Real-time Feasible Usage of Radial Basis Functions for Representing Unstructured Environments in Optimal Ship Control

Navigating the highly unstructured maritime environment poses significant challenges for autonomous ships, particularly in the vicinity of static obstacles and inland waterways. Real-time algorithms capable of comprehending the complexity of nearby grounding hazards are crucial for safe and efficient operations. Electronic Navigational Charts (ENCs) serve as the standard for representing the static environment, providing detailed polygon-based information about obstacles and grounding hazards. However, the non-convex nature of these polygons presents difficulties for optimal control and Model Predictive Control (MPC) schemes. This article introduces an accurate and computationally feasible method for extracting and representing non-convex static obstacle polygons, specifically tailored for use in numerical optimization-based planning, path-following, and trajectory tracking close to static hazards. By employing geometric surface interpolation techniques, Thin Plate Spline (TPS) type of Radial Basis Function (RBF) interpolants are derived from each grounding hazard polygon's point set. These surface approximation functions are then utilized as inequality constraints within a Nonlinear MPC (NMPC) planning scheme to facilitate trajectory tracking with anti-grounding functionality. The integration of surface functions enables the NMPC to consider higher-detail maps, enabling the proposed control system to closely follow trajectories within the unstructured environment's hazardous areas, demonstrated through proof-of-concept simulations.