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 semiglobal exponential stability (USGES) of the cross- and vertical-track errors using a body-velocity-based amplitude-phase representation of the North-East-Down (NED) kinematic differential equations. In this brief paper, we revisit the ALOS framework and introduce a novel spherical amplitude-phase representation. This formulation yields a more geometrically intuitive and physically observable description of the guidance errors and enables a significantly simplified stability proof. Unlike the previous model, which relied on a vertical crab angle derived from body-frame velocities, the new representation uses an alternative vertical crab angle and retains the USGES property. It also removes restrictive assumptions such as constant altitude/depth or zero horizontal crab angle, and remains valid for general 3-D maneuvers with nonzero roll, pitch, and flight-path angles.

翻译：近期提出的一种三维自适应视距路径跟踪算法，解决了船舶、飞行器及无人载具在风、浪、洋流等环境扰动下的耦合运动动力学问题。该稳定性分析通过基于体坐标系速度的北-东-下运动学微分方程幅相表示，建立了横向与垂向跟踪误差的一致半全局指数稳定性。本文重新审视了自适应视距框架，并提出了一种新颖的球面幅相表示法。该表述方式为制导误差提供了更具几何直观性与物理可观测性的描述，并使得稳定性证明得以显著简化。与先前依赖体坐标系速度导出垂向漂角的模型不同，新表示法采用了一种替代性垂向漂角定义，同时保持了USGES特性。该方法还消除了恒定高度/深度或零水平漂角等限制性假设，适用于滚转、俯仰及航迹角非零的一般三维机动场景。