Safe navigation through waterways of time-varying depth based on reachability analysis

In this paper we propose a novel methodology for finding safe time-space corridors (tubes) that enable navigation through natural waterways of time-varying depth while robustly minimizing the probabilities of suffering a grounding or crashing accident, satisfying the constraints imposed by local authorities, and arriving to the final destination before the time limits imposed by contract between the local authorities and the charterer or manager of the vessel. The objective is that these tubes can later be employed by different scheduling, planing or control algorithms with the objective of optimizing navigation in the waterway. The proposed approach is applied to the case of the Guadalquivir river in the south of Spain where navigation is conditioned by the irregular bathymetric profile of the river and by the effect of the tide.