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Gaurav S Sukhatme - One of the best experts on this subject based on the ideXlab platform.
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risk aware path planning for autonomous underwater vehicles using predictive Ocean Models
Journal of Field Robotics, 2013Co-Authors: Arvind Pereira, Jonathan Binney, Geoffrey A Hollinger, Gaurav S SukhatmeAbstract:Recent advances in Autonomous Underwater Vehicle (AUV) technology have facilitated the collection of Oceanographic data at a fraction of the cost of ship-based sampling methods. Unlike Oceanographic data collection in the deep Ocean, operation of AUVs in coastal regions exposes them to the risk of collision with ships and land. Such concerns are particularly prominent for slow-moving AUVs since Ocean current magnitudes are often strong enough to alter the planned path significantly. Prior work using predictive Ocean currents relies upon deterministic outcomes, which do not account for the uncertainty in the Ocean current predictions themselves. To improve the safety and reliability of AUV operation in coastal regions, we introduce two stochastic planners: (a) a Minimum Expected Risk planner and (b) a risk-aware Markov Decision Process, both of which have the ability to utilize Ocean current predictions probabilistically. We report results from extensive simulation studies in realistic Ocean current fields obtained from widely used regional Ocean Models. Our simulations show that the proposed planners have lower collision risk than state-of-the-art methods. We present additional results from field experiments where Ocean current predictions were used to plan the paths of two Slocum gliders. Field trials indicate the practical usefulness of our techniques over long-term deployments, showing them to be ideal for AUV operations.
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an investigation on the accuracy of regional Ocean Models through field trials
International Conference on Robotics and Automation, 2013Co-Authors: Ryan N Smith, Jonathan Kelly, Kimia Nazarzadeh, Gaurav S SukhatmeAbstract:Recent efforts in mission planning for underwater vehicles have utilised predictive Models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these Models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of Ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions of two autonomous gliders conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an Ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the Ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.
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an investigation on the accuracy of regional Ocean Models through field trials
Institute for Future Environments; Science & Engineering Faculty, 2013Co-Authors: Ryan N Smith, Jonathan Kelly, Kimia Nazarzadeh, Gaurav S SukhatmeAbstract:Recent efforts in mission planning for underwater vehicles have utilised predictive Models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these Models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of Ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an Ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the Ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.
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autonomous underwater vehicle trajectory design coupled with predictive Ocean Models a case study
International Conference on Robotics and Automation, 2010Co-Authors: Ryan N Smith, Arvind Pereira, Yi Chao, Peggy Li, David A Caron, Burton H Jones, Gaurav S SukhatmeAbstract:Data collection using Autonomous Underwater Vehicles (AUVs) is increasing in importance within the Oceanographic research community. Contrary to traditional moored or static platforms, mobile sensors require intelligent planning strategies to maneuver through the Ocean. However, the ability to navigate to high-value locations and collect data with specific scientific merit is worth the planning efforts. In this study, we examine the use of Ocean model predictions to determine the locations to be visited by an AUV, and aid in planning the trajectory that the vehicle executes during the sampling mission. The objectives are: a) to provide near-real time, in situ measurements to a large-scale Ocean model to increase the skill of future predictions, and b) to utilize Ocean model predictions as a component in an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. We present an algorithm designed to generate paths for AUVs to track a dynamically evolving Ocean feature utilizing Ocean model predictions. This builds on previous work in this area by incorporating the predicted current velocities into the path planning to assist in solving the 3-D motion planning problem of steering an AUV between two selected locations. We present simulation results for tracking a fresh water plume by use of our algorithm. Additionally, we present experimental results from field trials that test the skill of the model used as well as the incorporation of the model predictions into an AUV trajectory planner. These results indicate a modest, but measurable, improvement in surfacing error when the model predictions are incorporated into the planner.
Laurent Debreu - One of the best experts on this subject based on the ideXlab platform.
