Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points

Manyam, Satyanarayana G.; Rathinam, Sivakumar; Casbeer, David W.; García, Eloy

doi:10.1007/s10846-016-0459-4

Cited by 51 publications

(24 citation statements)

References 26 publications

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“…The idea has been used in the context of motion planning of robots by several authors including Jacobs and Canny (1992), Edison and Shima (2011), Cons et al (2014) and others. Alternative approaches for the DSPP are due to Goac et al (2013), Lee et al (2000), Rathinam and Khargonekar (2016) and Manyam et al (2017).…”

Section: Introductionmentioning

confidence: 99%

New heuristic algorithms for the Dubins traveling salesman problem

Babel

2020

J Heuristics

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The problem of finding a shortest curvature-constrained closed path through a set of targets in the plane is known as Dubins traveling salesman problem (DTSP). Applications of the DTSP include motion planning for kinematically constrained mobile robots and unmanned fixed-wing aerial vehicles. The difficulty of the DTSP is to simultaneously find an order of the targets and suitable headings (orientation angles) of the vehicle when passing the targets. Since the DTSP is known to be NP-hard there is a need for heuristic algorithms providing good quality solutions in reasonable time. Inspired by standard methods for the TSP we present a collection of such heuristics adapted to the DTSP. The algorithms are based on a technique that optimizes the headings of the targets of an open or closed subtour with given order. This is done by discretizing the headings, constructing an auxiliary network and computing a shortest path in the network. The first algorithm for the DTSP uses the order of the targets obtained from the solution of the Euclidean TSP. A second class of algorithms extends an open subtour by successively adding a new target and closes the tour if all targets have been added. A third class of algorithms starts with a closed subtour consisting of few targets and successively inserts a new target into the tour. The individual algorithms differ by the number of headings to be optimized in each iteration. Extensive simulation results show that the proposed methods are competitive with state-of-the-art methods for the DTSP concerning performance and superior concerning running time, which makes them applicable also to large-scale scenarios. Keywords Dubins traveling salesman problem • Curvature-constrained traveling salesman problem • Dubins vehicle • Heuristic methods B Luitpold Babel

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Section: Introductionmentioning

confidence: 99%

New heuristic algorithms for the Dubins traveling salesman problem

Babel

2020

J Heuristics

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“…Hence, the length of the RSL path varies only due to the third segment. 5 The value of φ 2 is a piecewise linear function of α, and the discontinuity as shown in the Fig. 5 is due to the modulus function which occurs when φ 2 goes to zero.…”

Section: B Counter Clockwise Tangential Directionmentioning

confidence: 98%

Shortest Dubins path to a circle

Manyam

Casbeer

Moll

et al. 2019

AIAA Scitech 2019 Forum

Self Cite

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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.

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“…The works that are specifically designed for aerial robots can be divided into (1) path smoothing and (2) trajectory planning. In the first group, in [12], the authors propose a kinematically feasible path for fixed-wing aerial robots that connects a series of waypoints, whereas a continuous curvature path smoothing for fixed-wing aerial robots is presented in [13]. In [5], [14], the authors propose a splinesbased optimization to plan a path for multirotor aerial robots.…”

Section: B State Of the Artmentioning

confidence: 99%

Towards trajectory planning from a given path for multirotor aerial robots trajectory tracking

Sánchez-López

Olivares-Méndez

Castillo-Lopez

et al. 2018

2018 International Conference on Unmanned Aircraft Systems (ICUAS)

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Planning feasible trajectories given desired collision-free paths is an essential capability of multirotor aerial robots that enables the trajectory tracking task, in contrast to path following. This paper presents a trajectory planner for multirotor aerial robots carefully designed considering the requirements of real applications such as aerial inspection or package delivery, unlike other research works that focus on aggressive maneuvering. Our planned trajectory is formed by a set of polynomials of two kinds, acceleration/deceleration and constant velocity. The trajectory planning is carried out by means of an optimization that minimizes the trajectory tracking time, applying some typical constraints as m-continuity or limits on velocity, acceleration and jerk, but also the maximum distance between the trajectory and the given path. Our trajectory planner has been tested in real flights with a big and heavy aerial platform such the one that would be used in a real operation. Our experiments demonstrate that the proposed trajectory planner is suitable for real applications and it is positively influencing the controller for the trajectory tracking task.

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Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points

Cited by 51 publications

References 26 publications

New heuristic algorithms for the Dubins traveling salesman problem

New heuristic algorithms for the Dubins traveling salesman problem

Shortest Dubins path to a circle

Towards trajectory planning from a given path for multirotor aerial robots trajectory tracking

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