On shortest Dubins path via a circular boundary

Jha, Bhargav; Chen, Zheng; Shima, Tal

doi:10.1016/j.automatica.2020.109192

Cited by 14 publications

(6 citation statements)

References 27 publications

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“…The analysis of the equations ( 9), ( 11), ( 13), (15) in Figs. 18,19 demonstrates that the function F CC becomes to equal zero at time t = 9π/4 and the other functions in the figures do not. CCC graphs: RLR-optimal interception case (µ = +1).…”

Section: Ccc-optimal Examplesmentioning

confidence: 96%

“…For example, recent studies devoted to the Dubins PP-problem deal with the case when the trajectory necessarily passes through a fixed intermediate point [10]. Also recently, the problems of constructing the shortest path to a circle [9] and the shortest path via a circular boundary [18] for Dubins car have been solved. These analytical results make it affordable to implement efficient on-board algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Minimum-time lateral interception of a moving target by a Dubins car

Buzikov¹,

Galyaev²

2021

Preprint

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This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation, every one of them is a continuous function of time. The optimal trajectory planning problem of constructing minimum-time trajectories for a Dubins car in the presence of an a priory known time-dependent wind vector field is a partial case of the considered problem. Using the properties of the three-dimensional reachable set of a Dubins car, it is proved that the optimal interception point belongs to a part of an analytically described surface in the three-dimensional space. The analytical description of the surface makes it possible to obtain 10 algebraic equations for calculating the parameters of the optimal control that implements the minimum-time lateral interception. These equations are generally transcendental and can be simplified for particular cases of target motion (e.g. resting target, straight-line uniform target motion). Finally, some particular cases of the optimal lateral interception validate the developments of the paper and highlight its necessity to consider each of 10 algebraic equations in the general case.

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Section: Ccc-optimal Examplesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Minimum-time lateral interception of a moving target by a Dubins car

Buzikov¹,

Galyaev²

2021

Preprint

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“…are the intelligent algorithms that use the idea of biology. When the dynamic constraints of the research object are considered, some special curves like Dubins Path, 21 Fermat Spiral (FS), 22 B-Spline curve, 23 and Clothoid curve 24 are often combined with the above algorithms to make the path of collision avoidance more smooth and continuous.…”

Section: Introductionmentioning

confidence: 99%

“…Figure21. The situations that the USV maintains the heading: (a) the speed of USV is higher than the obstacle and (b) the speed of USV is higher than the obstacle.…”

mentioning

confidence: 99%

A circle grid-based approach for obstacle avoidance motion planning of unmanned surface vehicles

Zhu

Xiao

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part M:

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Aiming at an obstacle avoidance problem with dynamic constraints for Unmanned Surface Vehicle (USV), a method based on Circle Grid Trajectory Cell (CGTC) is proposed. Firstly, the ship model and standardization rules are constructed to develop and constrain the trajectory, respectively. Secondly, by analyzing the properties of the circle grid, the circle grid tree is produced to guide the motion of the USV. Then, the kinematics and dynamics of the USV are considered through the on-line trajectory generator by designing a relational function that links the rudder angle, the heading angle, and the central angle of the circle grid. Finally, obstacle avoidance is achieved by utilizing the on-line trajectory generator to choose a safe, smooth, and efficient path for the USV. The experimental results indicate that the proposed method can avoid both static and dynamic obstacles, showing better performance in terms of distance cost and steering cost comparing with the related methods, and our method only takes 50% steering cost of the grid-based method; the collision avoidance path not only conforms to the USV dynamic characteristics but also provides a reference of steering command.

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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].…”

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confidence: 99%

Elongation of Curvature-Bounded Path

Chen,

Wang,

2021

Preprint

Self Cite

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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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On shortest Dubins path via a circular boundary

Cited by 14 publications

References 27 publications

Minimum-time lateral interception of a moving target by a Dubins car

Minimum-time lateral interception of a moving target by a Dubins car

A circle grid-based approach for obstacle avoidance motion planning of unmanned surface vehicles

Elongation of Curvature-Bounded Path

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