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Brinkman volume penalization for bathymetry in three-dimensional Ocean Models
Ocean Modelling, 2020Co-Authors: Laurent Debreu, Nicholas K.-r. Kevlahan, Patrick MarchesielloAbstract:Abstract Accurate and stable implementation of bathymetry boundary conditions remains a challenging problem. The dynamics of Ocean flow often depend sensitively on satisfying bathymetry boundary conditions and correctly representing their complex geometry. Generalized (e.g. σ ) terrain-following coordinates are often used in Ocean Models, but they require smoothing the bathymetry to reduce pressure gradient errors (Mellor et al., 1994). Geopotential z -coordinates are a common alternative that avoid pressure gradient and numerical diapycnal diffusion errors, but they generate spurious flow due to their “staircase” geometry. We introduce a new Brinkman volume penalization to approximate the no-slip boundary condition and complex geometry of bathymetry in Ocean Models. This approach corrects the staircase effect of z -coordinates, does not introduce any new stability constraints on the geometry of the bathymetry and is easy to implement in an existing Ocean model. The porosity parameter allows modelling subgrid scale details of the geometry. We illustrate the penalization and confirm its accuracy by applying it to three standard test flows: upwelling over a sloping bottom, resting state over a seamount and internal tides over highly peaked bathymetry features. In future work we will explore applying the penalization to more realistic bathymetry configurations, and moving boundaries such as melting/freezing ice shelves.
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The numerics of hydrostatic structured-grid coastal Ocean Models: state of the art and future perspectives
Ocean Modelling, 2018Co-Authors: Knut Klingbeil, Laurent Debreu, Florian Lemarié, Hans BurchardAbstract:The state of the art of the numerics of hydrodynamic non-hydrostatic structured-grid coastal Ocean Models is reviewed here. First, some fundamental differences in the hydrodynamics of the coastal Ocean, such as the large surface elevation variation compared to the mean water depth, are contrasted against large scale Ocean dynamics. Then the hydrodynamic equations as they are used in coastal Ocean Models as well as in large scale Ocean Models are presented, including parameterisations for turbulent transports. As steps towards discretisation, coordinate transformations and vertical and horizontal discretisations based on a finite-volume approach are discussed with focus on the specific requirements for coastal Ocean Models. As in large scale Ocean Models, splitting of internal and external modes is essential also for coastal Ocean Models, but specific care is needed when wetting an drying of inter-tidal flats is included. As one obvious characteristics of coastal Ocean Models, open boundaries occur and need to be treated in a way that correct model forcing from outside is transmitted to the model domain without reflecting waves from the inside. Here, also new developments in two-way nesting are presented. Single processes such as internal inertia-gravity waves, advection and turbulence closure Models are discussed with focus on the coastal scales. Some overview on existing hydrostatic structured-grid coastal Ocean Models is given, including their extensions towards non-hydrostatic Models. Finally, an outlook on future perspectives is made.
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On effective resolution in Ocean Models
Ocean Modelling, 2016Co-Authors: Yves Soufflet, Laurent Debreu, Patrick Marchesiello, Florian Lemarié, Julien Jouanno, Xavier Capet, Rachid BenshilaAbstract:The increase of model resolution naturally leads to the representation of a wider energy spectrum. As a result, in recent years, the understanding of Oceanic submesoscale dynamics has significantly improved. However, dissipation in submesoscale Models remains dominated by numerical constraints rather than physical ones. Effective resolution is limited by the numerical dissipation range, which is a function of the model numerical filters (assuming that dispersive numerical modes are efficiently removed). We present a Baroclinic Jet test case set in a zonally reentrant channel that provides a controllable test of a model capacity at resolving submesoscale dynamics. We compare simulations from two Models, ROMS and NEMO, at different mesh sizes (from 20 to 2 km). Through a spectral decomposition of kinetic energy and its budget terms, we identify the characteristics of numerical dissipation and effective resolution. It shows that numerical dissipation appears in different parts of a model, especially in spatial advection-diffusion schemes for momentum equations (KE dissipation) and tracer equations (APE dissipation) and in the time stepping algorithms. Effective resolution, defined by scale-selective dissipation, is inadequate to qualify traditional Ocean Models with low-order spatial and temporal filters, even at high grid resolution. High-order methods are better suited to the concept and probably unavoidable. Fourth-order filters are suited only for grid resolutions less than a few kilometers and momentum advection schemes of even higher-order may be justified. The upgrade of time stepping algorithms (from filtered Leapfrog), a cumbersome task in a model, appears critical from our results, not just as a matter of model solution quality but also of computational efficiency (extended stability range of predictor-corrector schemes). Effective resolution is also shaken by the need for non scale-selective barotropic mode filters and requires carefully addressing the issue of mode splitting errors. Possibly the most surprising result is that submesoscale energy production is largely affected by spurious diapycnal mixing (APE dissipation). This result justifies renewed efforts in reducing tracer mixing errors and poses again the question of how much vertical diffusion is at work in the real Ocean.
