Shortest paths of bounded curvature in the plane

Boissonnat, Jean‐Daniel; Cérézo, André; Leblond, Juliette

doi:10.1007/bf01258291

Cited by 174 publications

(75 citation statements)

References 3 publications

(10 reference statements)

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“…The paths in the family obtained by Dubins in [1] are time-optimal solutions of system (1). Later, Sussmann and Tang [5] and Boissonnat et al [6] obtained the same result by adopting an optimal control point of view. Exploiting this approach, we determined [2] the shortest paths between any given robot configuration and the obstacles populating its workspace both for the Reeds and Shepp car and for the Dubins car.…”

Section: Background Materialssupporting

confidence: 53%

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Shortest Paths to Obstacles for a Polygonal Dubins Car

Giordano

Vendittelli

2009

IEEE Trans. Robot.

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Abstract-In this paper, we characterize the time-optimal trajectories leading a Dubins car in collision with the obstacles in its workspace. Due to the constant velocity constraint characterizing the Dubins car model, these trajectories form a sufficient set of shortest paths between any robot configuration and the obstacles in the environment. Based on these paths, we define and give the algorithm for computing a distance function that takes into account the nonholonomic constraints and captures the nonsymmetric nature of the system. The developments presented here assume that the obstacles and the robot are polygons although the methodology can be applied to different shapes.

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Section: Background Materialssupporting

confidence: 53%

“…Our work relies on Dubins' results but adopts the optimal control approach proposed in [5] and [6]. In particular, the study of transversality conditions allows selecting a sufficient family of time-optimal trajectories whose length will determine the distance to the obstacles.…”

Section: Introductionmentioning

confidence: 99%

Shortest Paths to Obstacles for a Polygonal Dubins Car

Giordano

Vendittelli

2009

IEEE Trans. Robot.

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“…His intricate set of geometric statements and propositions show that "an R-geodesic is necessarily a continuous differentiable curve which consists of not more than three pieces, each of which is either a straight line segment or an arc of a circle of radius R" [22]. A simplified proof is later developed by two independent research teams, Boissonnat et al [7] and Sussmann and Tang [69], and it is based on techniques of modern control theory and the minimum principle of Pontryagin [59]. Fortune's analysis of the problem [27] establishes the controllability of Dubins car by proving that a feasible path exists for any starting and final settings of the problem.…”

Section: Related Workmentioning

confidence: 99%

“…Furthermore, along any C 2 piece of an optimal path either one of the following two cases holds [7]:…”

Section: (T) Y(t) α(T) U(t))mentioning

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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“…To further categorize the path planning methods and trajectory generation efforts, consider the several goals and flight conditions that were investigated. Flight in a horizontal plane 2-D was analyzed [5,6,17,33,44], along with considering the effects of constant winds [2][3][4]. Employing obstacle avoidance [2,[27][28][29][30][31][32] and target tracking [33][34][35][36][37][38][39][40][41] within the trajectory generation was addressed.…”

Section: Introductionmentioning

confidence: 99%

An adaptive dual-optimal path-planning technique for unmanned air vehicles

Whitfield

2016

Int. J. Simul. Multisci. Des. Optim.

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-A multi-objective technique for unmanned air vehicle path-planning generation through task allocation has been developed. The dual-optimal path-planning technique generates real-time adaptive flight paths based on available flight windows and environmental influenced objectives. The environmentally-influenced flight condition determines the aircraft optimal orientation within a downstream virtual window of possible vehicle destinations that is based on the vehicle's kinematics. The intermittent results are then pursued by a dynamic optimization technique to determine the flight path. This path-planning technique is a multi-objective optimization procedure consisting of two goals that do not require additional information to combine the conflicting objectives into a single-objective. The technique was applied to solar-regenerative high altitude long endurance flight which can benefit significantly from an adaptive real-time path-planning technique. The objectives were to determine the minimum power required flight paths while maintaining maximum solar power for continual surveillance over an area of interest (AOI). The simulated path generation technique prolonged the flight duration over a sustained turn loiter flight path by approximately 2 months for a year of flight. The potential for prolonged solar powered flight was consistent for all latitude locations, including 2 months of available flight at 60°latitude, where sustained turn flight was no longer capable.

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Shortest paths of bounded curvature in the plane

Cited by 174 publications

References 3 publications

Shortest Paths to Obstacles for a Polygonal Dubins Car

Shortest Paths to Obstacles for a Polygonal Dubins Car

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

An adaptive dual-optimal path-planning technique for unmanned air vehicles

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