## Quasi-Randomized Path Planning (2001)

Venue: | In Proc. IEEE Int’l Conf. on Robotics and Automation |

Citations: | 71 - 10 self |

### BibTeX

@INPROCEEDINGS{Branicky01quasi-randomizedpath,

author = {Michael S. Branicky and Steven M. Lavalle and Kari Olson and Libo Yang},

title = {Quasi-Randomized Path Planning},

booktitle = {In Proc. IEEE Int’l Conf. on Robotics and Automation},

year = {2001},

pages = {1481--1487}

}

### Years of Citing Articles

### OpenURL

### Abstract

We propose the use of quasi-random sampling techniques for path planning in high-dimensional conguration spaces. Following similar trends from related numerical computation elds, we show several advantages oered by these techniques in comparison to random sampling. Our ideas are evaluated in the context of the probabilistic roadmap (PRM) framework. Two quasi-random variants of PRM-based planners are proposed: 1) a classical PRM with quasi-random sampling, and 2) a quasi-random Lazy-PRM. Both have been implemented, and are shown through experiments to oer some performance advantages in comparison to their randomized counterparts. 1 Introduction Over two decades of path planning research have led to two primary trends. In the 1980s, deterministic approaches provided both elegant, complete algorithms for solving the problem, and also useful approximate or incomplete algorithms. The curse of dimensionality due to high-dimensional conguration spaces motivated researchers from the 199...

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Citation Context ...r, we take thesrst step towards answering these questions by illustrating some of the advantages of quasi-random sampling in the context of the probabilistic roadmap (PRM) framework for path planning =-=[1, 16]-=-; a glimpse is given in Figure 1. We present implemented, quasi-random variants of both the classical PRM [16] and the recent Lazy-PRM [4], and indicate some advantages over their randomized counterpa... |

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Citation Context ... been developed to address this issue. Creating nodes in narrow passages has been the main motivation of the enhancement step in [15], the generation of nodes near the conguration space obstacles in [=-=2-=-], the penetration of obstacles in [11], the Gaussian sampling in [5], the retraction to the conguration space medial axis in [2], and the use of the workspace medial axis in [10] and [23]. 3.2 Q-PRM ... |

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Citation Context ...e probabilistic roadmap (PRM) framework for path planning [1, 16]; a glimpse is given in Figure 1. We present implemented, quasi-random variants of both the classical PRM [16] and the recent Lazy-PRM =-=[4]-=-, and indicate some advantages over their randomized counterparts. Atsrst glance, the progression from deterministic to randomized, and then back to deterministic might appear absurd; thus, some expla... |

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Citation Context ... that use deterministic sampling to achieve performance that is often superior to random sampling. Quasi-random sampling ideas have improved computational methods in many areas, including integration =-=[25]-=-, optimization [21], image processing [8], and computer graphics [24]. It is therefore natural to ask: Can quasi-random sampling ideas also improve path planning methods designed for high degrees of f... |

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Citation Context ...r developments of specialized random sampling methods that improve performance for sharply-peaked integrands [13, 14, 18], and the recent development of specialized sampling methods for path planning =-=[1, 6, 11]-=-. In practice, random sampling methods require the construction of deterministic, pseudo-random samples. Thus, researchers began to question whether other deterministic samples could be designed which... |

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Citation Context ...ages has been the main motivation of the enhancement step in [15], the generation of nodes near the conguration space obstacles in [2], the penetration of obstacles in [11], the Gaussian sampling in [=-=5-=-], the retraction to the conguration space medial axis in [2], and the use of the workspace medial axis in [10] and [23]. 3.2 Q-PRM Overview Monte Carlo methods, like PRM and its uniform random sampli... |

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Citation Context ...r, we take thesrst step towards answering these questions by illustrating some of the advantages of quasi-random sampling in the context of the probabilistic roadmap (PRM) framework for path planning =-=[1, 16]-=-; a glimpse is given in Figure 1. We present implemented, quasi-random variants of both the classical PRM [16] and the recent Lazy-PRM [4], and indicate some advantages over their randomized counterpa... |

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Citation Context ...nd convergence was not dependent on dimension. There are interesting parallels between later developments of specialized random sampling methods that improve performance for sharply-peaked integrands =-=[13, 14, 18]-=-, and the recent development of specialized sampling methods for path planning [1, 6, 11]. In practice, random sampling methods require the construction of deterministic, pseudo-random samples. Thus, ... |

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Citation Context ...the nearest point in the sequence. For anysnite set P of N points in [0; 1] d , it is known that dN (P ) DN (P ) 1 d , in which dN is the dispersion (under the l 1 metric) and DN is the discrepancy [=-=21, 26-=-]. Hence, low-discrepancy point sets lead to low dispersion. The benets of low discrepancy and low dispersion point sets will be evaluated in the context of randomized path planning in Sections 3 and ... |

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Citation Context ... description of PRM presented here is based roughly on the initial algorithm described in [16]. It has inspired dierent versions of PRM planners that have been developed by dierent researchers (see [1=-=, 3, 6, 16]-=- and their references) . When applying roadmap path planners, there are two phases. During thesrst phase, nodes are generated and connections between the nodes are added to the roadmap. In the second ... |

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Citation Context ...on space obstacles in [2], the penetration of obstacles in [11], the Gaussian sampling in [5], the retraction to the conguration space medial axis in [2], and the use of the workspace medial axis in [=-=10]-=- and [23]. 3.2 Q-PRM Overview Monte Carlo methods, like PRM and its uniform random sampling cousins for integration and optimization, have been adopted for problems with high dimension to overcome the... |

