A spherical amplitude–phase formulation for 3-D adaptive line-of-sight (ALOS) guidance with USGES stability guarantees

A recently proposed 3-D adaptive line-of-sight (ALOS) path-following algorithm addressed coupled motion dynamics of marine craft, aircraft and uncrewed vehicles under environmental disturbances such as wind, waves and ocean currents. Stability analysis established uniform semi-global exponential stability (USGES) using a body-velocity-based amplitude–phase representation of the North–East–Down kinematic differential equations. However, the analysis is limited to straight-line paths, and restrictive assumptions are needed to ensure convergence of the vertical crab angle estimation error to zero. In this paper, we revisit the ALOS framework and introduce a novel spherical amplitude–phase design model that uses an alternative definition of the vertical crab angle. Our proposed formulation enables a significantly simplified stability proof, while retaining the USGES property for straight-line paths, removing restrictive assumptions on constant altitude/depth or zero horizontal crab angle, and remaining valid for general 3-D motion with nonzero roll, pitch and flight-path angles. We also show that the USGES result extends to a class of curved 3-D paths.