Finding the 3D shortest path with visibility graph and minimum potential energy

Jiang, Kaiwen; Seneviratne, L.S.; Earles, S. W. E.

doi:10.1109/iros.1993.583190

Cited by 10 publications

(10 citation statements)

References 14 publications

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“…Likewise, in order to construct a visibility graph (Jiang et al, 1993; Lozano-Pérez and Wesley, 1979), it is necessary to have a global Euclidean embedding of the configuration space, as well as a priori understanding of shortest line segments that constitute common tangents between obstacles and tangents from start/goal points to the obstacles. In addition, at the construction stage of a visibility graph, those tangents do not take into account the underlying non-uniform traversal costs, and hence are not the optimal tangent curves.…”

Section: Introductionmentioning

confidence: 99%

Towards optimal path computation in a simplicial complex

Bhattacharya

2019

The International Journal of Robotics Research

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Computing optimal path in a configuration space is fundamental to solving motion planning problems in robotics and autonomy. Graph-based search algorithms have been widely used to that end, but they suffer from drawbacks. We present an algorithm for computing the shortest path through a metric simplicial complex that can be used to construct a piece-wise linear discrete model of the configuration manifold. In particular, given an undirected metric graph, G, which is constructed as a discrete representation of an underlying configuration manifold (a larger “continuous” space typically of dimension greater than one), we consider the Rips complex, [Formula: see text], associated with it. Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what the graph does. Our algorithm requires only a local connectivity-based description of an abstract graph, [Formula: see text], and a cost/length function, [Formula: see text], as inputs. No global information such as an embedding or a global coordinate chart is required. The local nature of the proposed algorithm makes it suitable for configuration spaces of arbitrary topology, geometry, and dimension. We not only develop the search algorithm for computing shortest distances, but we also present a path reconstruction algorithm for explicitly computing the shortest paths through the simplicial complex. The complexity of the presented algorithm is comparable with that of Dijkstra’s search, but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent the geodesic paths in the original metric space significantly more closely.

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Section: Introductionmentioning

confidence: 99%

Towards optimal path computation in a simplicial complex

Bhattacharya

2019

The International Journal of Robotics Research

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“…In fact, finding the globally shortest path has been proven to be NP-hard in 3-D with polyhedral obstacles in the framework known as configuration space by Canny and Rief [17]. Approximation methods, which are the only practical approaches, seek paths whose length is 1+ times the actual minimal path [18], [19], [20], [21]. However, those methods are either only theoretical and only works for polyhedral obstacles, or have high complexity which are unsuitable for on-line implementation.…”

Section: Introductionmentioning

confidence: 99%

Shortest paths through 3-dimensional cluttered environments

Lü

Diaz-Mercado

Egerstedt

et al. 2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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This paper investigates the problem of finding shortest paths through 3-dimensional cluttered environments. In particular, an algorithm is presented that determines the shortest path between two points in an environment with obstacles which can be implemented on robots with capabilities of detecting obstacles in the environment. As knowledge of the environment is increasing while the vehicle moves around, the algorithm provides not only the global minimizer -or shortest path -with increasing probability as time goes by, but also provides a series of local minimizers. The feasibility of the algorithm is demonstrated on a quadrotor robot flying in an environment with obstacles.

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“…On the other hand, 3D path planning problems have been studied extensively for many years. There were several different approaches available including Evolutionary Algorithms (EA) (Hasircioglu et al, 2008;Mittal and Deb, 2007), VL (Jiang et al, 1993) and Dubin circles (Ambrosino et al, 2006), to name but three. In (Hasircioglu et al, 2008) EA and Bspline curves for off-line 3D path planning were used.…”

Section: Introductionmentioning

confidence: 99%

3d Path Planning for Unmanned Aerial Vehicles Using Visibility Line Based Method

2010

Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics

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In path planning, visibility graph (or visibility line (VL)) method is capable of producing shortest path from a starting point to a target point in an environment with polygonal obstacles. However, the run time increases exponentially as the number of obstacles grows, causing this method ineffective for real-time path planning. A 2D path planning framework based on VL has recently been introduced to find a 2D path in an obstaclerich environment with low run time. In this paper we propose 3D path planning algorithms based on the 2D framework. Several steps are used in the algorithms to find a 3D path. First, a local plane is generated from a local starting point to a target point. The plane is then rotated at several pre-defined angles. At each rotation, a shortest path is calculated using 2D algorithms. After rotations at all angles have been done, the shortest one is selected. Simulation results show that the proposed 3D algorithms are capable in finding paths in 3D environments and computationally efficient, thus suitable for real time application.

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Finding the 3D shortest path with visibility graph and minimum potential energy

Cited by 10 publications

References 14 publications

Towards optimal path computation in a simplicial complex

Towards optimal path computation in a simplicial complex

Shortest paths through 3-dimensional cluttered environments

3d Path Planning for Unmanned Aerial Vehicles Using Visibility Line Based Method

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