A small autonomous survey boat steered by plain line-of-sight (LOS) guidance never quite reaches its line in a cross current. The offset is delta * tan(asin(c/U)): 3.77 m for a 12 m look-ahead, 0.3 m/s current and 1 m/s boat speed. Our 3-degree-of-freedom simulation in research/marine-path reproduces that to within 1%.
Integral LOS removes the offset, and in 136 of 144 swept cases with current of at least 0.2 m/s it has the lower rms cross-track error. The 8 exceptions share one setting: a 6 m look-ahead with integral gain 2, where the loop oscillates by about 2.3 m even in still water.
The boat's damping, rudder and wave-force coefficients are placeholders, not sourced, so the ranking is a model property until it meets logged tracks. Next: source the coefficients, a JONSWAP sea, and an MPC arm. Code and table: research/marine-path.