Optimal navigation in planar time-varying flow: Zermelo’s problem revisited

Techy, Laszlo

doi:10.1007/s11370-011-0092-9

Cited by 31 publications

(34 citation statements)

References 12 publications

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“…The large-scale periodicity of the underlying flow is L, and we fixed δ = L/10. the best of our knowledge, only simple advecting flows have been studied so far for both ON [21,29,30] and RL [30].…”

Section: Introductionmentioning

confidence: 99%

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Biferale

Bonaccorso

Buzzicotti

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip velocity with fixed intensity, Vs, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasi-optimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process, and are therefore not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when Vs is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.Zermelo's point-to-point optimal navigation problem in the presence of a complex flow is key for a variety of geophysical and applied instances. In this work, we apply Reinforcement Learning to solve Zermelo's problem in a multi-scale 2d turbulent snapshot for both frozen-in-time velocity configurations and fully time-dependent flows. We show that our approach is able to find the quasi-optimal path to navigate from two distant points with high efficiency, even comparing with policies obtained from optimal control theory. Furthermore, we connect the learned policy with the topological flow structures that must be harnessed by the vessel to navigate fast. Our result can be seen as a first step towards more complicated applications to surface oceanographic problems and/or 3d chaotic and turbulent flows.

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Section: Introductionmentioning

confidence: 99%

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Biferale

Bonaccorso

Buzzicotti

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…There has also been some work that deals with trajectory optimization in the presence of wind. The classic Zermelo–Markov–Dubins problem has been studied in Bakolas and Tsiotras (, ) and Techy () to characterize optimal solutions, but they use sharp turns and constant speed, neither of which are practical. McGee et al () also uses a bounded turning radius assumption to yield minimum‐time trajectories with constant speed.…”

Section: Related Workmentioning

confidence: 99%

“…The dynamics of such systems must satisfy a variety of constraints imposed by the control system, flight performance charts (Prouty, ), and wind (McGee, Spry, & Hedrick, ; Seleck, Vana, Rollo, & Meiser, ; Techy, ). These constraints restrict the reachability of the system, that is, limit the set of feasible trajectories the vehicle can execute.…”

Section: Introductionmentioning

confidence: 99%

High performance and safe flight of full‐scale helicopters from takeoff to landing with an ensemble of planners

Choudhury

Dugar

Maeta

et al. 2019

Journal of Field Robotics

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Autonomous flight of unmanned full‐size rotor‐craft has the potential to enable many new applications. However, the dynamics of these aircraft, prevailing wind conditions, the need to operate over a variety of speeds and stringent safety requirements make it difficult to generate safe plans for these systems. Prior work has shown results for only parts of the problem. Here we present the first comprehensive approach to planning safe trajectories for autonomous helicopters from takeoff to landing. Our approach is based on two key insights. First, we compose an approximate solution by cascading various modules that can efficiently solve different relaxations of the planning problem. Our framework invokes a long‐term route optimizer, which feeds a receding‐horizon planner which in turn feeds a high‐fidelity safety executive. Secondly, to deal with the diverse planning scenarios that may arise, we hedge our bets with an ensemble of planners. We use a data‐driven approach that maps a planning context to a diverse list of planning algorithms that maximize the likelihood of success. Our approach was extensively evaluated in simulation and in real‐world flight tests on three different helicopter systems for duration of more than 109 autonomous hours and 590 pilot‐in‐the‐loop hours. We provide an in‐depth analysis and discuss the various tradeoffs of decoupling the problem, using approximations and leveraging statistical techniques. We summarize the insights with the hope that it generalizes to other platforms and applications.

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“…These forces and moments are even stronger when apparent mass effects are significant, as occurs for maritime vehicles, lighter-than-air vehicles, and ultralight aircraft, for example. While the simplicity of particle models makes them attractive for flow field estimation [14], [8], path planning [19], and guidance and control [17] in currents, some important flow effects can only be recovered using a rigid body dynamic model. Simplified dynamic models, as in [15], can be useful when the implicit assumption of a steady, uniform flow is appropriate, but analysis for more dynamic environments may require a higher fidelity model.…”

Section: Introductionmentioning

confidence: 99%

Vehicle Motion in Currents

Thomasson

Woolsey

2013

IEEE J. Oceanic Eng.

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In this paper, we present a nonlinear dynamic model for the motion of a rigid vehicle in a dense fluid flow that comprises a steady, nonuniform component and an unsteady, uniform component. In developing the basic equations, the nonuniform flow is assumed to be inviscid, but containing initial vorticity; further rotational flow effects may then be incorporated by modifying the angular rate used in the viscous force and moment model. The equations capture important flow-related forces and moments that are absent in simpler models. The dynamic equations are presented in terms of both the vehicle's inertial motion and its flow-relative motion. Model predictions are compared with exact analytical solutions for simple flows. Applications of the motion model include controller and observer design, stability analysis, and simulation of nonlinear vehicle dynamics in nonuniform flows. As illustrations, we use the model to analyze the motion of a cylinder in a plane laminar jet, a spherical Lagrangian drifter, and a slender underwater vehicle. For this last example, we compare predictions of the given model with those of simpler models and we demonstrate its use for flow gradient estimation. The results are applicable to not only underwater vehicles, but also to air vehicles of low relative density such as airships and ultralights.

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Optimal navigation in planar time-varying flow: Zermelo’s problem revisited

Cited by 31 publications

References 12 publications

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

High performance and safe flight of full‐scale helicopters from takeoff to landing with an ensemble of planners

Vehicle Motion in Currents

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