## MAPRM: A probabilistic roadmap planner with sampling on the medial axis of the free space (1999)

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Venue: | In Proc. IEEE Int. Conf. Robot. Autom. (ICRA |

Citations: | 156 - 37 self |

### BibTeX

@INPROCEEDINGS{Wilmarth99maprm:a,

author = {Steven A. Wilmarth and Nancy M. Amato and Peter F. Stiller},

title = {MAPRM: A probabilistic roadmap planner with sampling on the medial axis of the free space},

booktitle = {In Proc. IEEE Int. Conf. Robot. Autom. (ICRA},

year = {1999},

pages = {1024--1031}

}

### Years of Citing Articles

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### Abstract

Probabilistic roadmap planning methods have been shown to perform well in a number of practical situations, but their performance degrades when paths are required to pass through narrow passages in the free space. We propose a new method of sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space. We give algorithms that perform this retraction while avoiding explicit computation of the medial axis, and we show that sampling and retracting in this manner increases the number of nodes found in small volume corridors in a way that is independent of the volume of the corridor and depends only on the characteristics of the obstacles bounding it. Theoretical and experimental results are given to show that this improves performance on problems requiring traversal of narrow passages. 1

### Citations

2118 |
Robot motion planning
- Latombe
(Show Context)
Citation Context ...cs. Supported in part by the Air Force Office of Scientific Research. passages in configuration space. The medial axis or generalized Voronoi diagram has a long history of use in motion planning, see =-=[2, 8]-=-. This stems from the fact the medial axis MA(F ) of the free space F (the set of all collision-free configurations) has lower dimension than F but is still a complete representation for motion planni... |

962 | Probabilistic roadmaps for path planning in highdimensional configuration spaces
- Kavraki, Svestka, et al.
- 1996
(Show Context)
Citation Context ...feasibility and applicability. In particular, several algorithms, known collectively as probabilistic roadmap planners, have been shown to perform well in a number of practical situations, see, e.g., =-=[7]-=-. The idea behind these methods is to create a graph of randomly generated collision-free configurations with connections between these nodes made by a simple and fast local planning method. Actual gl... |

663 | A mathematical introduction to robotic manipulation
- Murray, Sastry
- 1994
(Show Context)
Citation Context ...a3 j RR T = I and det(R) = 1g point. If c = (R; p), we write c \Delta U or (R; p) \Delta U to mean the coordinates of all points of U with respect to the world frame when U is in configuration c. See =-=[10] for -=-more detail on SE(3). Now, given an obstacle V in the workspace R 3 , certain configurations of U are prohibited because they cause U to overlap V , i.e., fc 2 SE(3) j (c \Delta U) " V 6= ;g. We ... |

584 | Vornoi diagrams - survey of a fundamental geometric data structure
- Aurenhammer
- 1991
(Show Context)
Citation Context ...cs. Supported in part by the Air Force Office of Scientific Research. passages in configuration space. The medial axis or generalized Voronoi diagram has a long history of use in motion planning, see =-=[2, 8]-=-. This stems from the fact the medial axis MA(F ) of the free space F (the set of all collision-free configurations) has lower dimension than F but is still a complete representation for motion planni... |

233 | OBPRM: An obstacle-based PRM for 3D workspaces
- Amato, Bayazit, et al.
- 1998
(Show Context)
Citation Context ...igurations to nodes in the roadmap (again using the local planner) and then searching for a path in the roadmap connecting these nodes. Various sampling schemes and local planners have been used, see =-=[1, 6, 11]-=-. The algorithms are easy to implement, run quickly, and are applicable to a wide variety of robots. The main shortcoming of these methods is their poor performance on problems requiring paths that pa... |

174 | On finding narrow passages with probabilistic roadmap planners
- Hsu, Kavraki, et al.
- 1998
(Show Context)
Citation Context ...odify sampling to increase the number of nodes sampled in narrow corridors. Intuitively, such narrow corridors may be characterized by their large surface area to volume ratio: the methods in [1] and =-=[5]-=- have exploited this idea. In [1], nodes are sampled from the contact space, the set of configurations for which the workpiece is in contact (but not collision), with an obstacle. This method has solv... |

174 | V-clip: Fast and robust polyhedral collision detection
- Mirtich
- 1997
(Show Context)
Citation Context ...ces: if the pair can be connected with the local planner, insert an edge into the graph connecting them. 4.3 Implementation and experimental results We implemented MAPRM for rigid bodies using V-Clip =-=[9]-=- to provide collision detection and closest pair calculations. We used a single local planner: translation with simultaneous rotation about the principal axis of rotation. Normally in practice, connec... |

120 | Enhancing GJK: Computing minimum and penetration distances between convex polyhedra
- Cameron
- 1997
(Show Context)
Citation Context ...is shown in Figure 6. The workpiece is a cube of side length 2; the obstacle is a solid cube of side 5 Some work has been done on this shortest translation problem, but only for convex polyhedra, see =-=[3]-=-. Algorithm 4.2 Finding the nearest contact configuration Input. A configuration (R; p). Output. A shortest translation (R; q) from configuration (R; p) that puts U in contact (but not collision) with... |

116 | A probabilistic learning approach to motion planning
- Overmars, Ë‡Svestka
- 1994
(Show Context)
Citation Context ...igurations to nodes in the roadmap (again using the local planner) and then searching for a path in the roadmap connecting these nodes. Various sampling schemes and local planners have been used, see =-=[1, 6, 11]-=-. The algorithms are easy to implement, run quickly, and are applicable to a wide variety of robots. The main shortcoming of these methods is their poor performance on problems requiring paths that pa... |

82 | Mathematical theory of medial axis transform
- Choi, Choi, et al.
- 1997
(Show Context)
Citation Context ...ested in the medial axis of the free space, which lies in the configuration space and not in the workspace. Although this development could proceed assuming only piecewise real analytic boundary (see =-=[4]-=-), for simplicity we consider only sets P that are the disjoint union of a finite number of closed polygons (including the interior, possibly with holes). For x 2 P , we define BP (x) to be the larges... |

71 |
Random Networks in Configuration Space for Fast Path Planning
- Kavraki
- 1995
(Show Context)
Citation Context ...igurations to nodes in the roadmap (again using the local planner) and then searching for a path in the roadmap connecting these nodes. Various sampling schemes and local planners have been used, see =-=[1, 6, 11]-=-. The algorithms are easy to implement, run quickly, and are applicable to a wide variety of robots. The main shortcoming of these methods is their poor performance on problems requiring paths that pa... |

54 |
Distance metrics on the rigid-body motions with applications to mechanism design
- Park
- 1995
(Show Context)
Citation Context ...pling from the configuration space depends on the choice of metric. Our approach is use a Riemannian metric to impose the necessary geometric structure, but there are still many possible choices, see =-=[12]-=-. Rather than restricting our attention to a particular Riemannian metric, we enumerate our assumptions about the metric being used and give a retraction algorithm which will always work under these c... |