In this paper, we put forward a local weather routing framework based on reachability theory to plan a time-optimal risk avoidance path in face of sudden changes in sea conditions. Our framework comprises of two phases, where the escape phase directs the vessel to withdraw from risky heading-speed combinations dictated by MSC.1/Circ. 1228. Subsequently, in the return phase, the algorithm guides the vessel back to its original global route while staying outside dangerous zones. Notably, our application of a four-dimensional state space for the description of a vessel’s configuration can accommodate both the safety and kinematic constraints. In the proposed state space, the path-finding algorithm based on reachability theory can figure out the optimal heading and speed of vessel simultaneously, providing a formal assurance of safety and global time-optimality for returning. To achieve this objective, we formulate and solve a new variational-inequality (VI) governing the forward propagation of the reachable set with both angular and acceleration rate treated as control inputs. Last but not least, we provide a rigorous proof for the proposed VI in the framework of viscosity solution and demonstrate the validity of our approach in two test scenarios including one integrated with a realistic control architecture.
Read full abstract