Time-optimal paths for a Dubins airplane

Chitsaz, Hamidreza; LaValle, Steven M.

doi:10.1109/cdc.2007.4434966

Cited by 203 publications

(148 citation statements)

References 35 publications

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“…Some researchers consider problems with a more complex mobile robot configuration such as trailer-truck systems navigation [65]. Chitsaz and LaValle [13], on the other hand, extend Dubins car to having altitude, leading to problems studying a time-optimal trajectory for airplanes. Despite a wide variety of the aforementioned extensions, the assumption of constant speed and minimum turning radius (or angular acceleration in the case of [6]) restricts the analysis to the isotropic case.…”

Section: Related Workmentioning

confidence: 99%

Optimal path finding in direction, location, and time dependent environments

Dolinskaya

2012

Naval Research Logistics

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This article examines optimal path finding problems where cost function and constraints are direction, location, and time dependent. Recent advancements in sensor and data‐processing technology facilitate the collection of detailed real‐time information about the environment surrounding a ground vehicle, an airplane, or a naval vessel. We present a navigation model that makes use of such information. We relax a number of assumptions from existing literature on path‐finding problems and create an accurate, yet tractable, model suitable for implementation for a large class of problems. We present a dynamic programming model which integrates our earlier results for direction‐dependent, time and space homogeneous environment, and consequently, improves its accuracy, efficiency, and run‐time. The proposed path finding model also addresses limited information about the surrounding environment, control‐feasibility of the considered paths, such as sharpest feasible turns a vehicle can make, and computational demands of a time‐dependent environment. To demonstrate the applicability and performance of our path‐finding algorithm, computational experiments for a short‐range ship routing in dynamic wave‐field problem are presented. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

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Section: Related Workmentioning

confidence: 99%

Optimal path finding in direction, location, and time dependent environments

Dolinskaya

2012

Naval Research Logistics

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“…For this purpose, let us assume that the target dynamics is also modeled by an extended Dubins system (see [18]…”

Section: Description Of the Algorithmmentioning

confidence: 99%

Lyapunov and Minimum-Time Path Planning for Drones

et al. 2014

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In this paper, we study the problem of controlling an unmanned aerial vehicle (UAV) to provide a target supervision and/or to provide convoy protection to ground vehicles.We first present a control strategy based upon a Lyapunov-LaSalle stabilization method to provide supervision of a stationary target. The UAV is expected to join a pre-designed admissible circular trajectory around the target which is itself a fixed point in the space.Our strategy is presented for both HALE (High Altitude Long Endurance) and MALE (Medium Altitude Long Endurance) types UAVs. A UAV flying at a constant altitude (HALE type) is modeled as a Dubins vehicle (i.e. a planar vehicle with constrained turning radius and constant forward velocity). For a UAV that might change its altitude (MALE type), we use the general kinematic model of a rigid body evolving in R 3 . Both control strategies presented are smooth and unlike what is usually proposed in the literature these strategies asymptotically track a circular trajectory of exact minimum turning radius.We also present the time-optimal control synthesis for tracking a circle by a Dubins vehicle. This optimal strategy, although much simpler than the point-to-point time-optimal strategy obtained by P. Souères and J.-P. Laumond in the 1990s (see [45]), is very rich.Finally, we propose control strategies to provide supervision of a moving target, that are based upon the previous ones.

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“…Algorithms based on Pontryagin minimum principle and Lagrange multipliers have been widely used to reduce optimization problems to a boundary condition one (Chitsaz & LaValle, 2007). Sequential Gradient Restoration Algorithm (SGRA) represents an indirect method used for several problems like space trajectories optimization (Miele & Pritchard, 1969, Miele, 1970.…”

Section: Generic Optimization Algorithmsmentioning

confidence: 99%