1. Introduction
The underwater glider has found applications in the monitoring and data collection of ocean environments for oil field surveys, military operations, and deep-sea and coastal research (Schofield et al. 2007; Nicholson and Healey 2008). Since the sampling performance is tightly coupled with navigation performance, underwater glider navigation is of great interest within the oceanographic research community. As part of the effort to improve the sampling and navigation performance of underwater gliders for scientific missions, existing approaches such as underwater glider control for ocean sampling (Zhang et al. 2007; Leonard et al. 2010) and underwater glider control support systems (Creed et al. 2003; Paley et al. 2008; Fernández-Perdomo et al. 2010) have been studied.
Underwater gliders primarily use the global positioning system (GPS) to identify their position on the surface of water (Meldrum and Haddrell 1994). However, since GPS signals cannot propagate through seawater, gliders cannot rely on GPS for underwater localization, so their position is estimated via dead reckoning between regular surfacing events for GPS updates. Driven by buoyancy and mass controls, underwater gliders have low speed; hence, their trajectory is strongly affected by ocean currents, causing a difference between the dead reckoning trajectory and the actual trajectory. To increase navigation accuracy in dead reckoning, some underwater gliders have the capability to compute an estimate of average flow velocity along the glider trajectory between the last and current surfacing positions and to incorporate the flow estimate into dead reckoning to navigate underwater until the next surfacing event (Merckelbach et al. 2008). We refer to this navigation method based on dead reckoning coupled with the glider-derived flow estimate as the default glider navigation method.
The default glider navigation method may help increase the accuracy of navigation in a calm water environment. However, since the glider-derived flow estimate does not account for temporal and spatial changes in the flow field, the estimated flow may differ from the actual flow experienced by the glider, causing poor navigation performance. To overcome limitations caused by insufficient knowledge of flow, we propose an approach for the real-time guidance of underwater gliders assisted by predictions from ocean models. Ocean models can be largely categorized as either physics-based or empirical (also known as statistical) (Reikard and Rogers 2011). Typically, physics-based ocean models are generated by solving geophysical fluid dynamics with given initial and boundary conditions (e.g., Luettich et al. 1992; Bleck 2002; Shchepetkin and McWilliams 2005; Haidvogel et al. 2008), while empirical models are trained using a historical dataset (e.g., Frolov et al. 2012; Chang et al. 2014). To increase the accuracy of an ocean model, real-time direct/remote oceanographic observations from satellite, ships, buoys, and gliders can be used as feedback to adjust the model via data assimilation (Kalnay 2003). Lermusiaux (2006) analyzes the uncertainties of ocean models caused by practical simplifications, inexact representations, and parameterizations of the models. In the work, model uncertainties are represented as stochastic forcings and are estimated and predicted in a Bayesian framework. Szwaykowska and Zhang (2014) discuss the navigation of marine vehicles using ocean models and study the bound of growth in error between vehicle positions in the real ocean and those in the simulated ocean based on ocean models. The method of error analysis studied there may be applied to improve the accuracy of ocean models and the performance of navigation algorithms for marine vehicles.
Our study is motivated by field experiments off the coast near Long Bay, South Carolina, from winter to early spring in 2012 and in late winter in 2013 to study persistent wintertime phytoplankton bloom formation. In the experiments, Slocum gliders collected data while maintaining desired tracks in the survey domain. Unlike other areas such as Monterey Bay, California, where previous glider navigation experiments have been conducted (Singh et al. 2001; Fiorelli et al. 2006; see special issue of Deep-Sea Research Part II, 2009, Vol. 56, Issues 3–5), ocean currents off the coast of Long Bay are not only characterized by strong tides but also influenced by the Gulf Stream, which has complex and variable circulation downstream of the Charleston Bump (Legeckis 1979; Bane 1983). This combination of tides and the Gulf Stream causes significant temporal and spatial variations in the flow field and requires a better glider navigation method than the default glider navigation method.
In recent years, there have been active studies regarding the path planning and navigation of marine vehicles. Witt and Dunbabin (2008) studied optimal path planning under strong, time-varying currents and demonstrated experimental results. Soulignac (2011) presented an optimal path planning algorithm that guarantees the existence of a path in strong current fields. Fernández-Perdomo et al. (2010) developed a path planning algorithm based on A*, a graph-based optimal path planning algorithm (Hart et al. 1968), adapted for constant surfacing times. The algorithm incorporated a regional ocean model and generated the simulated glider trajectory using predictions from the model. However, the authors did not test the algorithm for real gliders and did not provide the validation of predicted flow from the ocean model by comparing with the observed flow from a glider. Pereira et al. (2013) also incorporated predictions from ocean models into path planning. However, the main objective of their algorithms is to minimize collision risks of gliders with ships by accounting for the uncertainty in predictions from ocean models, not to improve navigation accuracy.
