Optimal Trajectories of Curvature Constrained Motion in the Hamilton–Jacobi Formulation

Takei, Ryo; Tsai, Richard

doi:10.1007/s10915-012-9671-y

Cited by 39 publications

(41 citation statements)

References 37 publications

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“…However, an advantage of this approach is that the safereachable set is defined without explicit dependence on the dynamics of the agents. For example, although simple kinematic dynamics are considered here, it is possible to use FMM formulations to compute reachable sets for more complex dynamics such as the Dubin's car [25]. The computational approach also lends itself well to cases with spatially-varying velocity profiles, where the maximum speeds of the agents may change depending on position [27].…”

Section: Safe-reachable Set Based Cooperative Pursuitmentioning

confidence: 99%

Cooperative pursuit with Voronoi partitions

et al. 2016

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This work considers a pursuit-evasion game in which a number of pursuers are attempting to capture a single evader. Cooperation among multiple agents can be difficult to achieve, as it may require the selection of actions in the joint input space of all agents. This work presents a decentralized, real-time algorithm for cooperative pursuit of a single evader by multiple pursuers in bounded, simply-connected planar domains. The algorithm is based on minimizing the area of the generalized Voronoi partition of the evader. The pursuers share state information but compute their inputs independently. No assumptions are made about the evader's control strategies other than requiring the evader control inputs to conform to a speed limit. Proof of guaranteed capture is shown when the domain is convex and the players' motion models are kinematic. Simulation results are presented showing the efficiency and effectiveness of this strategy.

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Section: Safe-reachable Set Based Cooperative Pursuitmentioning

confidence: 99%

Cooperative pursuit with Voronoi partitions

et al. 2016

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“…A 2009 survey of motion planners applicable to UAS is presented in [27]. Examples of more-recent motion planners include RRT-AR [28], fast-marching squared [29], semi-Lagrangian schemes [30], and fast-marching trees [31]. Although these newer methods may be considered more suitable for continuous configuration spaces and may be able to handle differential constraints, this paper makes use of conventional A algorithm to illustrate the use of the candidate landing site risk assessment and occupancy estimates proposed in this article.…”

Section: Data Use In Emergency Path Planningmentioning

confidence: 99%

Evaluating Risk to People and Property for Aircraft Emergency Landing Planning

Donato

Atkins

2017

Journal of Aerospace Information Systems

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General aviation and small unmanned aircraft systems are less redundant, may be less thoroughly tested, and are flown at lower cruise altitudes than commercial aviation counterparts. These factors result in a higher probability of a forced or emergency landing scenario. Currently, general aviation relies on the pilot to select a landing site and plan a trajectory, even though workload in an emergency is typically high, and decisions must be made rapidly. Although sensors can provide local real-time information, awareness of more distant or occluded regions requires database and/or offboard data sources. This paper considers different data sources and how to process these data to inform an emergency landing planner regarding risks posed to property, people on the ground, and the aircraft itself. Detailed terrain data are used for selection of candidate emergency landing sites. Mobile phone activity is evaluated as a means of real-time occupancy estimation. Occupancy estimates are combined with population census data to estimate emergency landing risk to people on the ground. Openly available databases are identified and mined as part of an emergency landing planning case study. = total number of country codes n g = total number of grid cells n t = total number of time intervals R a = risk based on landing area R h = risk to people on ground R ls = overall landing site risk R p = risk to property on ground R v = risk to vehicle t = time, min t 10 m = starting time of 10 min time interval, min W h , W p , W v , W a = weights associated with landing site risks w = A transition cost weight Θ = median of maximum aggregated SMS and call activity during a day, for a day of the week λ census = occupancy from census datâ λ census = normalized occupancy from census data λ rt = real-time occupancy estimation λ 0 = A fixed transition cost element Φ = median of aggregated SMS and call activity for each grid cell, day of the week and time interval of the day Φ grid = sum of Φ for all grid cellŝ Φ = normalized Φ ϕ = aggregated SMS and call activitŷ ϕ = normalized ϕ ϕ 1 = activity in terms of SMS-in ϕ 2 = activity in terms of SMS-out ϕ 3 = activity in terms of call-in ϕ 4 = activity in terms of call-out ϕ 5 = activity in terms of internet ϕ i = modified activity feature for heat map plot

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“…The movement of the animalinside the square box is designed using the dynamics of curvatureconstrained motion. We used a dynamical system which is used to model Dubins and Reeds-Shepp's cars (Takei and Tsai, 2013). The dynamics are given as follows…”

Section: Appendixmentioning

confidence: 99%

An Oscillatory Network Model of Head Direction, Spatially Periodic Cells and Place Cells Using Locomotor Inputs

Soman

Muralidharan

Chakravarthy

2016

Preprint

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We propose a computational modeling approach that explains the formation of a range of spatial cells like head direction cells, grid cells, border cells and place cells which are believed to play a pivotal role in the spatial navigation of an animal. Most existing models insert special symmetry conditions in the models in order to obtain such symmetries in the outcome; our models do not require such symmetry assumptions.Our modeling approach is embodied in two models: a simple one (Model #1) and a more detailed version (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/080267 doi: bioRxiv preprint first posted online Oct. 12, 2016; neural hierarchy necessary to obtain the complete range of spatial cell responses found in the hippocampal system.

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Optimal Trajectories of Curvature Constrained Motion in the Hamilton–Jacobi Formulation

Cited by 39 publications

References 37 publications

Cooperative pursuit with Voronoi partitions

Cooperative pursuit with Voronoi partitions

Evaluating Risk to People and Property for Aircraft Emergency Landing Planning

An Oscillatory Network Model of Head Direction, Spatially Periodic Cells and Place Cells Using Locomotor Inputs

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