Controlled Lagrangian Particle Tracking: Error Growth Under Feedback Control

The method of Lagrangian particle tracking (LPT) is extended to autonomous underwater vehicles (AUVs) that are modeled as controlled particles. Controlled LPT (CLPT) evaluates the performance of ocean models used for the navigation of AUVs by computing the differences between predicted vehicle trajectories and actual vehicle trajectories. Such difference, measured by the controlled Lagrangian prediction error (CLPE), demonstrates growth rate that is influenced by the accuracy of the ocean model and the strength of the feedback control laws used for vehicle navigation. Despite the limited accuracy and resolution of the ocean model, the error growth can be bounded by feedback control when localization service is available, which is a unique property of CLPT. Theoretical relationship among CLPE growth rate, quality of ocean models, and feedback control are established for two control strategies: a transect-following controller and a station-keeping controller that are often used by AUVs. Upper bounds for error growth are derived and verified by both simulation and experimental data collected during the operations of underwater gliders in coastal ocean.