An $\bm{O(n\log n)}$ Shortest Path Algorithm Based on Delaunay Triangulation

Jan, Gene Eu; Sun, Chi‐Chia; Tsai, Wei Chun; Lin, Ting-Hsiang

doi:10.1109/tmech.2013.2252076

Cited by 45 publications

(23 citation statements)

References 19 publications

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“…In [4][5][6], Jan et al proposed two O(nlog n) time path-planning algorithms to obtain the near-shortest path in the Euclidian and quadric planes, respectively. Compared to the other approaches of reduced visibility graph, this fast method outperforms the rest of O(nlog n) algorithms in the general two-dimensional situation, except the path length compared to the shortest O(n 2 ) time shortest algorithm of visibility graph.…”

Section: Introductionmentioning

confidence: 99%

Path Planning on Quadric Surfaces and Its Application

Sun¹,

Jan²,

Lu³

et al. 2018

Advanced Path Planning for Mobile Entities

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In this chapter, recent near-shortest path-planning algorithms with O(nlog n) in the quadric plane based on the Delaunay triangulation, Ahuja-Dijkstra algorithm, and ridge points are reviewed. The shortest path planning in the general three-dimensional situation is an NP-hard problem. The optimal solution can be approached under the assumption that the number of Steiner points is infinite. The state-the-art method has at most 2.81% difference on the shortest path length, but the computation time is 4216 times faster. Compared to the other O(nlog n) time near-shortest path approach (Kanai and Suzuki, KS's algorithm), the path length of the Delaunay triangulation method is 0.28% longer than the KS's algorithm with three Steiner points, but the computation is about 31.71 times faster. This, however, has only a few path length differences, which promises a good result, but the best computing time. Notably, these methods based on Delaunay triangulation concept are ideal for being extended to solve the path-planning problem on the Quadric surface or even the cruise missile mission planning and Mars rover.

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Section: Introductionmentioning

confidence: 99%

Path Planning on Quadric Surfaces and Its Application

Sun¹,

Jan²,

Lu³

et al. 2018

Advanced Path Planning for Mobile Entities

Self Cite

View full text Add to dashboard Cite

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“…Hence, the search for an efficient solution to the problem continued and the idea of exact roadmaps was introduced in the literature which relies on the discretization of the given search space. This discretization of search space makes the algorithm computationally expensive for higher dimensional spaces, that is why the application of such algorithms like Cell Decomposition methods [19] [1], Delaunay Triangulations [10] and Dynamic Graph Search methods [4] [25] are limited to low dimensional spaces only [5]. Moreover the algorithms that combine the set of allowed motions with the graph search methods thus generating state lattices, such as in [8] [31] [30], also suffered from the undesirable effects of discretization.…”

Section: Introductionmentioning

confidence: 99%

Intelligent bidirectional rapidly-exploring random trees for optimal motion planning in complex cluttered environments

Qureshi

Ayaz

2015

Robotics and Autonomous Systems

192

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The sampling based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been proposed that ensures asymptotic optimality. Subsequently its bidirectional version has also been introduced in the literature known as Bidirectional-RRT* (B-RRT*). We introduce a new variant called Intelligent Bidirectional-RRT* (IB-RRT*) which is an improved variant of the optimal RRT* and bidirectional version of RRT* (B-RRT*) algorithms and is specially designed for complex cluttered environments. IB-RRT* utilizes the bidirectional trees approach and introduces intelligent sample insertion heuristic for fast convergence to the optimal path solution using uniform sampling heuristics. The proposed algorithm is evaluated theoretically and experimental * This is the authors' version of the paper published in Elsevier Robotics and Autonomous Systems Journal. The source code of this paper is available at: github.com/ahq1993. results are presented that compares IB-RRT* with RRT* and B-RRT*. Moreover, experimental results demonstrate the superior efficiency of IB-RRT* in comparison with RRT* and B-RRT in complex cluttered environments.

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“…With their theoretical foundation in network science, path planning algorithms are well adopted in robotics [3]- [9]. In previous work, the most common requirement has been minimizing the path length [10]- [14]. Shortest paths are very effective criteria for mobile robot path planning, as the path length is often proportional to the traversal time, especially when the terrain is flat.…”

Section: Introductionmentioning

confidence: 99%

A Constraint-Aware Heuristic Path Planner for Finding Energy-Efficient Paths on Uneven Terrains

Ganganath

Cheng

Tse

2015

IEEE Trans. Ind. Inf.

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Motions of mobile robots need to be optimized to minimize their energy consumption to ensure long periods of continuous operations. Shortest paths do not always guarantee the minimum energy consumption of mobile robots. Moreover, they are not always feasible due to climbing constraints of mobile robots, especially on steep terrains. We utilize a heuristic search algorithm to find energy-optimal paths on hilly terrains using an established energy-cost model for mobile robots. The terrains are represented using grid-based elevation maps. Similar to A*-like heuristic search algorithms, the energy-cost of traversing through a given location of the map depends on a heuristic energy-cost estimation from that particular location to the goal. Using zigzag-like path patterns, the proposed heuristic function can estimate heuristic energy-costs on steep terrains that cannot be estimated using traditional methods. We proved that the proposed heuristic energy-cost function is both admissible and consistent. Therefore, the proposed path planner can always find feasible energy-optimal paths on any given terrain without node revisits, provided that such paths exist. Results of tests on real-world terrain models presented in this paper demonstrate the promising computational performance of the proposed path planner in finding energy-efficient paths.

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An $\bm{O(n\log n)}$ Shortest Path Algorithm Based on Delaunay Triangulation

Cited by 45 publications

References 19 publications

Path Planning on Quadric Surfaces and Its Application

Path Planning on Quadric Surfaces and Its Application

Intelligent bidirectional rapidly-exploring random trees for optimal motion planning in complex cluttered environments

A Constraint-Aware Heuristic Path Planner for Finding Energy-Efficient Paths on Uneven Terrains

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