In this paper, we present a glider navigation strategy applied to the Long Bay deployments. First, the paper introduces a novel method of ocean current modeling for short-term forecasts to guide gliders. To effectively deal with highly variable and complex flow in the Long Bay deployments, we develop a hybrid ocean model based on flow data from a tidal ocean model and observations from gliders. The method first approximates slowly varying nontidal flow from glider-derived flow estimates and then adds rapidly varying tidal flow to the nontidal flow. The method adjusts the ocean model based on the most recent ocean observations from gliders as feedback. The adjustment is computed only in about a minute in real time on a single processor; hence, this method is computationally more efficient than typical applications of data assimilation in oceanography [e.g., Kalman filtering and variational techniques such as three-dimensional/four-dimensional variational data assimilation (3DVAR/4DVAR)]. We verify the method by comparing simulated flow with observed flow during a glider deployment.
Given flow predictions, we implement a path planning algorithm based on a flow-canceling controller to generate waypoints. We predict the trajectory of a glider under flow and generate waypoints based on the predicted trajectory, so that waypoints guide the glider to track the predicted trajectory. A similar approach to our waypoint design was previously studied in Smith et al. (2010) (see “alternate” waypoints in there). 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. The entire process of flow prediction, path planning, and waypoint updates is performed off-board the gliders by a glider navigation support system, the Glider-Environment Network Information System (GENIoS), automating glider navigation.
We test and verify the proposed method of glider navigation through the Long Bay deployments. To compare with our method, we also test the default glider navigation method through a series of simulated experiments. Our method guides gliders toward a target using a set of waypoints generated by path planning, but in the default glider navigation method, gliders swim toward a target without guidance. The test environment for the default glider navigation method is reconstructed from the data collected during the Long Bay deployments. Based on the experimental and simulation results, we evaluate the performance of both glider navigation methods by computing 1) the distance between the glider and the target at each surfacing event and 2) the difference between the predicted surfacing position under flow and the actual surfacing position. The 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 significant temporal and spatial variations.
The rest of the paper is organized as follows. Section 2 provides background information and motivation for our glider deployments and glider navigation method. Section 3 briefly introduces our glider navigation support system that was used in the deployments and the simulations. Then, we present our glider control and path planning strategy in section 4 and provide experimental and simulation results in section 5. Last, section 6 discusses conclusions and future work.
2. Background and motivation
In this section, we introduce the mechanisms of Slocum glider navigation and the description of the Long Bay deployments. Our study on glider navigation is motivated by the Long Bay experiments, in which we deployed Slocum gliders from winter to early spring in 2012 and in late winter in 2013. We present glider missions in the Long Bay deployments and the challenges in the glider operations encountered there.
a. The Slocum glider
Because of its long range and high endurance, the Slocum glider has become a robust sensor platform within the oceanographic community for long-duration ocean sampling field experiments. The Slocum glider generates forward propulsion by changing its mass distribution and buoyancy, converting its vertical velocity to horizontal motion along sawtooth underwater paths (Davis et al. 2002; Rudnick et al. 2004). The Slocum glider typically travels at low speed (the horizontal through-water speed is approximately 0.25–0.35 m s−1), yet it is capable of collecting data in the ocean for several weeks without a recharge.
The glider navigates via dead reckoning, which estimates the position of the glider using estimates of glider speed, compass heading, and flow velocity. While navigating, the glider regularly comes to the surface of water for GPS updates and data transfers to a dockserver, which is a designated onshore computer for data transmission through satellite links. Figure 1 illustrates glider navigation from the (
a: surfacing
b: acquisition of the first valid GPS fix
c: surface drift and data transmission
d: diving.
Navigation by the Slocum glider. While dead reckoning, the Slocum glider updates its estimated underwater position, forming a dead reckoning trajectory. Since the glider cannot obtain GPS signals underwater, the actual trajectory of the glider is unknown, but the figure shows the actual trajectory for illustration purposes.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Navigation by the Slocum glider. While dead reckoning, the Slocum glider updates its estimated underwater position, forming a dead reckoning trajectory. Since the glider cannot obtain GPS signals underwater, the actual trajectory of the glider is unknown, but the figure shows the actual trajectory for illustration purposes.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Navigation by the Slocum glider. While dead reckoning, the Slocum glider updates its estimated underwater position, forming a dead reckoning trajectory. Since the glider cannot obtain GPS signals underwater, the actual trajectory of the glider is unknown, but the figure shows the actual trajectory for illustration purposes.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Given a list of waypoints or a desired path of travel during the 
The glider swims in sawtooth underwater patterns during the subsurface phase, sampling most of the water column along the glider trajectory. Hence, the glider-derived flow velocity estimated in the plane may be interpreted as an estimate of the depth-averaged flow velocity over the subsurface phase. In other words, Eq. (1) is an approximation of path integral of flow over the water column that a glider experiences during one subsurface phase. The glider uses a constant flow estimate to navigate underwater until it comes back to the surface. This constant estimate does not account for temporal and spatial changes in the flow field during navigation, which may cause poor navigation performance.