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Numerical delicacies associated with the use of isoneutral mixing operators in Ocean Models
2013Co-Authors: Florian Lemarié, Laurent Debreu, Patrick MarchesielloAbstract:Ocean Models usually rely on a tracer mixing operator which diffuses along isoneutral directions. This requirement is imposed by the highly adiabatic nature of the Oceanic interior, and a numerical simulation needs to respect these small levels of dianeutral mixing to maintain physically realistic results. This is a key issue nowadays in Oceanic numerical Models (e.g., Hansen et al., 2011 "Earth's energy imbalance and implications"). For non-isopycnic Models, rotated mixing operators must therefore be used. In continuation of the pioneering work of Griffies et al. (1998) and Beckers et al. (2000) in this field, we, first, exhaustively present the performance of various space-time discretizations in terms of stability, accuracy, tracer variance dissipation and min-max violations for the harmonic and biharmonic rotated operators. From this study, we can anticipate the flaws of the different schemes in practical situations. Because global climate Models are now targeting increasingly higher horizontal resolution, the question of the viability of an isoneutral biharmonic operator is not only relevant for the regional modeling community but also for the Ocean climate community. A new way of handling the temporal discretization of this type of operator is thus introduced. This scheme requires only the resolution of a simple one-dimensional tridiagonal system in the vertical direction to provide the same stability limit of the non-rotated operator. The results are illustrated by idealized numerical experiments of the diffusion of a passive tracer along isoneutral directions as well as fully realistic eddy-resolving and eddy-permitting configurations. Those numerical results show that rotated operators must be used with care and can sometimes lead to an accumulation of dispersive errors which can be seen in T/S diagrams. Furthermore, we will offer a discussion on some possible alternatives to the use of rotated operators.
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On the Stability and Accuracy of the Harmonic and Biharmonic Isoneutral Mixing Operators in Ocean Models
Ocean Modelling, 2012Co-Authors: Florian Lemarié, Laurent Debreu, Alexander Shchepetkin, Jim McwilliamsAbstract:Ocean Models usually rely on a tracer mixing operator which diffuses along isoneutral directions. This requirement is imposed by the highly adiabatic nature of the Oceanic interior, and a numerical simulation needs to respect these small levels of dianeutral mixing to maintain physically realistic results. For non-isopycnic Models this is however non-trivial due to the non-alignment of the vertical coordinate isosurfaces with local isoneutral directions, rotated mixing operators must therefore be used. This paper considers the numerical solution of initial boundary value problems for the harmonic (Laplacian) and biharmonic rotated diffusion operators. We provide stability criteria associated with the conventional space-time discretizations of the isoneutral Laplacian operator currently in use in general circulation Models. Furthermore, we propose and study possible alternatives to those schemes. A new way to handle the temporal discretization of the rotated biharmonic operator is also introduced. This scheme requires only the resolution of a simple one-dimensional tridiagonal system in the vertical direction to provide the same stability limit of the non-rotated operator. The performance of the various schemes in terms of stability and accuracy is illustrated by idealized numerical experiments of the diffusion of a passive tracer along isoneutral directions.
Stephen M. Griffies - One of the best experts on this subject based on the ideXlab platform.
