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

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.

Uniform Semiglobal Exponential Stability of Integral Line-of-Sight Guidance Laws∗∗This work was partly supported by the Research Council of Norway through the Centres of Excellence funding scheme, project no. 223254 - AMOS

“…modifies the integral term used in Børhaug et al (2008) to achieve integral action using adaptive sideslip estimation, and is able to prove USGES for a closed loop kinematic model of an underactuated marine vehicle following Dubins paths (Dubins (1957)). Lekkas and Fossen (2014) proves that a similar system is globally κ-exponentially stable when following paths parametrized as monotone cubic Hermite splines. This paper considers a 3-DOF vessel model including the kinematics and dynamics of the vessel, as well as kinematic disturbances from constant and irrotational ocean currents.…”

Predictor-based LOS guidance law for path following of underactuated marine surface vehicles with sideslip compensation

“…While such disadvantage may not be remarkable by using recently developed digital processors. In contrast to the ILOS guidance method (Bϕhaug et al, 2008;Lekkas and Fossen, 2014), where the integral of the tracking error is added to compensate the drift force due to environmental disturbances, the proposed PLOS guidance law avoids the drawback caused by the integral term, such as reduced stability margin. Moveover, the ILOS guidance law deals with the sideslip in a passive way as it merely reacts to the tracking Fig.…”

“…The LOS guidance principle has been widely used in path following and its properties have been thoroughly studied in the literature (Lee et al, 2010;Oh and Sun, 2010;Bϕhaug et al, 2008;Lekkas and Fossen, 2014;Fossen et al, 2014). The main idea of LOS guidance is to mimic the actions of a helmsman, which steer the vehicle towards a lookahead distance ahead of the projection point of the vehicle along the path.…”

“…To tackle the sideslip angle issue and compensate for its influence, some efforts have been made by researchers (Hac and Simpson, 2000;Bϕhaug et al, 2008;Lekkas and Fossen, 2014;Fossen et al, 2014). The straightforward solution to solve this problem is to measure the sideslip angle.…”

“…The ILOS guidance law is originally proposed in Bϕhaug et al (2008) where the task is to converge to straight lines. In Lekkas and Fossen (2014), a κ-exponentially stable ILOS guidance law is derived for curved paths. The third method is the adaptive LOS (ALOS) guidance, which treats the sideslip angle as an unknown constant parameter to be estimated.…”