We introduce the pseudocode of the default glider navigation method used in the built-in navigation system of the Slocum glider in algorithm 1 (Teledyne Webb Research 2014; Table 1). Once a glider dives into the ocean, the dead reckoning algorithm starts estimating the position of the glider by measuring the vertical speed, the pitch, and the heading of the glider. The vertical speed and the pitch are used to estimate the horizontal through-water speed. Then, the algorithm computes the glider position under flow using the glider speed, the heading, and the estimated flow at each time step with step size 
Algorithm 1: Pseudocode of the default glider navigation method (dead reckoning coupled with glider-estimated flow) for the kth subsurface phase.
b. The Long Bay experiments and glider missions
Sustained wintertime phytoplankton blooms are observed off the coast of Long Bay in multiyear satellite chlorophyll images (Fig. 2). In most areas of the South Atlantic Bight shelf, upwelling associated with Gulf Stream frontal eddies is a major mechanism of nutrient input, driving phytoplankton growth at the shelf edge. Just upstream of the Long Bay study area, the Charleston Bump deflects the Gulf Stream offshore, effectively shutting down direct frontal eddy nutrient input to Long Bay (Lee et al. 1991). Prior in situ observations (Atkinson et al. 1996) suggest recurring input of nutrients from the upper slope to the outer shelf off Long Bay from winter to early spring, but they do not provide evidence of a physical mechanism that accounts for both the alongshelf and seasonal patterns of the winter phytoplankton blooms associated with Long Bay.
Survey domain near Long Bay, processed at Skidaway Institute of Oceanography based on MODIS Aqua chlorophyll imagery. High concentrations at the shelf break persist through much of winter and are distinct from high chlorophyll values adjacent to the coast. The figure shows the locations of moored instruments LB1, LB2, and LB3 with yellow rectangles, and the three transect tracks of survey cruises with dotted lines in the cross-shore direction.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Survey domain near Long Bay, processed at Skidaway Institute of Oceanography based on MODIS Aqua chlorophyll imagery. High concentrations at the shelf break persist through much of winter and are distinct from high chlorophyll values adjacent to the coast. The figure shows the locations of moored instruments LB1, LB2, and LB3 with yellow rectangles, and the three transect tracks of survey cruises with dotted lines in the cross-shore direction.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Survey domain near Long Bay, processed at Skidaway Institute of Oceanography based on MODIS Aqua chlorophyll imagery. High concentrations at the shelf break persist through much of winter and are distinct from high chlorophyll values adjacent to the coast. The figure shows the locations of moored instruments LB1, LB2, and LB3 with yellow rectangles, and the three transect tracks of survey cruises with dotted lines in the cross-shore direction.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
To study the mechanisms of phytoplankton bloom formation in the outer shelf to the upper-slope region near Long Bay, we deployed various oceanic sensing platforms in a field experiment (LB2012) from January to April 2012. To observe the vertically resolved property fluxes, we deployed three moored instruments at three locations on the shelf/slope: LB1 (inner shelf, 30-m depth), LB2 (shelf break, 75-m depth), and LB3 (upper slope, 175-m depth), as shown in Fig. 2. Near-continuous cross-shelf and upper-slope observations were obtained by two Slocum gliders, which collected temperature, salinity, pressure, chlorophyll fluorescence, dissolved oxygen (DO), colored dissolved organic matter (CDOM), and turbidity data. One glider (Ramses) with a maximum operable depth of 200 m operated as a virtual mooring, maintaining its position at the edge of the Gulf Stream near LB3. The other glider (Pelagia) with a maximum operable depth of 100 m conducted a cross-shelf section between LB1 and LB3 (or LB2 depending on ocean conditions). The combined dataset from both gliders help us identify the physical and biological drivers of phytoplankton bloom formation in the study domain. In a follow-up experiment (LB2013) in late February 2013, one moored profiler sampled at LB2 and one Slocum glider (Modena) with a maximum operable depth of 200 m surveyed between LB+20 (33-m depth) and LB+40 (130-m depth), which are 20 and 40 km offshore from LB1 in the cross-shore direction, respectively.
