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Pursuit-Evasion Games in Dynamic Flow Fields via Reachability Set Analysis

Sun, W., P. Tsiotras, T. Lolla, D. N. Subramani, and P. F. J. Lermusiaux, 2017. Pursuit-Evasion Games in Dynamic Flow Fields via Reachability Set Analysis. 2017 American Control Conference. In press.

In this paper, we adopt a reachability-based approach to deal with the pursuit-evasion differential game between two players in the presence of dynamic environmental disturbances (e.g., winds, sea currents). We give conditions for the game to be terminated in terms of reachable set inclusions. Level set equations are defined and solved to generate the reachable sets of the pursuer and the evader. The corresponding time-optimal trajectories and optimal strategies can be retrieved immediately afterwards. We validate our method by applying it to a pursuit-evasion game in a simple flow field, for which an analytical solution is available.We then implement the proposed scheme to a problem with a more realistic flow field.

Autonomy for Surface Ship Interception

Mirabito, C., D.N. Subramani, T. Lolla, P.J. Haley, Jr., A. Jain, P.F.J. Lermusiaux, C. Li, D.K.P. Yue, Y. Liu, F.S. Hover, N. Pulsone, J. Edwards, K.E. Railey, G. Shaw, 2017. Autonomy for Surface Ship Interception. In: Oceans '17 MTS/IEEE Aberdeen, 19-22 June 2017, In press.

The optimal interception of ships sailing on the ocean surface has numerous applications, including search and rescue operations, inspections of ship’s hulls, ship repair and refueling, naval operations and planning, and recovery of underwater platforms. Interest in utilizing autonomous undersea vehicles (AUVs) for these operations has been increasing in recent years. In that case, the optimal recovery of these underwater vehicles by surface ships is also crucial. The time-sensitive nature of these operations render the search for an optimal route from a given point of deployment to a (possibly moving) target of paramount importance. However, numerous factors, including complex coastal geometry, time-varying and complicated currents, and a moving ship wake (further disrupting the local near-ship currents) make this a very challenging problem. Our present research motivation is thus to apply and extend our theory and schemes for optimal path planning of autonomous vehicles operating for long durations in strong and dynamic currents to the optimal interception of surface vessels. The long-term goal is to develop autonomy for AUVs to enable intercept and proximity operations with underway surface vessels, predicting and optimally using dynamic wakes, surface waves, and underwater currents. After extending our time-optimal path planning to the ship interception problem, we study a set of simulated experiments for the Buzzards Bay, Vineyard Sound, and Elizabeth Islands region in Massachusetts. We combine realistic data-assimilative ocean modeling with rigorous time- optimal control and simple ship and wake modeling. To show the versatility of the autonomy approach and also illustrate how it is needed even for the simplest of the cases, we consider several different scenarios: environments with no flow at all but with several straits, cases with time-varying currents, and finally proximity operations considering the effects of ship wakes. We extended our time-optimal path planning to ship interception and illustrated results for varied scenarios in the southern littoral of Massachusetts for varied ship and AUV speeds, start locations, and behaviors, with and without currents, and with and without ship wake effects.

Data-driven Learning and Modeling of AUV Operational Characteristics for Optimal Path Planning

Edwards, J., J. Smith, A. Girard, D. Wickman, D. N. Subramani, C. S. Kulkarni, P.J. Haley, Jr., C. Mirabito, S. Jana, P. F. J. Lermusiaux, 2017. Data-driven Learning and Modeling of AUV Operational Characteristics for Optimal Path Planning. In: Oceans '17 MTS/IEEE Aberdeen, 19-22 June 2017, In press.

The utilization of Autonomous Underwater Vehicles (AUVs) such as propelled vehicles, gliders, and floats is rapidly growing for a wide range of missions and ocean regions. For optimized utilization, the operational characteristics of the AUVs need to be modeled as accurately as needed by the optimization and specific needs of the ocean missions considered. The advent of machine learning and data sciences provides an opportunity to augment the classic engineering modeling and laboratory analyses by learning the AUV operational characteristics in situ, during and after each sea operations. Such data-driven learning is critical because, from mission to mission, the AUV usage frequently differs, the dynamic ocean environment changes, and the configuration of the AUV itself changes. For the latter, considering propelled vehicles, it is for example very common for fins and buoyancy to be modified, for payloads to be changed, and for the internal content and overall body of the AUVs to be altered. We illustrated the use of in-situ-data-driven learning and modeling of operational characteristics of AUVs for path planning. The operations and learning experiments were conducted in the Buzzards Bay, Vineyard Sound, and Martha Vineyard’s region for several AUV configurations, missions, and ocean conditions. Specifically, we identified and applied simple methods to estimate the relationships between thruster RPM with forward vehicle speed and to confirm that the specific fin configuration affects the net forward speed of the REMUS 600. Such data-based learning should be completed in real-time so as to ensure accurate F(t) models and thus time-optimal performances. These results can be employed for other types of optimal path planning and AUV missions, including energy, sensing, and surveillance optimality.

