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Time-Optimal Multi-Waypoint Mission Planning in Dynamic Environments

Ferris, D.L., D.N. Subramani, C.S. Kulkarni, P.J. Haley, and P.F.J. Lermusiaux, 2018. Time-Optimal Multi-Waypoint Mission Planning in Dynamic Environments. In: Oceans '18 MTS/IEEE Charleston, 22-25 October 2018. doi:10.1109/oceans.2018.8604505

The present paper demonstrates the use of exact equations to predict time-optimal mission plans for a marine vehicle that visits a number of locations in a given dynamic ocean current field. This problem bears close resemblance to that of the classic “traveling salesman”, albeit with the added complexity that the vehicle experiences a dynamic flow field while traversing the paths. The paths, or “legs”, between all goal waypoints are generated by numerically solving the exact time-optimal path planning level-set differential equations. Overall, the planning proceeds in four steps. First, current forecasts for the planning horizon is obtained utilizing our data-driven 4-D primitive equation ocean modeling system (Multidisciplinary Simulation Estimation and Assimilation System; MSEAS), forced by high-resolution tidal and real-time atmopsheric forcing fields. Second, all tour permutations are enumerated and the minimum number of times the time-optimal PDEs are to be solved is established. Third, due to the spatial and temporal dynamics, a varying start time results in different paths and durations for each leg and requires all permutations of travel to be calculated. To do so, the minimum required time-optimal PDEs are solved and the optimal travel time is computed for each leg of all enumerated tours. Finally, the tour permutation for which travel time is minimized is identified and the corresponding time-optimal paths are computed by solving the backtracking equation. Even though the method is very efficient and the optimal path can be computed serially in real-time for common naval operations, for additional computational speed, a high-performance computing cluster was used to solve the level set calculations in parallel. Our equation and software is applied to simulations of realistic naval applications in the complex Philippines Archipelago region. Our method calculates the global optimum and can serve two purposes: (a) it can be used in its present form to plan multiwaypoint missions offline in conjunction with a predictive ocean current modeling system, or (b) it can be used as a litmus test for approximate future solutions to the traveling salesman problem in dynamic flow fields.


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, and G. Shaw, 2017. Autonomy for Surface Ship Interception. In: Oceans '17 MTS/IEEE Aberdeen, 1-10, 19-22 June 2017, DOI: 10.1109/OCEANSE.2017.8084817

In recent years, the use of autonomous undersea vehicles (AUVs) for highly time-critical at-sea operations involving surface ships has received increased attention, magnifying the importance of optimal interception. Finding the optimal route to a moving target is a challenging procedure. In this work, we describe and apply our exact time-optimal path planning methodology and the corresponding software to such ship interception problems. A series of numerical ship interception experiments is completed in the southern littoral of Massachusetts, namely in Buzzards Bay and Vineyard Sound around the Elizabeth Islands and Martha’s Vineyard. Ocean currents are estimated from a regional ocean modeling system. We show that complex coastal geometry, ship proximity, and tidal current phases all play key roles influencing the time-optimal vehicle behavior. Favorable or adverse currents can shift the optimal route from one island passage to another, and can even cause the AUV to remain nearly stationary until a favorable current develops. We also integrate the Kelvin wedge wake model into our path planning software, and show that considering wake effects significantly complicates the shape of the time-optimal paths, requiring AUVs to execute sequences of abrupt turns and tacking maneuvers, even in highly idealized scenarios. Such behavior is reminiscent of ocean animals swimming in wakes. In all cases, it is shown that our level set partial differential equations successfully guide the time-optimal vehicles through regions with the most favorable currents, avoiding regions with adverse effects, and accounting for the ship wakes when present.

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

Edwards, J., J. Smith, A. Girard, D. Wickman, P.F.J. Lermusiaux, D.N. Subramani, P.J. Haley, Jr., C. Mirabito, C.S. Kulkarni, and, S. Jana, 2017. Data-driven Learning and Modeling of AUV Operational Characteristics for Optimal Path Planning. In: Oceans '17 MTS/IEEE Aberdeen, 1-5, 19-22 June 2017, DOI: 10.1109/OCEANSE.2017.8084779

Autonomous underwater vehicles (AUVs) are used to execute an increasingly challenging set of missions in commercial, environmental and defense industries. The resources available to the AUV in service of these missions are typically a limited power supply and onboard sensing of its local environment. Optimal path planning is needed to maximize the chances that these AUVs will successfully complete long endurance missions within their power budget. A time-optimal path planner has been recently developed to minimize AUV mission time required to traverse a dynamic ocean environment at a specified speed through the water. For many missions, time minimization is appropriate because the AUVs operate at a fixed propeller speed. However, the ultimate limiting constraint on AUV operations is often the onboard power supply, rather than mission time. While an empirical or theoretical relationship between mission time and power could be applied to estimate power usage in the path planner, the real power usage and availability on an AUV varies mission-to-mission, as a result of multiple factors, including vehicle buoyancy, battery charge cycle, fin configuration, and water type or quality. In this work, we use data collected from two mid-size AUVs operating in various conditions to learn the mission-to-mission variability in the power budget so that it could be incorporated into the mission planner.

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, 1-10, 19-22 June 2017, DOI: 10.1109/OCEANSE.2017.8084776

We report the results of sea exercises that demonstrate the real-time capabilities of our fundamental time-optimal path planning theory and software with real ocean vehicles. The exercises were conducted with REMUS 600 Autonomous Underwater Vehicles (AUVs) in the Buzzards Bay and Vineyard Sound Regions on 21 October and 6 December 2016. Two tests were completed: (i) 1-AUV time-optimal tests and (ii) 2-AUV race tests where one AUV followed a time-optimal path and the other a shortest-distance path between the start and finish locations. The time-optimal planning proceeded as follows. We first forecast, in real-time, the physical ocean conditions in the above regions and times utilizing our MSEAS multi-resolution primitive equation ocean modeling system. Next, we planned time-optimal paths for the AUVs using our level-set equations and real-time ocean forecasts, and accounting for operational constraints (e.g. minimum depth). This completed the planning computations performed onboard a research vessel. The forecast optimal paths were then transferred to the AUV operating system and the vehicles were piloted according to the plan. We found that the forecast currents and paths were accurate. In particular, the time-optimal vehicles won the races, even though the local currents and geometric constraints were complex. The details of the results were analyzed off-line after the sea tests.

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 American Control Conference (ACC), Seattle, WA, 2017, pp. 4595-4600. doi: 10.23919/ACC.2017.7963664

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.

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.