Marine Vessel Reachable Set Calculation for Real-Time Collision Avoidance

The patent applies segmentation by dividing the high-dimensional state space into multiple lower-dimensional subspaces. Instead of computing the reachable set for the entire 6-dimensional marine vessel system at once, the method partitions the state space and computes reachable sets for individual subsystems or state variables separately, then combines the results. This segmentation reduces the computational complexity from exponential in the full dimension to manageable levels in reduced dimensions, enabling real-time computation while preserving accuracy.

The patent employs dimensionality change techniques by transforming the high-dimensional nonlinear reachability problem into a series of lower-dimensional problems. The method introduces auxiliary variables or uses coordinate transformations that map the complex 6-dimensional marine vessel state space into a framework where computation can be performed in reduced dimensions. This dimensional transformation maintains the essential safety assessment capabilities while avoiding the exponential computational burden of the curse of dimensionality.

The patent applies partial action by computing reachable sets for critical subsystems or state variables with higher priority for collision avoidance, rather than computing all aspects of the full 6-dimensional state space with equal detail. The method identifies which dimensions of the state space most critically affect safety (e.g., position and velocity in collision-prone directions) and allocates computational resources preferentially to those dimensions. This partial computation approach achieves sufficient real-time performance with available onboard processing power while maintaining adequate safety assessment for the most critical parameters.