The observational domain is characterized by strong tidal and Gulf Stream currents, which can hinder glider navigation. Strong tides are largely aligned with the cross-shore direction over the shelf off Long Bay. In addition, circulation at the shelf break is dominated by a strong current called the Gulf Stream, which has highly variable and complex circulation because of eddies and filaments that develop and propagate along its shoreward front. The complex ocean dynamics in this region form steep temporal and spatial gradients in flow off the coast of Long Bay, and ocean currents here often exceed the forward speed of a glider. The typical speed of the tidal and Gulf Stream currents on the shelf is 0.2–0.3 and 0.5–0.75+ m s−1, respectively. The maximum glider-estimated current 1.67 m s−1 in the Gulf Stream is shown in Fig. 3.
Flow speed near Long Bay. The black solid line is the speed of glider-estimated depth-averaged flow in the 2012 Long Bay deployment, and the gray shaded area indicates the range of the typical horizontal through-water speed of the glider.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Flow speed near Long Bay. The black solid line is the speed of glider-estimated depth-averaged flow in the 2012 Long Bay deployment, and the gray shaded area indicates the range of the typical horizontal through-water speed of the glider.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Flow speed near Long Bay. The black solid line is the speed of glider-estimated depth-averaged flow in the 2012 Long Bay deployment, and the gray shaded area indicates the range of the typical horizontal through-water speed of the glider.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
3. Glider navigation support by GENIoS
In the early 2000s, the concept of the Autonomous Ocean Sampling Network (AOSN) (Curtin et al. 1993) fueled interest in automated multiglider control systems. In 2006, as part of the AOSN field experiments, various research groups took part in the Adaptive Sampling and Prediction (ASAP) experiment in Monterey Bay, California. In ASAP, homogeneous and heterogeneous fleets of two specific types of underwater gliders, Slocum and Spray gliders, were deployed. To support automated glider operations, Paley et al. (2008) developed and tested the Glider Coordinated Control System (GCCS). Feedback control in GCCS enables the automation of both individual glider navigation and fleet coordination. An individual glider navigates by simply following waypoints generated by GCCS in such a way as to maintain the coordination of a glider fleet along a sampling trajectory. The design of the sampling trajectory is determined adaptively based on a classical linear estimation technique called objective analysis, so that a fleet of gliders can sample optimally distributed measurements, improving collective survey performance.
The glider control capability of GCCS is well-verified through ASAP (Leonard et al. 2010). However, the ocean dynamics near Monterey Bay in the ASAP experiment significantly differ from those near Long Bay. Considering the strong tidal and Gulf Stream currents off Long Bay, glider control strategies of GCCS were not applicable to the Long Bay experiments. For example, in ASAP, when a glider came to the surface, GCCS started predicting the following surfacing event of the glider and generated a list of waypoints based on the predicted surfacing data. Then, the next time the glider came to the surface, GCCS sent the pregenerated waypoints to the glider. In addition, GCCS did not incorporate flow fields in path planning. These settings for waypoint generation in ASAP may decrease navigation accuracy under a strong, highly variable flow field. Therefore, navigating gliders in the Long Bay experiments required the most recent glider surfacing data and near-real-time ocean flow data.
To support the Long Bay experiments under strong, highly variable flow, we extended GCCS into GENIoS, which is composed of the following modules: glider planner, glider simulator, environmental input manager, and dockserver handler, shown in Fig. 4 [please refer to Paley et al. (2008) for details about the glider planner and the glider simulator]. Compared to GCCS, GENIoS incorporates the following two major additional features associated with the environmental input manager and the dockserver handler, respectively: 1) user-defined or general oceanic environmental inputs (e.g., oceanic general circulation models) for planning a glider trajectory and computing waypoints, and 2) a communication interface with dockservers for obtaining the most recent glider surfacing data and sending waypoints based on the recently received surfacing data in real time.
