Real Time Reachability Analysis for Marine Vessels
Abstract: Safety verification of continuous dynamical systems require the computationof the reachable set. The reachable set comprises those states the systemcan reach at a specific point in time. The present work aims to compute thisreachable set for the marine vessel, in the presence of uncertainties in thedynamic modeling of the system and in the presence of external disturbancesin the form of wind, waves and currents. The reachable set can then be usedto check if the vessel collides with an obstacle. The dynamic model used isthat of a nonlinear maneuvering model for the marine vessel. The dynamicson the azipod actuators are also considered.Several methods are considered to solve the reachability problem for themarine vessel. The first method considered is that of the Hamilton JacobiReachability analysis, where a dynamic game between the control input andthe disturbance input is played. This results in a dynamic programmingproblem known as the Hamilton Jacobi Bellman Isaacs (HJBI) equation. Itis solved using the Level-Set method, but it suffers from the curse of dimensionality.The other method considered is the use of set-theoretic approach,where an over-approximation of the reachable set is computed, in the contextof safety verification. But on the downside, large sets of admissible controlyields highly over-approximated reachable sets, which cannot be usedIn order to overcome the disadvantages posed by the first two methods,emphasizing on the real-time computation, a third method is developed, wherea supervised classification algorithm is used to compute the reachable setboundary. The dataset required for the classification algorithm is computedby solving a 2 Point Boundary Value Optimal Control Problem for the marinevessel. The features for classification algorithm can be extended, so as toinclude the uncertainties and disturbances in the system. The computationtime is greatly reduced and the accuracy of the method is comparable to theexact reachable set computation.
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