Integral LOS Path Following for Curved Paths Based on a Monotone Cubic Hermite Spline Parametrization

TLDR

The study tackles planar 3‑DOF vehicle motion by addressing both path planning and guidance challenges. The authors employ monotone cubic Hermite spline interpolation to generate smooth paths and modify the LOS guidance law with a time‑varying lookahead distance based on cross‑track error, additionally deriving a κ‑exponentially stable integral LOS law that compensates sideslip and constant disturbances. The proposed approach yields faster, less oscillatory path tracking and demonstrates κ‑exponential stability of the cascaded guidance–heading controller, with the integral LOS law effectively canceling constant disturbances.

Abstract

This paper addresses two interrelated problems concerning the planar three degree-of-freedom motion of a vehicle, namely, the path planning problem and the guidance problem. The monotone cubic Hermite spline interpolation (CHSI) technique by Fritsch and Carlson is employed to design paths that provide the user with better shape control and avoid wiggles and zigzags between the two successive waypoints. The conventional line-of-sight (LOS) guidance law is modified by proposing a time-varying equation for the lookahead distance, which is a function of the cross-track error. This results in a more flexible maneuvering behavior that can contribute to reaching the desired path faster as well as obtaining a diminished oscillatory behavior around the desired path. The guidance system along with a heading controller form a cascaded structure, which is shown to be κ-exponentially stable when the control task is to converge to the path produced by the aforementioned CHSI method. In addition, the issue of compensating for the sideslip angle β is discussed and a new κ-exponentially stable integral LOS guidance law, capable of eliminating the effect of constant external disturbances for straight-line path following, is derived.