Data flow diagram of GENIoS. The glider simulator simulates gliders according to the 3D kinematics model of the glider and produces glider sensing and navigational data very similar to the data from the real glider. When GENIoS is controlling a real glider, the simulator obtains the real glider data via the dockserver handler interface. The glider planner designs predicted trajectories for the real/simulated gliders using the glider data produced by the glider simulator and transmits waypoints computed based on the predicted trajectories to the dockserver via the dockserver handler interface. The environmental input manager provides simulated or predicted ocean environments to the simulator and the planner.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Data flow diagram of GENIoS. The glider simulator simulates gliders according to the 3D kinematics model of the glider and produces glider sensing and navigational data very similar to the data from the real glider. When GENIoS is controlling a real glider, the simulator obtains the real glider data via the dockserver handler interface. The glider planner designs predicted trajectories for the real/simulated gliders using the glider data produced by the glider simulator and transmits waypoints computed based on the predicted trajectories to the dockserver via the dockserver handler interface. The environmental input manager provides simulated or predicted ocean environments to the simulator and the planner.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Data flow diagram of GENIoS. The glider simulator simulates gliders according to the 3D kinematics model of the glider and produces glider sensing and navigational data very similar to the data from the real glider. When GENIoS is controlling a real glider, the simulator obtains the real glider data via the dockserver handler interface. The glider planner designs predicted trajectories for the real/simulated gliders using the glider data produced by the glider simulator and transmits waypoints computed based on the predicted trajectories to the dockserver via the dockserver handler interface. The environmental input manager provides simulated or predicted ocean environments to the simulator and the planner.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
For the fast acquisition of the latest surfacing information and the fast transmission of waypoints, GENIoS incorporates the dockserver handler interface, which enables direct data communication between GENIoS and the dockserver via network protocols such as the secure shell protocol (SSH) and the secure file transfer protocol (SFTP). Figure 5 shows the mechanism of the dockserver handler. The Slocum glider communicates with glider pilots via terminal software on a remote computer. The most commonly used terminal for the data communication of the Slocum glider is the glider terminal provided by Teledyne Webb Research. Using the glider terminal, a pilot can start glider missions, check the glider or mission status, change the settings of navigational/sampling strategies, and transfer collected glider data. While a mission is running, the glider terminal logs all text outputs, including surfacing information transmitted from a glider. Using the dockserver handler interface, GENIoS continuously monitors glider log files on the dockserver. When the latest glider surfacing information is reported on the dockserver, GENIoS obtains glider-navigation-related information without waiting for the glider data files to be transmitted and processed, enabling as fast a waypoint computation as possible after a glider surfaces.
Diagram of the GENIoS dockserver handler. The handler obtains glider information by polling log files on the dockserver and checks for new information. First, the handler checks the status of the glider mission. If mission information is updated on the dockserver, then the handler checks whether the information is about a new mission or an ongoing mission. If it is a new mission, then the handler updates all the glider parameters in the simulator and the planner affected by a mission change (e.g., the glider surfacing interval). Then, the handler checks for new surface information such as surfacing, waypoint transmission, waypoint reload, and diving.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Diagram of the GENIoS dockserver handler. The handler obtains glider information by polling log files on the dockserver and checks for new information. First, the handler checks the status of the glider mission. If mission information is updated on the dockserver, then the handler checks whether the information is about a new mission or an ongoing mission. If it is a new mission, then the handler updates all the glider parameters in the simulator and the planner affected by a mission change (e.g., the glider surfacing interval). Then, the handler checks for new surface information such as surfacing, waypoint transmission, waypoint reload, and diving.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Diagram of the GENIoS dockserver handler. The handler obtains glider information by polling log files on the dockserver and checks for new information. First, the handler checks the status of the glider mission. If mission information is updated on the dockserver, then the handler checks whether the information is about a new mission or an ongoing mission. If it is a new mission, then the handler updates all the glider parameters in the simulator and the planner affected by a mission change (e.g., the glider surfacing interval). Then, the handler checks for new surface information such as surfacing, waypoint transmission, waypoint reload, and diving.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
In addition to the fast acquisition of glider data and the fast transmission of waypoints, the dockserver handler interface also enables GENIoS to transmit a waypoint list to a dockserver in parallel with the data transmission between the dockserver and a glider, enabling a seamless waypoint update. During the Long Bay experiment, the entire process of waypoint computation and update required less than 2 min on average out of approximately 25 min of the total surface time until a new set of waypoints was ready to send to a glider. Moreover, the interface handles any data communication related to the status of a glider and its ongoing mission, enabling autonomous glider operation through scripted glider handling.
To more thoroughly understand the behavior of gliders in the ocean and to account for the most recent ocean observations, we developed the environmental input manager that helps GENIoS employ various real/simulated oceanic data in real time. First, for actual field experiments, it brings ocean data from the general ocean model or the ocean observation system into GENIoS for the guidance of glider navigation in real time through the Open-Source Project for a Network Data Access Protocol (OPeNDAP) framework (Cornillon et al. 2003). Thus far, we have incorporated Wave Radar (WERA), a type of HF radar; the South Atlantic Bight and Gulf of Mexico (SABGOM) model (Hyun and He 2010); the Hybrid Coordinate Ocean Model (HYCOM) (Bleck 2002); the Advanced Circulation (ADCIRC) model output (Luettich et al. 1992). Employing oceanic data through the environmental input manager enables the guidance of underwater gliders by GENIoS to be more adaptive to environmental changes predicted by oceanic data models. Second, for simulated experiments, the environmental input manager allows GENIoS to navigate a glider under a simulated field using a user-defined flow model, enabling us to analyze glider behaviors in unexpected or episodic conditions.
