–0.88%. The observed convergence order is noisy (1.1–3.2). Stylised and preliminary; the trapezoid side’s ramp sampling is not varied.

A figure from its own output

Paper, code and results

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

More in Robot manufacturing loops

• 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).
• How fine must the MuJoCo contact settings be for a moving grasp?How fine must MuJoCo contact settings be for a moving grasp? On all seven toy-gripper parts, solref 0.2 ms and below reproduce the jaw-force bound (0.98–1.04×) at 100–800 m/s²; 0.5 ms fails at 400 and above, and the adequate value falls with acceleration (stylised, upward load only).
• Is it the contact time constant or the timestep that breaks a moving grasp?Is it solref or the timestep that breaks a moving MuJoCo grasp? On a 24-cell grid only 6 cells hold; a coarse step always fails, a finer step does not rescue a marginal solref, and solref 0.1 ms holds at steps of 0.1 ms and below (stylised).
• Is MuJoCo's refsafe clamp what breaks a moving grasp at a coarse timestep?Does MuJoCo's refsafe clamp break a moving grasp at a coarse timestep? Switching it off changes 7 of 32 grid cells' outcomes (11 hold on, 10 off), 10 runs go unstable, and the non-monotone timestep behaviour survives (stylised).
• Does an off-centre centre of mass need a harder grasp?Does an off-centre centre of mass need a harder grasp? Ball-pad elliptic-cone bound matches MuJoCo within 1.1% (5× force at 20 mm offset); flat-pad MuJoCo lies between an equal-split and a best-split corner-contact bound (stylised).

All 53 Robot manufacturing loops projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

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.