On Tightly Bounding the Dubins Traveling Salesman's Optimum

Manyam, Satyanarayana G.; Rathinam, Sivakumar

doi:10.1115/1.4039099

Cited by 26 publications

(29 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A solution of the Dubins traveling salesman problem for a given sequence of the targets (the green disks) with the total number of samples

N

, final path length

scriptL

, and lower bound

L_{U}

. The found solution is the blue curve, and the red curve is its lower bound determined as a solution of the Dubins interval problem with the cost

L_{U}

(Manyam & Rathinam, ). The uniform sampling utilizes 32 heading values per each target.…”

Section: Related Workmentioning

confidence: 99%

“…A very important result on the tight lower bound of the DTP has been proposed in Manyam and Rathinam () which has been further evaluated in (Manyam, Rathinam, and Casbeer (), but unfortunately without reporting the computational requirements. The computation of the tight lower bound is based on the solution of the so‐called the Dubins interval problem (DIP) introduced in Manyam, Rathinam, Casbeer and Garcia ().…”

Section: Related Workmentioning

confidence: 99%

“…Thus, for the interval of the full range

2 π

, the solution of DIP is a straight line segment connecting the locations. The tight lower bound (Manyam & Rathinam, ) has been utilized to guide sampling of the possible heading intervals and the heading values themselves in Faigl et al, (), where the authors show improved results over a uniform sampling of the heading (see Figure for an example of the DTSP solution based on the DTP and DIP).…”

Section: Related Workmentioning

confidence: 99%

“…The 2‐Opt heuristic is computationally inexpensive procedure

O (n^{3})

which can improve the solution about few percentage points. In addition, the final trajectory is determined by the high‐quality DTP solver (Faigl et al, ) which utilizes a tight lower bound (Manyam & Rathinam, ) to stop the refinement of the heading samples when the maximal number of samples 1,024 is reached or when the ratio of the trajectory length to the lower bound solution is less than 1.01. Notice, the sensing range

δ

can be easily individualized for each particular object of interest by a simple usage of the particular range in the winner selection.…”

Section: Unsupervised Learning For M‐dtspn and 3d Bézier Curve‐based mentioning

confidence: 99%

See 3 more Smart Citations

Unsupervised learning‐based flexible framework for surveillance planning with aerial vehicles

Faigl

Váňa

Pěnička

et al. 2018

Journal of Field Robotics

View full text Add to dashboard Cite

The herein studied problem is motivated by practical needs of our participation in the Mohamed Bin Zayed International Robotics Challenge (MBZIRC) 2017 in which a team of unmanned aerial vehicles (UAVs) is requested to collect objects in the given area as quickly as possible and score according to the rewards associated with the objects. The mission time is limited, and the most time‐consuming operation is the collection of the objects themselves. Therefore, we address the problem to quickly identify the most valuable objects as surveillance planning with curvature‐constrained trajectories. The problem is formulated as a multivehicle variant of the Dubins traveling salesman problem with neighborhoods (DTSPN). Based on the evaluation of existing approaches to the DTSPN, we propose to use unsupervised learning to find satisfiable solutions with low computational requirements. Moreover, the flexibility of unsupervised learning allows considering trajectory parametrization that better fits the motion constraints of the utilized hexacopters that are not limited by the minimal turning radius as the Dubins vehicle. We propose to use Bézier curves to exploit the maximal vehicle velocity and acceleration limits. Besides, we further generalize the proposed approach to 3D surveillance planning. We report on evaluation results of the developed algorithms and experimental verification of the planned trajectories using the real UAVs utilized in our participation in MBZIRC 2017.

show abstract

“…A solution of the Dubins traveling salesman problem for a given sequence of the targets (the green disks) with the total number of samples

N

, final path length

scriptL

, and lower bound

L_{U}

. The found solution is the blue curve, and the red curve is its lower bound determined as a solution of the Dubins interval problem with the cost

L_{U}

(Manyam & Rathinam, ). The uniform sampling utilizes 32 heading values per each target.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…Thus, for the interval of the full range

2 π

Section: Related Workmentioning

confidence: 99%

“…The 2‐Opt heuristic is computationally inexpensive procedure

O (n^{3})

δ

can be easily individualized for each particular object of interest by a simple usage of the particular range in the winner selection.…”

Section: Unsupervised Learning For M‐dtspn and 3d Bézier Curve‐based mentioning

confidence: 99%

See 2 more Smart Citations

Unsupervised learning‐based flexible framework for surveillance planning with aerial vehicles

Faigl

Váňa

Pěnička

et al. 2018

Journal of Field Robotics

View full text Add to dashboard Cite

show abstract

“…There are several results in the literature related to the Dubins paths [1]- [6] . In [1], [2], the analysis of the accessibility regions of Dubins paths is done and the Dubins synthesis problem are presented.…”

Section: Introductionmentioning

confidence: 99%

Shortest Dubins path to a circle

Manyam

Casbeer

Moll

et al. 2019

AIAA Scitech 2019 Forum

Self Cite

View full text Add to dashboard Cite

The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle. The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle.

show abstract

Optimal solution of the Generalized Dubins Interval Problem: finding the shortest curvature-constrained path through a set of regions

Váňa

Faigl

2020

Auton Robot

View full text Add to dashboard Cite

On Tightly Bounding the Dubins Traveling Salesman's Optimum

Cited by 26 publications

References 28 publications

Unsupervised learning‐based flexible framework for surveillance planning with aerial vehicles

Unsupervised learning‐based flexible framework for surveillance planning with aerial vehicles

Shortest Dubins path to a circle

Optimal solution of the Generalized Dubins Interval Problem: finding the shortest curvature-constrained path through a set of regions

Contact Info

Product

Resources

About