4. Path planning assisted by predictive ocean models
For the Long Bay deployments, we develop a new computationally efficient hybrid method of ocean current modeling. The method approximates the tidal and nontidal components of flow by using tidal ocean model ADCIRC and a glider-derived flow estimate. We test the method in the Long Bay deployments by implementing it in path planning on an onshore computer. To plan a path of a glider under flow, we design a flow-canceling controller. Using predicted flow from our ocean current model and the flow-canceling controller, our path planning algorithm computes the predicted trajectory of a glider under flow and generates waypoints based on the predicted trajectory.
a. Ocean current modeling
To increase navigation accuracy, the default navigation method of the Slocum glider computes the flow estimate based on the dead reckoning error accumulated over an underwater travel leg of a glider and navigates the glider for its next leg of underwater travel. Since ocean currents contain tidal components, there is a phase difference between real flow experienced by the glider underwater and glider-estimated flow computed prior to diving, illustrated in Fig. 6. This out-of-phase flow estimate may be acceptable if the influence of flow on the glider navigation is trivial or if a surfacing interval is small, so that the glider can update its estimated flow frequently. However, this phase difference significantly reduces navigation accuracy under a flow field with strong temporal variations. Thus, instead of using glider-derived flow estimates, incorporating predictions from ocean models into navigation may help mitigate the phase problem.
Illustration of a phase difference between real (“true”) flow (red solid lines) and glider-derived flow (green dashed lines) estimated by Modena in LB2013. To represent real flow, an estimated flow that has the same phase with real flow is reconstructed from glider-derived flow estimates collected during the experiment. Since, according to Eq. (1), a glider-derived flow estimate is average flow velocity over one subsurface phase interval, the mean flow (blue dotted lines) is generated by shifting the glider-derived flow estimates by dead reckoning time of each subsurface phase to help illustrate the phase difference. As the figure shows, the default glider navigation method may suffer from the phase difference between the actual flow and the estimated flow.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Illustration of a phase difference between real (“true”) flow (red solid lines) and glider-derived flow (green dashed lines) estimated by Modena in LB2013. To represent real flow, an estimated flow that has the same phase with real flow is reconstructed from glider-derived flow estimates collected during the experiment. Since, according to Eq. (1), a glider-derived flow estimate is average flow velocity over one subsurface phase interval, the mean flow (blue dotted lines) is generated by shifting the glider-derived flow estimates by dead reckoning time of each subsurface phase to help illustrate the phase difference. As the figure shows, the default glider navigation method may suffer from the phase difference between the actual flow and the estimated flow.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Illustration of a phase difference between real (“true”) flow (red solid lines) and glider-derived flow (green dashed lines) estimated by Modena in LB2013. To represent real flow, an estimated flow that has the same phase with real flow is reconstructed from glider-derived flow estimates collected during the experiment. Since, according to Eq. (1), a glider-derived flow estimate is average flow velocity over one subsurface phase interval, the mean flow (blue dotted lines) is generated by shifting the glider-derived flow estimates by dead reckoning time of each subsurface phase to help illustrate the phase difference. As the figure shows, the default glider navigation method may suffer from the phase difference between the actual flow and the estimated flow.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
We employ the predictive tidal ocean model ADCIRC for glider navigation in the Long Bay experiment. ADCIRC solves shallow water equations by using a finite element method with a generalized wave continuity formulation in 2D and 3D. Blanton et al. (2004) introduced an implemented version of ADCIRC for the South Atlantic Bight and rigorously validated the model at multiple locations near the coast and on the shelf in the South Atlantic Bight. This implementation is a tidal database based on simulation runs using ADCIRC and provides depth-averaged flow predictions. The database stores tidal harmonic constituents of sea surface height and depth-averaged flow velocity of the barotropic tide as the amplitude and phase angle of equilibrium tidal constituents in the u and υ directions at each grid point, respectively.
b. Flow-canceling algorithm
Path planning of a glider navigating to the target position under the influence of flow. Given position 
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Path planning of a glider navigating to the target position under the influence of flow. Given position
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Path planning of a glider navigating to the target position under the influence of flow. Given position
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
c. Path planning and waypoint generation
We introduce our path planning and waypoint generation algorithm in algorithm 2 (Table 2). In the algorithm, to predict a reference trajectory, we used the particle model with flow that is introduced in Paley (2007). Suppose a glider is predicted to dive at time 
Algorithm 2: Path planning and waypoint generation for the glider using predictions from an ocean model.
