A snapshot twin of a spinning lidar ignores that the platform moves during the sweep: how biased is the map, what does one scan reveal, and what do yaw and acceleration do?

research/sweep-twin

A snapshot-scan twin of a spinning lidar ignores motion during the sweep: length biased by exactly vτ/2 (0.5 m at 10 m/s), parallel walls converge by vτ/2π·(1/d₁+1/d₂), one scan gives speed to 0.13 m/s, yaw scales bearings by −κβ/(1+κ), acceleration biases odometry by a·t_f without accumulating.

12 tests

What it found

Real sensor: 2-D lidar at 10 Hz firing each beam at a different time while the platform moves; twin: all beams at t = 0. At 10 m/s the front and back walls are placed 0.25 and 0.75 m short, so apparent room length is biased by exactly vτ/2 = 0.50 m while the width is exact, and deskewing with the true motion removes it. Parallel walls appear to converge by ≈ vτ/(2π)(1/d₁+1/d₂) (1.94° measured vs 2.05° first order), so a wall-angle estimator certified on the snapshot twin inherits a heading bias; inverting that angle recovers speed from a single scan to 0.13 m/s at 1 cm range noise (first-order bias −1.8%). Yaw scales bearings by exactly −κβ/(1+κ), and acceleration biases scan-to-scan odometry by exactly a t_f in velocity, bounded and non-accumulating. Stylised: 2-D rectangular room, constant velocity or acceleration along one axis, known platform motion.

A figure from its own output

Figure produced by research/sweep-twin: convergence — sweep-twin/experiments/convergence.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.