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

• Published in: IEEE transactions on control systems technology 2014-11, Vol.22 (6), p.2287-2301
• Main Authors: Lekkas, Anastasios M., Fossen, Thor I.
• Format: Article
• Language: English
• Subjects: Cascaded systems; constant environmental forces; Constants; Control systems; Guidance (motion); integral line-of-sight (LOS) guidance; Integrals; Interpolation; Mathematical analysis; Mobile robots; monotone cubic Hermite interpolation; Parametrization; Path planning; Polynomials; Splines; Splines (mathematics); time-varying lookahead distance; Waypoints
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2014.2306774

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.