Based on a predicted trajectory, we compute waypoints for a glider such that by following a series of waypoints, the glider can track the predicted trajectory. A similar idea is introduced in Smith et al. (2010), where waypoints for a predicted trajectory under flow are introduced as “alternate” waypoints. We form a series of waypoints by linear interpolation such that the estimated travel time between two neighboring waypoints meets the waypoint interval 
5. Results
In this section, we provide the experimental and simulation results of our glider navigation method compared to the default navigation method. First, we describe the experimental and simulation setup. We also validate our EHOM algorithm by comparing the predicted flow generated by EHOM with the glider-estimated flow collected during the Long Bay deployments. Based on the glider data from the deployments, we generate reconstructed flow to simulate gliders driven by the default glider navigation method. Then, we evaluate the qualitative and quantitative performance of the proposed and default navigation methods.
a. Experimental and simulation setup
In the Long Bay deployments, gliders typically surfaced every 4–5 h, communicating with a dockserver via Iridium satellite communication at each surfacing event. The surface time consists of data transmission, surface dialogue display, command wait and delay, waypoint transfer and reload, and GPS updates (in the order of larger to smaller time cost). The data transmission time depends on the user-defined setup of the glider mission (e.g., the list of variables that are sent to the shore and the frequency at which they are subsampled for the mission). Our setup in the Long Bay deployments was minimal, so that the expected data transmission time was 10–12 min out of approximately 25 min of the total surface time.
While gliders were at the surface of water communicating with a dockserver, waypoints were generated using algorithm 2 (Table 2). The length of the prediction horizon was W = 12 h to provide redundant waypoints in case that the waypoint transfer fail because of communication abortion. The waypoint interval was chosen to be 
(top) Glider-derived flow estimates (blue lines) by Modena in LB2013 with the predicted flow (red lines) by EHOM in the x and y directions. At each surfacing event, the predicted flow for the midpoint between the current and next surfacing positions was generated from the current surfacing event to the next with the time step size of 5 min. (bottom) Absolute values of errors between the glider-derived flow estimates and the flow forecasts in the x and y directions.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
(top) Glider-derived flow estimates (blue lines) by Modena in LB2013 with the predicted flow (red lines) by EHOM in the x and y directions. At each surfacing event, the predicted flow for the midpoint between the current and next surfacing positions was generated from the current surfacing event to the next with the time step size of 5 min. (bottom) Absolute values of errors between the glider-derived flow estimates and the flow forecasts in the x and y directions.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
(top) Glider-derived flow estimates (blue lines) by Modena in LB2013 with the predicted flow (red lines) by EHOM in the x and y directions. At each surfacing event, the predicted flow for the midpoint between the current and next surfacing positions was generated from the current surfacing event to the next with the time step size of 5 min. (bottom) Absolute values of errors between the glider-derived flow estimates and the flow forecasts in the x and y directions.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
To compare our navigation method with the default glider navigation method, we simulated gliders driven by the default glider navigation method. The navigation parameters for a simulated glider corresponding to each of the real gliders are determined from the experimental data collected during the deployments. All the simulated gliders dive and climb at the desired pitch angle of 26° between 3 m below the surface of water and 3 m above the bottom of water, where the overall depth ranges from 30 (LB1) to 175 m (LB3). The observed vertical speed of Ramses and Modena is 0.17 m s−1 with the horizontal through-water speed of 0.31–0.32 m s−1. The glider Pelagia was found to perform with a much slower through-water speed due to instrument configuration. Based on the experimental data, we set its vertical speed to 0.133 m s−1 with the horizontal through-water speed of 0.24–0.25 m s−1.
To simulate gliders in an ocean environment similar to that where the real gliders navigated in the Long Bay deployments, we reconstruct flow from glider-derived flow estimates collected during the deployments. The basic idea of reconstructing flow is similar to that of the EHOM algorithm. Given the surfacing data of a glider for k surfacing events, we compute estimates of average tidal flow at each surfacing event using Eq. (2). By subtracting the average tidal flow estimates 
b. Navigation performance using predictive ocean models
The qualitative evaluation of the performance of navigation methods is shown in Fig. 9, which represents an ideal case with a perfect model. The figure displays the trajectories of two simulated gliders navigating a transect line (the red line) from LB2 (the bottom right) to LB1 (the top left) under a simulated flow field. 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 predicted 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. This result shows that our method can provide more precise control under flow.
Trajectories of simulated gliders driven by the default and proposed navigation methods for the transect track (the red line). The dark blue line with rectangles is the trajectory of the glider using our method, and the light blue line with circles is the trajectory of the glider using the default navigation method.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Trajectories of simulated gliders driven by the default and proposed navigation methods for the transect track (the red line). The dark blue line with rectangles is the trajectory of the glider using our method, and the light blue line with circles is the trajectory of the glider using the default navigation method.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Trajectories of simulated gliders driven by the default and proposed navigation methods for the transect track (the red line). The dark blue line with rectangles is the trajectory of the glider using our method, and the light blue line with circles is the trajectory of the glider using the default navigation method.