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Vertical resolution of baroclinic modes in global Ocean Models
Ocean Modelling, 2017Co-Authors: K. D. Stewart, A. Mcc. Hogg, Stephen M. Griffies, Aidan Heerdegen, Marshall L. Ward, Paul Spence, Matthew H. EnglandAbstract:Abstract Improvements in the horizontal resolution of global Ocean Models, motivated by the horizontal resolution requirements for specific flow features, has advanced modelling capabilities into the dynamical regime dominated by mesoscale variability. In contrast, the choice of the vertical grid remains a subjective choice, and it is not clear that efforts to improve vertical resolution adequately support their horizontal counterparts. Indeed, considering that the bulk of the vertical Ocean dynamics (including convection) are parameterized, it is not immediately obvious what the vertical grid is supposed to resolve. Here, we propose that the primary purpose of the vertical grid in a hydrostatic Ocean model is to resolve the vertical structure of horizontal flows, rather than to resolve vertical motion. With this principle we construct vertical grids based on their abilities to represent baroclinic modal structures commensurate with the theoretical capabilities of a given horizontal grid. This approach is designed to ensure that the vertical grids of global Ocean Models complement (and, importantly, to not undermine) the resolution capabilities of the horizontal grid. We find that for z -coordinate global Ocean Models, at least 50 well-positioned vertical levels are required to resolve the first baroclinic mode, with an additional 25 levels per subsequent mode. High-resolution Ocean-sea ice simulations are used to illustrate some of the dynamical enhancements gained by improving the vertical resolution of a 1/10° global Ocean model. These enhancements include substantial increases in the sea surface height variance (∼30% increase south of 40°S), the barotropic and baroclinic eddy kinetic energies (up to 200% increase on and surrounding the Antarctic continental shelf and slopes), and the overturning streamfunction in potential density space (near-tripling of the Antarctic Bottom Water cell at 65°S).
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Ocean Modeling in an Eddying Regime - Formulating the Equations of Ocean Models
Ocean Modeling in an Eddying Regime, 2008Co-Authors: Stephen M. Griffies, Alistair AdcroftAbstract:the purpose of this chapter is to formulate the equations of Ocean Models and to outline solution methods. Global Ocean climate Models, including those representing mesoscale eddies, are traditionally based on the hydrostatic primitive equations. We nonetheless discuss extensions to the more fundamental non-hydrostatic equations, which are used in certain fine resolution process studies, such as for convection and mixing, and increasingly for coastal and regional modeling. the target audience for this chapter includes students and researchers interested in fundamental physical and numerical aspects of Ocean Models. We thus aim to present a reasonably concise yet thorough accounting of the rationalization required to pose the problem of Ocean modeling. We take a first principles perspective to allow readers with little background in Ocean fluid mechanics to follow the full development. this goal necessitates starting from the basics as we develop the model equations and methods. For this purpose, much material was culled from various research papers and textbooks, such as Gill [1982], Pedlosky [1987], Lion et al. [1992], Marshall et al. [1997], Haidvogel and Beckmann [1999], Griffies et al. [2000a], Griffies [2004, 2005], Vallis [2006], Higdon [2006], and Muller [2006]. Our presentation focuses on developing the fluid mechanics of the Ocean and weaves into this discussion elements appropriate for the formulation of Ocean Models. We begin with a discussion of Ocean fluid kinematics in Section 2 where we introduce mass conservation as well as the notions of dia-surface transport. Section 3 then focuses on tracer budgets, which follow quite naturally from mass budgets, only with the introduction of possible nontrivial fluxes of tracer which occur in the absence of mass fluxes. Section 4 introduces a dynamical description that arises from the use of Newton’s Second Law of Motion applied to continuous fluid parcels. Section 5 presents the equation of state for density and discusses the material evolution of density. Section 6 derives some energetic properties of the equations of motion, with energetics providing a guiding principle for developing certain numerical solution methods. Section 7 introduces notions of non-equilibrium thermodynamics, a subject which forms the basis for establishing budgets of heat within the Ocean. Section 8 linearizes the dynamical equations to deduce various linear modes of motion fundamental to Ocean dynamics. these motions also have direct relevance to the development of methods used to solve the Ocean equations. they furthermore motivate certain approximations or filters used to simplify the supported dynamical modes, with certain approximations described in Section 9. Section 10 presents an overview of vertical coordinates. The Formulating the Equations of Ocean Models
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tracer conservation with an explicit free surface method for z coordinate Ocean Models
Monthly Weather Review, 2001Co-Authors: Stephen M. Griffies, R C Pacanowski, Martin Schmidt, V BalajiAbstract:This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate Ocean Models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid Models. Additionally, the effects of the undulating free surface height are directly incorporated into the baroclinic momentum and tracer equations. The novel issues related to local and global tracer conservation when allowing for the top cell to undulate are the focus of this work. The method presented here is quasi-conservative locally and globally of tracer when the baroclinic and tracer time steps are equal. Important issues relevant for using this method in regional as well as large-scale climate Models are discussed and illustrated, and examples of scaling achieved on parallel computers provided.
