## Efficient Distance Computation between Non-Convex Objects (1994)

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Venue: | In Proceedings of International Conference on Robotics and Automation |

Citations: | 195 - 0 self |

### BibTeX

@INPROCEEDINGS{Quinlan94efficientdistance,

author = {Sean Quinlan},

title = {Efficient Distance Computation between Non-Convex Objects},

booktitle = {In Proceedings of International Conference on Robotics and Automation},

year = {1994},

pages = {3324--3329}

}

### Years of Citing Articles

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### Abstract

This paper describes an efficient algorithm for computing the distance between non-convex objects. Objects are modeled as the union of a set of convex components. From this model we construct a hierarchical bounding representation based on spheres. The distance between objects is determined by computing the distance between pairs of convex components using preexisting techniques. The key to efficiency is a simple search routine that uses the bounding representation to ignore most of the possible pairs of components. The efficiency can further be improved by accepting a relative error in the returned result. Several empirical trials are presented to examine the performance of the algorithm. 1. Introduction Computing the distance between objects is a common problem in robotics. Using a mathematical model of two objects, we find a point on each object such that the distance between the points is minimized. If one object is a robot and the other object is the union of all the obstacles i...

### Citations

1986 |
Robot Motion Planning
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Citation Context ...nce computation; two objects are in collision if and only if the distance between the objects is zero. Collision detection has been used extensively in robotics for applications such as path planning =-=[8]-=-, and in computer graphics for physical based modeling [9]. For such applications, collision detection often consumes a significant percentage of the execution time and much research has been directed... |

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Computational Geometry: An Introduction
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Citation Context ... The median can be found in O(n) via the classic algorithm [14] or, more simply, if we perform an initial sort of the leaf nodes along each of the three axes and carry out some additional bookkeeping =-=[15]-=-. The disadvantage of these algorithms is the higher constant factor in the expected execution time. A close analogy can be drawn between the relative benefits of quicksort, which has worst case O(n 2... |

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Citation Context ...other object is the union of all the obstacles in the environment, such information describes how close the robot is to collision. Distance computation has been used for real-time collision avoidance =-=[1]-=-, real-time path modification [2], and optimal path planning [3]. Previous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pai... |

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Data Structures and Algorithm
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Citation Context ...st case of O(n 2 ). The worst case execution time can be reduced to O(nlogn) if we use the median rather than the average to partition a set. The median can be found in O(n) via the classic algorithm =-=[14]-=- or, more simply, if we perform an initial sort of the leaf nodes along each of the three axes and carry out some additional bookkeeping [15]. The disadvantage of these algorithms is the higher consta... |

277 | A fast procedure for computing the distance between complex objects in three-dimensional space
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- 1988
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Citation Context ...nd optimal path planning [3]. Previous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pairs of line segments. Gilbert et al. =-=[5]-=-, Bobrow [6], and Lin and Canny [7] present algorithms that find the distance between two convex polyhedra. Each of these three algorithms iteratively finds pairs of points, one on each object, such t... |

134 | Elastic bands: Connecting path planning and control
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Citation Context ...the obstacles in the environment, such information describes how close the robot is to collision. Distance computation has been used for real-time collision avoidance [1], real-time path modification =-=[2]-=-, and optimal path planning [3]. Previous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pairs of line segments. Gilbert et a... |

20 |
A direct minimization approach for obtaining the distance between convex polyhedra
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Citation Context ...ath planning [3]. Previous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pairs of line segments. Gilbert et al. [5], Bobrow =-=[6]-=-, and Lin and Canny [7] present algorithms that find the distance between two convex polyhedra. Each of these three algorithms iteratively finds pairs of points, one on each object, such that the dist... |

19 | D.: Non-penetrating rigid body simulation
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- 1993
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Citation Context ... number of components that are examined. Similarly, bounding representations approximately model an object with simple primitives such as rectangles. Efficient algorithms, such as described by Baraff =-=[11]-=-, determine if collision has occurred between the bounding representation and only then are components of the original model examined. In this paper, we present an efficient algorithm for distance com... |

15 |
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Citation Context ...ids, may better approximate components of the underlying model, however, we feel the simplicity of the sphere makes it the preferred bounding shape. A collision detection algorithm by del Pobil et al =-=[12]-=- also uses spheres to build a bounding representation. The bounding representation consists of an approximately balanced binary tree. Each node of the tree contains a single sphere and the tree has ha... |

14 |
Hierarchical object models for efficient anti-collision algorithms
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Citation Context ...cted at finding efficient algorithms. Two related approaches for efficient collision detection are hierarchical models and bounding representations. A hierarchical model, such as proposed by Faverjon =-=[10]-=-, describes an object at various levels of detail. The collision detection algorithm uses the different levels of detail to reduce the number of components that are examined. Similarly, bounding repre... |

7 |
On fast computation of distance between line segments
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- 1985
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Citation Context ...n used for real-time collision avoidance [1], real-time path modification [2], and optimal path planning [3]. Previous work on the distance computation problem has focused on convex objects. Lumelsky =-=[4]-=- describes an efficient algorithm for pairs of line segments. Gilbert et al. [5], Bobrow [6], and Lin and Canny [7] present algorithms that find the distance between two convex polyhedra. Each of thes... |

3 |
Optimal robot plant planning using the minimum-time criteriron
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Citation Context ...t, such information describes how close the robot is to collision. Distance computation has been used for real-time collision avoidance [1], real-time path modification [2], and optimal path planning =-=[3]-=-. Previous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pairs of line segments. Gilbert et al. [5], Bobrow [6], and Lin and... |

2 |
A Fast Alogrithm for Incremental Distance Calculation
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Citation Context ...ous work on the distance computation problem has focused on convex objects. Lumelsky [4] describes an efficient algorithm for pairs of line segments. Gilbert et al. [5], Bobrow [6], and Lin and Canny =-=[7]-=- present algorithms that find the distance between two convex polyhedra. Each of these three algorithms iteratively finds pairs of points, one on each object, such that the distance between the points... |

2 |
Analytical Mathods for Dynamic Simulation of Nonpenetrating Rigid Bodies
- Baraff
- 1989
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Citation Context ...if the distance between the objects is zero. Collision detection has been used extensively in robotics for applications such as path planning [8], and in computer graphics for physical based modeling =-=[9]-=-. For such applications, collision detection often consumes a significant percentage of the execution time and much research has been directed at finding efficient algorithms. Two related approaches f... |