How often should a mapping team rendezvous when its twin's odometry drift has no bias?

research/rendezvous-twin

How often a mapping team should rendezvous when its twin's odometry drift has no bias: real error is exactly √(1+ρ) times the claim, cost-optimal interval solves a cubic, twin regret 0.19–34.6%, shared bias cancels in the pairwise frame (5.3%→0.10%), and repair needs a long-lag ground-truth fit.

8 tests

What it found

Robots reset their dead-reckoning error at rendezvous; the real error variance is s²t + b²t² (white noise plus a per-run bias rate), but a twin fitted on short-horizon increments sees only the first term, so it plans a rendezvous every 10 and claims a peak error std of 3.16. The real optimum solves a cubic; at a bias/noise ratio ρ = 0.1/0.3/1/3 the twin's interval has 0.19/1.35/8.65/34.6% regret, the real error is exactly √(1+ρ) times the claim, and under an error budget the twin breaches it for 8–55% of every cycle. In the pairwise frame used for map merging a shared bias cancels (twin regret 5.3% → 0.10% at bias correlation 0.9). Repair needs ground-truth error at a long lag as well as a short one and about 5–10 runs to beat the twin reliably. Variance law and pairwise law checked by Monte Carlo. Stylised: one-dimensional Gaussian error, constant per-run bias, perfect reset.

A figure from its own output

Figure produced by research/rendezvous-twin: interval_vs_b2 — rendezvous-twin/experiments/interval_vs_b2.svg, written by the project's own experiment code.

Paper, code and results

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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.