Time-Optimal Path Planning: Real-Time Sea Exercises

Subramani, D. N., P. F. J. Lermusiaux, P.J. Haley, Jr., C. Mirabito, S. Jana, C. S. Kulkarni, A. Girard, D. Wickman, J. Edwards, J. Smith, 2017. Time-Optimal Path Planning: Real-Time Sea Exercises. In: Oceans '17 MTS/IEEE Aberdeen, 19-22 June 2017, In press.

Autonomous underwater vehicles (AUVs) are employed in many applications such as ocean sensing, search and rescue operations, acoustic surveillance, and oil and gas exploitation. With advances in AUV capability and increasing mission complexity, there is a demand for predicting all reachable locations, prolonging endurance, and reducing operational costs by optimally utilizing ocean flow forecasts for navigation. For such optimal navigation, we recently developed new theory, schemes, and computational systems for exact partial differential equation-based path planning. This new level-set path planning was applied in realistic re-analysis simulations for the sustained coordinated operation of multiple collaborative AUVs for time-, coordination- and energy- optimal missions. In the present paper, our goal is to demonstrate our level-set path planning in real-time sea exercises with real AUVs in shallow coastal ocean regions with strong and dynamic currents. Our specific objectives are to report the (i) improvements to our 4-D primitive equation ocean modeling system for accurately forecasting the currents in the Buzzard’s Bay and Vineyard Sound region, (ii) results of the time-optimal path planning of REMUS 600 AUVs using our fundamental theory and real-time forecasts, (iii) portability of our software systems for real-time optimal path prediction in multiple regions and its ability to work with the AUV navigation software. These exercises were the first sea tests of our new theory and software. Our ocean forecasts had skill and time-optimal path forecasts worked with REMUS 600’s. We also identified relationships between the REMUS 600’s rpm and nominal in-water speed. The results open a new era of optimal AUV missions.

A Stochastic Optimization Method for Energy-based Path Planning

Subramani, D. N., Lolla, T., Haley Jr., P. J., Lermusiaux, P. F. J., 2015. A stochastic optimization method for energy-based path planning. In: Ravela, S., Sandu, A. (Eds.), DyDESS 2014. Vol. 8964 of LNCS. Springer, pp. 347-358.

We present a novel stochastic optimization method to compute energy-optimal paths, among all time-optimal paths, for vehicles traveling in dynamic unsteady currents. The method defines a stochastic class of instantaneous nominal vehicle speeds and then obtains the energy-optimal paths within the class by minimizing the total time-integrated energy usage while still satisfying the strong-constraint time-optimal level set equation. This resulting stochastic level set equation is solved using a dynamically orthogonal decomposition and the energy-optimal paths are then selected for each arrival time, among all stochastic time-optimal paths. The first application computes energy-optimal paths for crossing a steady front. Results are validated using a semi-analytical solution obtained by solving a dual nonlinear energy-time optimization problem. The second application computes energy-optimal paths for a realistic mission in the Middle Atlantic Bight and New Jersey Shelf/Hudson Canyon region, using dynamic data-driven ocean field estimates.

Autonomous & Adaptive Oceanographic Front Tracking On Board Autonomous Underwater Vehicles

Petillo, S., H. Schmidt, P.F.J. Lermusiaux, D. Yoerger and A. Balasuriya, 2015. Autonomous & Adaptive Oceanographic Front Tracking On Board Autonomous Underwater Vehicles. Proceedings of IEEE OCEANS'15 Conference, Genoa, Italy, 18-21 May, 2015.

Oceanic fronts, similar to atmospheric fronts, occur at the interface of two fluid (water) masses of varying characteristics. In regions such as these where there are quantifiable physical, chemical, or biological changes in the ocean environment, it is possible—with the proper instrumentation—to track, or map, the front boundary.

In this paper, the front is approximated as an isotherm that is tracked autonomously and adaptively in 2D (horizontal) and 3D space by an autonomous underwater vehicle (AUV) running MOOS-IvP autonomy. The basic, 2D (constant depth) front tracking method developed in this work has three phases: detection, classification, and tracking, and results in the AUV tracing a zigzag path along and across the front. The 3D AUV front tracking method presented here results in a helical motion around a central axis that is aligned along the front in the horizontal plane, tracing a 3D path that resembles a slinky stretched out along the front.

To test and evaluate these front tracking methods (implemented as autonomy behaviors), virtual experiments were conducted with simulated AUVs in a spatiotemporally dynamic MIT MSEAS ocean model environment of the Mid-Atlantic Bight region, where a distinct temperature front is present along the shelfbreak. A number of performance metrics were developed to evaluate the performance of the AUVs running these front tracking behaviors, and the results are presented herein.

