Variable L0 Guidance Strategy: Enlarged Operational Envelope and Path-Following

This paper presents a geometric and theoretical study of an exponentially varying look-ahead parameter for UAV path-following guidance. Conventional guidance laws with a fixed look-ahead distance often drive the vehicle into turn-rate saturation when the heading or cross-track error is large, leading to constrained maneuvers and higher control effort. The proposed variable L0 strategy reshapes the look-ahead profile so that the guidance command adapts to the evolving tracking error geometry. A detailed investigation shows that this adaptation significantly enlarges the region in which the commanded turn rate remains unsaturated, allowing the vehicle to operate smoothly over a broader range of error conditions. For representative settings, the unsaturated operational envelope increases by more than 70% relative to the constant L0 formulation. These geometric insights translate to smoother trajectories, earlier recovery from saturation, and reduced control demand. Simulation studies on straight-line and elliptical paths demonstrate the merits of the variable look-ahead strategy, highlighting its control-efficient and reliable path-following performance.