Path planning in time dependent flow fields using level set methods

Lolla, Tapovan; Ueckermann, Mattheus P.; Yiğit, Konuralp; Haley, Patrick J.; Lermusiaux, Pierre F. J.

doi:10.1109/icra.2012.6225364

Cited by 132 publications

(96 citation statements)

References 26 publications

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“…The common difficulty here is in han-94 dling the large number of degrees of freedom (DOF) of 95 the robot. Every extension to this basic problem adds in 96 computational complexity (Lolla, 2012;Latombe, 1991). 97 Motion planning for multi DOF systems such as robotic 98 arms (Canny, 1988;Latombe, 1991), including cooper-99 ative control (Paley et al, 2008;Leonard and Fiorelli, 100 2001) and coordination (Bahr et al, 2009;Davis et al, 101 2009) have been extensively studied.…”

Section: Prior Work 91mentioning

confidence: 99%

“…Other underwater path planning approaches 188 include Lagrangian Coherent Structures (Zhang et al,189 2008), case based reasoning (Vasudevan and Ganesan, 190 1996) and evolution (Alvarez et al, 2004). We refer to 191 (Lolla, 2012;Lolla et al, 2014c) for more extensive re-192 views.…”

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confidence: 99%

“…Owing to the proba-643 bilistic nature of RRTs, it is challenging to obtain rigor-644 ous estimates of their cost for path planning in dynamic 645 flows. See (Lolla, 2012) for a detailed discussion. We are 646 not aware of published rigorous estimates of the com-647 putational costs of other approximate algorithms for 648 time-optimal path planning in dynamic currents.…”

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confidence: 99%

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Time-optimal path planning in dynamic flows using level set equations: theory and schemes

et al. 2014

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We develop an accurate partial differential equation based methodology that predicts the timeoptimal paths of autonomous vehicles navigating in any continuous, strong and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow-fields such as unsteady doublegyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned, even in the presence of complex flows in domains with obstacles. Finally, we present, and support through illustrations,

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Section: Prior Work 91mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Time-optimal path planning in dynamic flows using level set equations: theory and schemes

et al. 2014

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“…Significant hardware and sensor improvements [19] as well as algorithmic performance guarantees [9], [10] have further encouraged interest. However, there are open challenges about how mobile sensor platforms can most effectively sample and interact with strong, circulating flows [3], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Active Singularities for Multivehicle Motion Planning in an N-Vortex System

Lagor

Paley

2015

Dynamic Data-Driven Environmental Systems Science

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Abstract. This paper presents a path-planning paradigm for distributed control of multiple sensor platforms in a geophysical flow well-approximated by a point-vortex model. We utilize Hamiltonian dynamics to generate control vector fields for vehicle motion in N -vortex flows using the concept of an active singularity whose strength is a tunable control input. We introduce active singularities that are virtual point vortices possibly collocated with virtual point sources or sinks. We provide a principled method to stabilize relative equilibria of these virtual vortices in the presence of the actual point vortices, which represent the underlying geophysical flow. We illustrate how these relative equilibria may be useful for vehicle path planning and sampling in a geophysical flow. Preliminary results presented here are based on an adaptive control design.

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“…For general reviews on oceanic path planning, we refer to (Lolla, 2012;Lolla et al 2014a;Lermusiaux et al, 2016) and for general reviews on oceanic adaptive sampling to (Curtin et al 1993;Leonard et al 2007;Lermusiaux, 2007;Roy et al, 2007). Recent efforts for autonomous adaptive sampling include: adaptive sampling via Error Subspace Statistical Estimation (ESSE) with non-linear predictions of error reductions (Lermusiaux 2007); control of coordinated patterns for ocean sampling (Zhang et al, 2007); a mathematical approach to optimally sampling targeted environmental hotspots in the 'MASP uncertainty framework' or multi-robot adaptive sampling problem (Low, et al 2013); Mixed Integer Linear Programming (MILP) for optimal-sampling path planning (Yilmaz et al 2008); nonlinear optimal-sampling path planning using genetic algorithms (Heaney, et al 2007); dynamic programming and onboard routing for optimal-sampling path planning (Wang, et al 2009); command and control of surface kayaks over the Web, directly read from model instructions (Xu et al, 2008); automated sensor networks aiming to facilitate ocean scientific studies (Schofield et al, 2010), and optimal design of glider-sampling networks (Alvarez and Mourre, 2012;Ferri et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Validation of genetic algorithm-based optimal sampling for ocean data assimilation

et al. 2016

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Abstract-Regional ocean models are capable of forecasting conditions for usefully long intervals of time (days) provided that initial and ongoing conditions can be measured. In resource-limited circumstances, the placement of sensors in optimal locations is essential. Here, a nonlinear optimization approach to determine optimal adaptive sampling that uses the Genetic Algorithm (GA) method is presented. The method determines sampling strategies that minimize a user-defined physics-based cost function. The method is evaluated using identical twin experiments, comparing hindcasts from an ensemble of simulations that assimilate data selected using the GA adaptive sampling and other methods. For skill metrics, we employ the reduction of the ensemble root-mean-square-error (RMSE) between the "true" data-assimilative ocean simulation and the different ensembles of data-assimilative hindcasts. A 5-glider optimal sampling study is set up for a 400 km x 400 km domain in the Middle Atlantic Bight region, along the New Jersey shelf-break. Results are compared for several ocean and atmospheric forcing conditions. Index Terms-Genetic algorithms, ocean technology, optimization methods sampling methods, adaptive sampling, computational ocean modeling, data assimilation, error subspace statistical estimation, OSSE

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Path planning in time dependent flow fields using level set methods

Cited by 132 publications

References 26 publications

Time-optimal path planning in dynamic flows using level set equations: theory and schemes

Time-optimal path planning in dynamic flows using level set equations: theory and schemes

Active Singularities for Multivehicle Motion Planning in an N-Vortex System

Validation of genetic algorithm-based optimal sampling for ocean data assimilation

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