Adaptive Sampling Using Fleets of Underwater Gliders in the Presence of Fixed Buoys using a Constrained Clustering Algorithm

Cococcioni M., B. Lazzerini and P.F.J. Lermusiaux, 2015. Adaptive Sampling Using Fleets of Underwater Gliders in the Presence of Fixed Buoys using a Constrained Clustering Algorithm. Proceedings of IEEE OCEANS'15 Conference, Genoa, Italy, 18-21 May, 2015.

This paper presents a novel way to approach the problem of how to adaptively sample the ocean using fleets of underwater gliders. The technique is particularly suited for those situations where the covariance of the field to sample is unknown or unreliable but some information on the variance is known. The proposed algorithm, which is a variant of the well-known fuzzy C-means clustering algorithm, is able to exploit the presence of non-maneuverable assets, such as fixed buoys. We modified the fuzzy C-means optimization problem statement by including additional constraints. Then we provided an algorithmic solution to the new, constrained problem.

Path Planning in Time Dependent Flow Fields using Level Set Methods

Lolla, T.; Ueckermann, M.P.; Yigit, K.; Haley, P.J.; Lermusiaux, P.F.J., 2012, Path planning in time dependent flow fields using level set methods, 2012 IEEE International Conference on Robotics and Automation (ICRA), 166-173, 14-18 May 2012, doi: 10.1109/ICRA.2012.6225364.

We develop and illustrate an efficient but rigorous methodology that predicts the time-optimal paths of ocean vehicles in dynamic continuous flows. The goal is to best utilize or avoid currents, without limitation on these currents nor on the number of vehicles. The methodology employs a new modified level set equation to evolve a wavefront from the starting point of vehicles until they reach their desired goal locations, combining flow advection with nominal vehicle motions. The optimal paths of vehicles are then computed by solving particle tracking equations backwards in time. The computational cost is linear with the number of vehicles and geometric with spatial dimensions. The methodology is applicable to any continuous flows and many vehicles scenarios. Present illustrations consist of the crossing of a canonical uniform jet and its validation with an optimization problem, as well as more complex time varying 2D flow fields, including jets, eddies and forbidden regions.

Adaptive Acoustical-Environmental Assessment for the Focused Acoustic Field-05 At-sea Exercise

Wang, D., P.F.J. Lermusiaux, P.J. Haley, W.G. Leslie and H. Schmidt, 2006. Adaptive Acoustical-Environmental Assessment for the Focused Acoustic Field-05 At-sea Exercise, Oceans 2006, 6pp, Boston, MA, 18-21 Sept. 2006, doi: 10.1109/OCEANS.2006.306904.

Variabilities in the coastal ocean environment span a wide range of spatial and temporal scales. From an acoustic viewpoint, the limited oceanographic measurements and today’s ocean modeling capabilities can’t always provide oceanic-acoustic predictions in sufficient detail and with enough accuracy. Adaptive Rapid Environmental Assessment (AREA) is a new adaptive sampling concept being developed in connection with the emergence of the Autonomous Ocean Sampling Network (AOSN) technology. By adaptively and optimally deploying in-situ measurement resources and assimilating these data in coupled nested ocean and acoustic models, AREA can dramatically improve the ocean estimation that matters for acoustic predictions and so be essential for such predictions. These concepts are outlined and preliminary methods are developed and illustrated based on the Focused Acoustic Forecasting-05 (FAF05) exercise. During FAF05, AREA simulations were run in real-time and engineering tests carried out, within the context of an at-sea experiment with Autonomous Underwater Vehicles (AUV) in the northern Tyrrhenian sea, on the eastern side of the Corsican channel.

Path Planning Methods for Adaptive Sampling of Environmental and Acoustical Ocean Fields

Yilmaz, N.K., C. Evangelinos, N.M. Patrikalakis, P.F.J. Lermusiaux, P.J. Haley, W.G. Leslie, A.R. Robinson, D. Wang and H. Schmidt, 2006a. Path Planning Methods for Adaptive Sampling of Environmental and Acoustical Ocean Fields, Oceans 2006, 6pp, Boston, MA, 18-21 Sept. 2006, doi: 10.1109/OCEANS.2006.306841.

Adaptive sampling aims to predict the types and locations of additional observations that are most useful for specific objectives, under the constraints of the available observing network. Path planning refers to the computation of the routes of the assets that are part of the adaptive component of the observing network. In this paper, we present two path planning methods based on Mixed Integer Linear Programming (MILP). The methods are illustrated with some examples based on environmental ocean fields and compared to highlight their strengths and weaknesses. The stronger method is further demonstrated on a number of examples covering multi-vehicle and multi-day path planning, based on simulations for the Monterey Bay region. The framework presented is powerful and flexible enough to accommodate changes in scenarios. To demonstrate this feature, acoustical path planning is also discussed.