Optimal trajectory generation for a glider in time-varying 2D ocean flows B-spline model

The problem of showing that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater vehicles (AUVs) known as gliders is investigated. This paper extends our preliminary results in couple ways. First, the ocean current flows are modeled by 3D B-spline functions in which the input variables are latitude, longitude and time, and the output variable is the ocean current velocity in 2D. The 3D (2D and time-varying) B-spline model of the ocean current is utilized in the Nonlinear Trajectory Generation (NTG) algorithm to find the optimal trajectory of the glider. The trajectories found using the 2D and time-varying B-spline ocean flows model are compared with the trajectories from 2D B-spline model in which the time is assumed to be constant in the ocean current model. In the second part of the paper, the dynamical glider model is established and controlled by gyroscopic forces rather than the simplified kinematic glider model as in the previous work. Finally, numerical solutions of several scenarios and animations of glider trajectories are presented. The results show that the 2D and time-varying B-spline ocean model not only can make the whole trajectory generating process much easier, but also the glider can reach the same destination in a comparable time and with much less energy than it does with the previous 2D ocean current model for both the kinematic and dynamic glider models. Both of the kinematic and dynamic glider optimal trajectories, successfully generated with 2D and time varying ocean current B-spline models, are shown to correspond to LCS.