How firmly should a robot grip when its friction twin is too clean?

What it found

A pinch grasp slips if μF < w₀ and crushes if F exceeds a fragility limit; with log-normal friction and crush force the expected loss is a sum of two normal CDFs in ln F and its optimum solves a quadratic. A twin whose friction spread is 0.1 instead of 0.3 grips softer, claims a risk of 1.1×10⁻⁵ and delivers 0.069 (4.0× the optimum; 11.6× at spread 0.05). A near-zero-spread twin has a flat zero-risk plateau, so its ‘optimal’ force is a tie-break: real slip 0.50 at the lower edge, 0.015 at the upper. Biased friction costs ≈ ½J″Δx² (85% of the optimum at −0.3 in log-friction), and a widened randomisation width can cancel a known bias but costs 1.5× the optimum if the bias is of opposite sign. A plug-in from n real friction measurements has regret matched by the delta method within 5% for n ≥ 50. Stylised: static friction threshold, chosen parameters, no contact dynamics or reactive re-grasp.

A figure from its own output

Paper, code and results

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

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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.