## Sensor Based Motion Planning: The Hierarchical Generalized Voronoi Graph (1996)

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Citations: | 78 - 9 self |

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@MISC{Choset96sensorbased,

author = {Howie Choset},

title = {Sensor Based Motion Planning: The Hierarchical Generalized Voronoi Graph},

year = {1996}

}

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### Abstract

The hierarchical generalized Voronoi graph (HGVG) is a roadmap that can serve as a basis for sensor based robot motion planning. A key feature of the HGVG is its incremental construction procedure that uses only line of sight distance information. This work describes basic properties of the HGVG and the procedure for its incremental construction using local range sensors. Simulations and experiments verify this approach. 1 Introduction Sensor based motion planning incorporates sensor information, reflecting the current state of the environment, into a robot's planning process, as opposed to classical planning, which assumes full knowledge of the world's geometry prior to planning. Sensor based planning is important for realistic deployment of robots because: (1) the robot often has no a priori knowledge of the world; (2) the robot may have only a coarse knowledge of the world because of limited computer memory; (3) the world model is bound to contain inaccuracies which can be overcom...

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Citation Context ...xed stepping direction. However, gradient ascent can be a computationally expensive procedure because of its slow convergence. Also, the constant step direction leads to undesirable roadmap artifacts =-=[15]-=-. Our approach borrows some basic ideas and techniques from numerical continuation methods [24]. Continuation methods are used to trace the roots of the expression G 1 (y; ) = 0 as the parametersis va... |

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Citation Context ...d to non-planar problems. In [36], an incremental approach to create a Voronoi diagram-like structure, which is limited to the case of a plane, was introduced. Prior work (e.g., Avis and Bhattacharya =-=[3]-=-) describes the Voronoi graph, an extension of the Voronoi diagram extended into higher dimensions. The Voronoi graph is the locus of points in m dimensions equidistant to m point sites. The generaliz... |

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6 |
Vision-Basied Motion Planning and Exploration Algorithms for Mobile Robots
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Citation Context ...th does not reflect the topology of the free space (the region of the environment not occupied by obstacles) and thus, it cannot be used to guide future robot excursions. Taylor and Kriegman's method =-=[43]-=- has a provably correct solution, uses realistic sensor assumptions, and need not require prior knowledge of the goal's location. In this method, the robot forms a graph of a bounded free space by cir... |

6 |
Simpli ed voronoi diagrams
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(Show Context)
Citation Context ...hat is, it is the set of points in m dimensions equidistant tom convex obstacles. Though the GVG introduced in this work appears to be new, a disconnected GVG-like structure for SE(3) is described in =-=[3]-=-. The GVG can be thought of as the natural extension of the GVD into higher dimensions. However, unlike the GVD, the GVG is not necessarily connected in dimensions greater than two, and thus, in gener... |

5 |
Descent Algorithm for a Class of Convex Nondifferentiable Functions
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(Show Context)
Citation Context ...and only if fv i 2 R m : i = 1; : : : ; ng positively span R m . Lemma A.22 [Goldman and Tucker] It requires a minimum of (m + 1) vectors to positively span R m . The results of Scheimber and Olivera =-=[41] state tha-=-t the second derivative of D, termed a generalized hesian, is always positive or contains only positive values. In a sense, the graph of the function D is always "concave up." Therefore, the... |

1 |
Linear Inequalities and Related Systems, chapter Polyhedral Convex Cones
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- 1956
(Show Context)
Citation Context ... ; m+ 1g if and only if 1. m of the m+ 1 vectors are linearly independent, and 2. a strictly positive sum of the m+1 vectors is the zero vector, i.e., P i=m+1 i=1si v i = 0 wheresi ? 0 for all i. See =-=[33, 23]-=- for proof. Lemma A.19 A set of n arbitrary vectors fv i 2 R m : i = 1; : : : ; ng positvely spans R m if and only if there exists a v i such that for all w 2 R m , hw; v i i ? 0. Proof: Let w = P n i... |