Anastasios M. Lekkas

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

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.

Trajectory tracking and ocean current estimation for marine underactuated vehicles

In this work, a guidance system for 2-D straight-path tracking applications of underactuated marine vessels exposed to unknown ocean currents is developed. A relative velocity kinematic model is considered, hence making the method suitable for underwater vehicles where absolute velocities might not be available. The total position error vector has two components, the along-track error (tangent to the path) and the cross-track error (normal to the path). Two adaptive nonlinear observers are designed in order to estimate the current components w.r.t. the path-fixed frame and the origin of the error dynamics is shown to be globally κ-exponentially stable. The guidance algorithm uses this information and generates appropriate relative surge speed reference trajectories for minimizing the along-track error, while an augmented version of the line-of-sight (LOS) guidance is designed for minimization of the cross-track error. Moreover, the estimates from the nonlinear observers can be used to compute the ocean current vector w.r.t. the inertial frame.

A Time-Varying Lookahead Distance Guidance Law for Path Following

Abstract This paper presents a modified version of a well known line-of-sight (LOS) guidance algorithm for path-following. The proposed method employs a time-varying equation for the lookahead distance which depends on the cross-track error. A sliding mode controller is designed in order to stabilize the vehicle heading angle to the desired value specified by the guidance system. The guidance system along with the controller form a cascaded structure which is shown to be globally κ-exponentially stable when the control task is to converge to a straight line. The effectiveness of the proposed strategy is demonstrated by simulations indicating that the variable lookahead distance algorithm can contribute to obtaining a diminished oscillatory behavior around the desired path.

Minimization of cross-track and along-track errors for path tracking of marine underactuated vehicles

This paper deals with developing a guidance scheme for minimizing the position error of a marine underactuated vehicle during a path-tracking scenario. The desired position is determined by a virtual vehicle, which is assumed to navigate on the desired path, and the position error is analyzed in two components: a) the along-track error, and b) the cross-track error. Initially, perfect heading tracking is assumed and the well-known Line-of-Sight (LOS) guidance is used to minimize the cross-track error. Moreover, by using the vehicle kinematics and assuming perfect velocity tracking, a surge velocity guidance law for minimizing the along-track error is proposed. Then, the perfect velocity and heading tracking assumptions are relaxed and the stability of the total system, including the heading and velocity controllers, is studied and the system is shown to be globally κ-exponentially stable. The results are supported by computer simulations.

Continuous Curvature Path Planning using Voronoi diagrams and Fermat's spirals

Abstract This paper presents a two-dimensional curvature-continuous path planning algorithm based on Voronoi diagrams and Fermats spiral segments. The map and the obstacles position are assumed to be known a-priori and static. Despite the disposition of the obstacles, the Voronoi diagram always presents at least one collision-free path, maximally distant from all the obstacles. If more than one flyable path is available, the shortest one is selected. The result is further refined to obtain a more practical path that is piecewise linear with discontinuous curvature and velocity. Fermats spirals are used to smooth the path and provide curvature-continuity. A maximum threshold for the curvature is set so that the result of the algorithm respects kinematics and dynamics constraints of the vehicle. Moreover a minimum clearance from the obstacles can be chosen to respect additional safety constraints. The final result of the algorithm is a simple and intuitive path composed only by straight lines and spiral segments.

A Quaternion-Based LOS Guidance Scheme for Path Following of AUVs

Abstract This paper presents a quaternion version of the well-known Line-of-Sight (LOS) guidance algorithm for marine applications. The transformation from Euler angles is achieved by exploiting the nature of the quaternion structure and using fundamental half-angle formulae from trigonometry. First, the Euler angles version of the LOS guidance algorithm is briefly presented for two uncoupled cases: a) the horizontal xy -plane, and b) the vertical zx -plane. Then, a coupled case is also considered and the transformation procedure is presented for all three cases. The vehicle considered pertains to a 5-DOF kinematics model where the roll angle is neglected, typical of torpedo-shaped Autonomous Underwater Vehicles (AUVs). Naturally, the Euler angles representation of the system involves singularities which, in the general 3-D space navigation case, should be avoided. The presented method aims at providing a singularity-free and computationally-efficient version of the conventional LOS algorithm.

A 3D dynamic Voronoi diagram-based path-planning system for UUVs

This paper proposes a rapid path-planning and replanning system for Unmanned Underwater Vehicles (UUVs) that navigate in environments where subsea structures and other vehicles may be present. The proposed method is based on the Voronoi diagram, which is used to generate an initial set of connected waypoints (a roadmap) in the three-dimensional (3D) space, ensuring a certain clearance to avoid collisions with obstacles or grounding (e.g. collision with the ground). A 3D continuous path, composed by straight segments and circumference arcs, connects the aforementioned waypoints. If the vehicle encounters any moving or static obstacle and a collision risk is detected, the path is replanned online. In this context, an evaluation of the risk must be performed, and a list of traffic rules inspired by the International Regulations for Preventing Collisions at Sea (COLREGs, which are adopted for surface vessels), and by the Traffic and Collision Avoidance System (TCAS, which is adopted for aerial vehicles), is proposed for underwater vehicles. Those rules define the replanning procedure, so that an effective and safe collision avoidance maneuver can be performed whenever necessary. Simulations are performed on an subsea factory scenario, and results are presented to show the effectiveness of the proposed method.