Provably Safe Finite-Time Guidance for Marine Vehicles

Abstract

We consider a new control strategy for marine navigation, equipped with finite-time convergence characteristics. We provide mathematical guarantees for waypoint reaching and obstacle avoidance for different encounter scenarios, by deriving conditions under which (i) convergence to waypoint and (ii) safe obstacle avoidance is achieved while (iii) satisfying input constraints. We propose a predefined-time heading control to enforce ship heading error convergence and waypoint reaching in finite time. Using this as a building block, we develop a provably safe algorithm for safe waypoint navigation by strategically and automatically introducing intermediate virtual waypoints. Using Imazu problems as benchmarks, we show that the proposed method is better than other existing strategies such as Velocity Obstacle Avoidance and biased Line-of-Sight methods, in terms of the safe distance between the ship and the obstacles, cross track error, control effort, waypoint reaching time and ship path length.