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biharmonic friction with a smagorinsky like viscosity for use in large scale eddy permitting Ocean Models
Monthly Weather Review, 2000Co-Authors: Stephen M. Griffies, Robert HallbergAbstract:This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scale-selective, state-dependent friction operator for use in eddy-permitting geophysical fluid Models. This friction should prove most useful for large-scale Ocean Models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnal-coordinate Ocean Models.
George L Mellor - One of the best experts on this subject based on the ideXlab platform.
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the three dimensional current and surface wave equations
Journal of Physical Oceanography, 2003Co-Authors: George L MellorAbstract:Surface wave equations appropriate to three-dimensional Ocean Models apparently have not been presented in the literature. It is the intent of this paper to correct that deficiency. Thus, expressions for vertically dependent radiation stresses and a definition of the Doppler velocity for a vertically dependent current field are obtained. Other quantities such as vertically dependent surface pressure forcing are derived for inclusion in the momentum and wave energy equations. The equations include terms that represent the production of turbulence energy by currents and waves. These results are a necessary precursor for three-dimensional Ocean Models that handle surface waves together with wind- and buoyancy-driven currents. Although the third dimension has been added here, the analysis is based on the assumption that the depth dependence of wave motions is provided by linear theory, an assumption that is the basis of much of the wave literature.
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the pressure gradient conundrum of sigma coordinate Ocean Models
Journal of Atmospheric and Oceanic Technology, 1994Co-Authors: George L Mellor, Tal EzerAbstract:Abstract Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in Ocean or atmospheric numerical Models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent. In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are c...
Ryan N Smith - One of the best experts on this subject based on the ideXlab platform.
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an investigation on the accuracy of regional Ocean Models through field trials
International Conference on Robotics and Automation, 2013Co-Authors: Ryan N Smith, Jonathan Kelly, Kimia Nazarzadeh, Gaurav S SukhatmeAbstract:Recent efforts in mission planning for underwater vehicles have utilised predictive Models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these Models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of Ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions of two autonomous gliders conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an Ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the Ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.
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an investigation on the accuracy of regional Ocean Models through field trials
Institute for Future Environments; Science & Engineering Faculty, 2013Co-Authors: Ryan N Smith, Jonathan Kelly, Kimia Nazarzadeh, Gaurav S SukhatmeAbstract:Recent efforts in mission planning for underwater vehicles have utilised predictive Models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these Models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of Ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an Ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the Ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.
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autonomous underwater vehicle trajectory design coupled with predictive Ocean Models a case study
International Conference on Robotics and Automation, 2010Co-Authors: Ryan N Smith, Arvind Pereira, Yi Chao, Peggy Li, David A Caron, Burton H Jones, Gaurav S SukhatmeAbstract:Data collection using Autonomous Underwater Vehicles (AUVs) is increasing in importance within the Oceanographic research community. Contrary to traditional moored or static platforms, mobile sensors require intelligent planning strategies to maneuver through the Ocean. However, the ability to navigate to high-value locations and collect data with specific scientific merit is worth the planning efforts. In this study, we examine the use of Ocean model predictions to determine the locations to be visited by an AUV, and aid in planning the trajectory that the vehicle executes during the sampling mission. The objectives are: a) to provide near-real time, in situ measurements to a large-scale Ocean model to increase the skill of future predictions, and b) to utilize Ocean model predictions as a component in an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. We present an algorithm designed to generate paths for AUVs to track a dynamically evolving Ocean feature utilizing Ocean model predictions. This builds on previous work in this area by incorporating the predicted current velocities into the path planning to assist in solving the 3-D motion planning problem of steering an AUV between two selected locations. We present simulation results for tracking a fresh water plume by use of our algorithm. Additionally, we present experimental results from field trials that test the skill of the model used as well as the incorporation of the model predictions into an AUV trajectory planner. These results indicate a modest, but measurable, improvement in surfacing error when the model predictions are incorporated into the planner.