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
To quantify the performance of navigation methods, we compare the navigation results of real gliders driven by our method and that of simulated gliders driven by the default navigation method at each surfacing event. In the simulation, there exist the errors and limitations of the glider model, the controller design, and the ocean model. Hence, to keep the errors from accumulating, we reset the position of simulated gliders to the same position of real gliders after one surfacing interval. Let us consider target position 
To evaluate the overall performance of our method compared to the default navigation method, we propose two performance metrics. Let us define 
in which the predicted surfacing positions of the real and simulated gliders are 
To study the navigation progress of real and simulated gliders over one subsurface phase, we examine 
Figure 10 shows the performance of navigation for transect gliders Pelagia and Modena. Pelagia traversed a transect line between LB1 and LB2 (
Performance of the proposed and default navigation methods for the transect mission for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March and (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February. Performance evaluated using metrics (top panels) 
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Performance of the proposed and default navigation methods for the transect mission for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March and (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February. Performance evaluated using metrics (top panels)
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Performance of the proposed and default navigation methods for the transect mission for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March and (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February. Performance evaluated using metrics (top panels)
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
In Fig. 11, Ramses kept station near LB3 as a virtual mooring at the edge of the Gulf Stream. The top plots of the figure display the performance of glider navigation based on the first metric, 
Performance of the proposed and default navigation methods for the virtual mooring mission for Ramses (a) from 1400 UTC 26 February to 1600 UTC 28 February and (b) from 2000 UTC 23 March to 0300 UTC 26 March. Performance evaluated using metrics (top panel of each pair) 
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Performance of the proposed and default navigation methods for the virtual mooring mission for Ramses (a) from 1400 UTC 26 February to 1600 UTC 28 February and (b) from 2000 UTC 23 March to 0300 UTC 26 March. Performance evaluated using metrics (top panel of each pair)
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Performance of the proposed and default navigation methods for the virtual mooring mission for Ramses (a) from 1400 UTC 26 February to 1600 UTC 28 February and (b) from 2000 UTC 23 March to 0300 UTC 26 March. Performance evaluated using metrics (top panel of each pair)
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Glider-estimated flow during the deployments for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March, (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February, (c) Ramses from 1400 UTC 26 February to 1600 UTC 28 February, and (d) Ramses from 2000 UTC 23 March to 0300 UTC 26 March. Figure shows the Euclidean norm of the flow and provides the mean μ and the variance 
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Glider-estimated flow during the deployments for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March, (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February, (c) Ramses from 1400 UTC 26 February to 1600 UTC 28 February, and (d) Ramses from 2000 UTC 23 March to 0300 UTC 26 March. Figure shows the Euclidean norm of the flow and provides the mean μ and the variance
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
Glider-estimated flow during the deployments for (a) Pelagia from 0300 UTC 17 March to 0530 UTC 19 March, (b) Modena from 2030 UTC 25 February to 2230 UTC 28 February, (c) Ramses from 1400 UTC 26 February to 1600 UTC 28 February, and (d) Ramses from 2000 UTC 23 March to 0300 UTC 26 March. Figure shows the Euclidean norm of the flow and provides the mean μ and the variance
Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-14-00098.1
6. Conclusions and future work
This paper presents a glider navigation strategy that improves the navigation performance of the glider by incorporating predictive ocean models. Our method uses the EHOM algorithm that models ocean currents around gliders and guides them by path planning. Using our glider navigation support system, GENIoS, the proposed method was successfully applied into the LB2012 and LB2013 experiments, in which we deployed gliders in the ocean where strong tides and the Gulf Stream current make highly variable ocean circulation. This challenging ocean condition emphasized the importance of a better glider navigation method. GENIoS also helped simulate gliders driven by the default glider navigation method under reconstructed flow. To examine the performance of real gliders driven by our method and that of simulated gliders driven by the default glider navigation method, we evaluated two proposed performance metrics. The study results demonstrated the effectiveness and benefits of the proposed method over the default glider navigation method in the presence of temporal and spatial variations. While the paper presents the proposed approach applied to underwater gliders, it can be extended to any autonomous underwater vehicles to improve their performance of navigation.
In this paper, EHOM generated predicted flow for the experiments and the simulation. However, since the algorithm relies on glider-derived flow estimates to generate the nontidal component of flow, the validity of the predicted flow is guaranteed only in the local area around gliders (i.e., the spatial variability is limited). To provide broad spatial variability, we will employ HF-radar observations, whose historic dataset can be employed to predict ocean surface currents (e.g., Frolov et al. 2012). Then, we will reevaluate the ocean current prediction algorithm and the glider navigation performance. Along with the ocean current modeling algorithm, we will improve our glider control algorithm for our future deployments.
Acknowledgments
The authors thank two anonymous reviewers for their comments. The research work is supported by ONR Grants N00014-09-1-1074 and N00014-10-10712 (YIP), and NSF Grants ECCS-0841195 (CAREER), CNS-0931576, OCE-1032285, and IIS-1319874.
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