A descent method for the Dubins traveling salesman problem with neighborhoods

Chen, Zheng; Sun, Chenhao; Shao, Xueming; Zhao, Wenyi

doi:10.1631/fitee.2000041

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…For example, in forthcoming work, the points are allowed to slide along straight lines. Alternately, in the work of Chen et al, each point is confined to its own disk [3] Since the point m lies midway between the two circles around which the curve wraps, it must travel with velocity 1 2 v. By Lemma 2.1, the first variation of the curve p 1 p 2 m is…”

Section: A Generalisation To Variable Pointsmentioning

confidence: 99%

A Gradient Descent Method for The Dubins Traveling Salesman Problem

Kirszenblat¹,

Ayala²,

Rubinstein³

2021

Preprint

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We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature-constrained tour through a finite number of points in the euclidean plane. The problem finds applications in path planning for robotic vehicles and unmanned aerial vehicles, where a minimum turning radius prevents the vehicle from taking sharp turns. In this paper, we focus on the case where any two points are separated by at least four times the minimum turning radius, which is most interesting from a practical standpoint. The bounding procedure efficiently determines the optimal order in which to visit the points. The gradient descent method, which is inspired by a mechanical model, determines the optimal trajectories of the tour through the points in a given order, and its computation time scales linearly with the number of points. In experiments on nine points, the bounding procedure typically explores no more than a few sequences before finding the optimal sequence, and the gradient descent method typically converges to within 1% of optimal in a single iteration. Path planning and Dubins path and Curvature constraint and Travelling salesman problem and Convex optimization

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Section: A Generalisation To Variable Pointsmentioning

confidence: 99%

A Gradient Descent Method for The Dubins Traveling Salesman Problem

Kirszenblat¹,

Ayala²,

Rubinstein³

2021

Preprint

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“…Due to the importance of using curvature-bounded paths in real-world scenarios, the shortest curvature-bounded path with more complex environmental and boundary constraints have been widely studied. Examples include, but not limited to, shortest curvature-bounded paths passing through multiple waypoints [12,30,32], passing through multiple regions [21,28,42], encircling a target [29,36], avoiding obstacles [7,14,18,37], intercepting a moving target [22,[39][40][41], and moving in tunnel-like environments [38] or in uniform current drift [13,15,19].…”

mentioning

confidence: 99%

Elongation of Curvature-Bounded Path

Chen,

Wang,

2021

Preprint

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The paper is concerned with elongating the shortest curvature-bounded path between two oriented points to an expected length. The elongation of curvature-bounded paths to an expected length is fundamentally important to plan missions for nonholonomic-constrained vehicles in many practical applications, such as coordinating multiple nonholonomic-constrained vehicles to reach a destination simultaneously or performing a mission with a strict time window. In the paper, the explicit conditions for the existence of curvature-bounded paths joining two oriented points with an expected length are established by applying the properties of the reachability set of curvature-bounded paths. These existence conditions are numerically verifiable, allowing readily checking the existence of curvaturebounded paths between two prescribed oriented points with a desired length. In addition, once the existence conditions are met, elongation strategies are provided in the paper to get curvature-bounded paths with expected lengths. Finally, some examples of minimum-time path planning for multiple fixed-wing aerial vehicles to cooperatively achieve a triangle-shaped flight formation are presented, illustrating and verifying the developments of the paper.

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