A kinematic-bicycle twin ignores tyre slip: how wrong is its turning radius, and does calibrating that reveal where a twin-tuned steering loop goes unstable?

research/slip-twin

A kinematic-bicycle twin of a car ignores tyre slip: steady-turn radius is off by exactly 1 + Kv²/L (twin 4–63% too small, half at the characteristic speed), calibrating K fixes that but both twins certify steering gains stable at every speed while 11 of 30 real gain pairs lose stability below 60 m/s.

10 tests

What it found

Real car: linear single-track model with tyre slip; twin: ψ′=vδ/L. Steering with the twin’s angle gives radius R(1+Kv²/L) for understeer gradient K, matched by simulation (R=100 m: 104.6, 118.5, 174.0, 266.4 m at 5, 10, 20, 30 m/s; twin 4–63% too small, exactly half at the characteristic speed 23.26 m/s; oversteer car up to 136% too large at 20 m/s). Fitting K removes that error exactly, yet both the kinematic and the calibrated twin certify δ=−k_py−k_dψ as stable at every speed and gain, while 11 of a 30-point gain grid lose stability on the real car below 60 m/s (k_p=0.4, k_d=0.5: 14.0 m/s; confirmed in the time domain, 1.1×10⁻⁹ m at 8 m/s vs 4.6×10⁷ m at 20 m/s). An oversteer car with feedback loses stability at 23.7 m/s, below its open-loop critical speed 26.33 m/s. Stylised: linear tyres, constant speed, no actuator lag or delay; the closed-loop limit is not derived in closed form.

A figure from its own output

Figure produced by research/slip-twin: radius_vs_speed — slip-twin/experiments/radius_vs_speed.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.