### Glider Computed Tomography (Glider CT)

The underwater glider is a robust ocean sensor platform, which has found applications in the sampling and monitoring of ocean environments for oil field surveys, military operations, and deep-sea and coastal research. Since the sampling and monitoring performance of gliders significantly relies on the navigation performance of gliders, underwater glider navigation is of great interest. Due to its energy efficient propulsion mechanism, the underwater glider is characterized by long range and high endurance, yet low speed. As a result, the trajectory of the underwater glider is strongly perturbed by ocean currents, affecting its navigation accuracy. Therefore, it is crucial to incorporate the knowledge of ocean currents into navigation to improve the navigation performance of gliders. Our work focuses on developing approximated methods for modeling and estimating ocean currents to guide autonomous underwater gliders more effectively. Since GPS signals cannot propagate through sea water, an underwater glider estimates its underwater position via dead-reckoning and regularly comes to the surface for GPS updates. To improve the navigation performance, an underwater glider computes an estimate of average flow velocity along the trajectory between the last and current surfacing positions. This flow estimate is incorporated into navigation until the following surfacing event. However, the estimate does not account for the temporal/spatial changes of the flow field during navigation, and our recent work [1] emphasized the importance of incorporating the temporal/spatial variability of flow fields into navigation in field deployments. The work in [1] aims at developing a navigation method that performs better than the default glider navigation method in the presence of a flow field with high temporal and spatial variations. From winter to early spring in 2012 and in late winter in 2013, we deployed gliders near Long Bay, SC where the ocean currents is characterized by strong tidal and Gulf Stream currents (see Fig. 1). To effectively deal with strong and highly variable flow in the Long Bay deployments, a novel method of ocean current modeling is proposed for short-term forecasts to guide gliders. We design a hybrid ocean model based on flow data from a tidal ocean model and observations from a glider. The method first approximates slowly-varying non-tidal flow from glider-derived flow estimates and then adds rapidly-varying tidal flow to the non-tidal flow. The method adjusts the ocean model based on the most recent ocean observations from gliders as feedback in real-time. Incorporating flow predictions from the proposed ocean model, we implement a path planning algorithm to generate waypoints. We simulate a glider trajectory under flow and generate waypoints from the simulated glider trajectory. Since ocean flow varies in time and the error between predicted flow and real flow may increase over time, we run the path planning algorithm based on the latest glider and flow data and update waypoints every time a glider comes to the surface. Fig. 2 shows the qualitative evaluation of the performance of the default and proposed glider navigation methods. The figure displays the trajectories of two simulated gliders navigating a transect line (the red line). The starting position is marked by a yellow star. After 14 surfacing events, both gliders managed to reach the target end point. Given waypoints generated using predictive flow via path planning, the glider driven by our method (the dark blue line with rectangles) followed the transect line very closely under flow and reached the target end point smoothly. On the contrary, the glider driven by the default navigation method (the light blue line with circles) meandered along the transect line and swayed around the target end point. This result shows that our method can provide more precise control under flow. We also test and verify the proposed method of glider navigation through the Long Bay deployments. The experimental results show that compared to the default glider navigation method, our method improves the performance of navigation and provides better reliability and predictability in the presence of flow with strong temporal and spatial variations. In our previous work in [2], we developed the Glider CT algorithm that reconstructs the spatial map of a depth-averaged flow field from the difference between the nominal and dead-reckoning trajectories of gliders, which is referred to as the dead-reckoning error. The Glider CT problem is formulated from the fact that the dead-reckoning error accumulated along the glider trajectory is determined by a line integral of the difference between real flow experienced by the glider and glider-estimated flow incorporated in navigation. The constructed system is highly nonlinear, and by solving the system equations, Glider CT reconstructs a flow field. The work in [3] extends our previous work in [2] by analyzing the Glider CT algorithm and providing the convergence proof of the algorithm. While existing approaches that deal with similar problems require the knowledge of gradients of the system equations, Glider CT solves nonlinear equations without the computation of gradients. The Glider CT algorithm is validated through experiments. In the experiments, we imitate the motion of underwater gliders under a flow field using Khepera III robots under a simulated flow field. We place a light source in a target domain and simulate a flow field based on light intensity. By applying the dead-reckoning strategy of gliders, we estimate the dead-reckoning trajectories of Khepera III robots. The nominal trajectories under a simulated flow field are obtained by controlling the motion of Khepera III robots as if their trajectories are affected by the field. Fig. 3 shows the experimental results. The magnitude of flow in the true field (ftrue) ranges from 0.028 to 0.119 m/s, and that in the reconstructed field (freconst) ranges from 0.0212 to 0.0725 m/s. We compute the error between the true and reconstructed fields by e=ftrue-freconst. The root-mean-square errors in the x and y components are (erms)x=0.0182 m/s and (erms)y=0.0169 m/s, respectively. We analyze that the error is partially affected by the limitation of motor control for the differential wheels of Khepera III robots. Despite the limitation of motor control, the experimental result show a promising performance of the algorithm in a practical application.(see summary)