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Citation Context ... superior to random sampling. Quasi-random sampling ideas have improved computational methods in many areas, including integration [25], optimization [21], image processing [8], and computer graphics =-=[24]-=-. It is therefore natural to ask: Can quasi-random sampling ideas also improve path planning methods designed for high degrees of freedom? Is randomization really necessary? a. b. Figure 1: a) A proba... |

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Citation Context ...terministic point sets, have been shown to be both computationally ecient and accurate for a variety of applications including 360-dimensional integrations performed insnance and bounded optimization =-=[27, 28]-=- Simply put, Quasi-random Roadmap (Q-PRM) algorithms aim to replace specialized, quasi-random points for the randomly chosen points in Step 3 of the roadmap generation algorithm above. An example of t... |

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Citation Context ... subset of the third. In the last three classes, it has been possible to obtain low-discrepancy point sets that perform better than random sampling for numerical integration and optimization problems =-=[9, 21, 25]-=-. A grid corresponds to the usual uniform quantization of each of the coordinate axes. A lattice is a generalization that preserves the convenient neighborhood structure of a grid, but is generated by... |

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Citation Context ...obstacles in [2], the penetration of obstacles in [11], the Gaussian sampling in [5], the retraction to the conguration space medial axis in [2], and the use of the workspace medial axis in [10] and [=-=23]-=-. 3.2 Q-PRM Overview Monte Carlo methods, like PRM and its uniform random sampling cousins for integration and optimization, have been adopted for problems with high dimension to overcome the curse of... |

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Citation Context ...stic sampling to achieve performance that is often superior to random sampling. Quasi-random sampling ideas have improved computational methods in many areas, including integration [25], optimization =-=[21]-=-, image processing [8], and computer graphics [24]. It is therefore natural to ask: Can quasi-random sampling ideas also improve path planning methods designed for high degrees of freedom? Is randomiz... |

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Citation Context ...crepancy for rectangle R. The discrepancy of point set P is obtained bysnding the maximum such dierence over all possible rectangles. Thus, one measure of the discrepancy that has been proposed (see [=-=19-=-] for a litany of others plus discussion) is the L1 -discrepancy of thesrst N points of a d-dimensional sequence, S, in [0; 1] d : sup [a;b)[0;1] d jfs 1 ; : : : ; s N g \ [a; b)j N d Y i=1 (b i a i )... |

12 | Path planning in expansive con spaces - Hsu, Latombe, et al. |

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Citation Context ...gh-dimensional functions. Deterministic grid-based quadrature formulas led to the same combinatorial explosion that was experienced years later in grid-based path planning methods. About 50 years ago =-=[20]-=-, this frustration led to the development of numerical integration techniques (Monte Carlo) based on random sampling of the function domain, and convergence was not dependent on dimension. There are i... |

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Citation Context ...e performance that is often superior to random sampling. Quasi-random sampling ideas have improved computational methods in many areas, including integration [25], optimization [21], image processing =-=[8]-=-, and computer graphics [24]. It is therefore natural to ask: Can quasi-random sampling ideas also improve path planning methods designed for high degrees of freedom? Is randomization really necessary... |

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Citation Context ...nd convergence was not dependent on dimension. There are interesting parallels between later developments of specialized random sampling methods that improve performance for sharply-peaked integrands =-=[13, 14, 18]-=-, and the recent development of specialized sampling methods for path planning [1, 6, 11]. In practice, random sampling methods require the construction of deterministic, pseudo-random samples. Thus, ... |

2 |
Quasi-random roadmaps: Using deterministic low discrepancy point sets to break the curse of dimensionality in motion planning. Submitted to the 4th Int
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(Show Context)
Citation Context ...equal to its PRM counterpart. We present some theoretical advantages of quasi-random versus random points, as well as some compelling experimental results, in the next section. More results appear in =-=[7, 22-=-]. 3.3 Comparing PRM and Q-PRM The following table shows the results of experiments performed on narrow corridor problems that have the same geometry as the example in Figure 1. The conguration spaces... |

2 |
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(Show Context)
Citation Context ...e are notoriously dicult tosnd at random. Indeed, several planners have been developed to address this issue. Creating nodes in narrow passages has been the main motivation of the enhancement step in =-=[1-=-5], the generation of nodes near the conguration space obstacles in [2], the penetration of obstacles in [11], the Gaussian sampling in [5], the retraction to the conguration space medial axis in [2],... |

1 |
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(Show Context)
Citation Context ...nd convergence was not dependent on dimension. There are interesting parallels between later developments of specialized random sampling methods that improve performance for sharply-peaked integrands =-=[13, 14, 18]-=-, and the recent development of specialized sampling methods for path planning [1, 6, 11]. In practice, random sampling methods require the construction of deterministic, pseudo-random samples. Thus, ... |

1 |
Quasi-random roadmap methods (QRM): Derandomizing probabilistic motion planning
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(Show Context)
Citation Context ...equal to its PRM counterpart. We present some theoretical advantages of quasi-random versus random points, as well as some compelling experimental results, in the next section. More results appear in =-=[7, 22-=-]. 3.3 Comparing PRM and Q-PRM The following table shows the results of experiments performed on narrow corridor problems that have the same geometry as the example in Figure 1. The conguration spaces... |