Optimal Path Finding in Direction, Location and Time Dependent Environments

This paper examines optimal path finding problems where cost function and constraints are direction, location and time dependent. Recent advancements in sensor and data-processing technology facilitate the collection of detailed real-time information about the environment surrounding a ground vehicle, an airplane or a naval vessel. We present a navigation model that makes use of such information. We relax a number of assumptions from existing literature on path-finding problems and create an accurate, yet tractable, model suitable for implementation for a large class of problems. We present a dynamic programming model which integrates our earlier results for direction-dependent, time and space homogeneous environment and, consequently, improves its accuracy, efficiency and run-time. The proposed path finding model also addresses limited information about the surrounding environment, control-feasibility of the considered paths, such as sharpest feasible turns a vehicle can make, and computational demands of a time-dependent environment. To demonstrate the applicability and performance of our path-finding algorithm, computational experiments for a short-range ship routing in dynamic wave-field problem are presented.