Models and motion planning

Mark De Berg; Matthew J. Katz; Mark Overmars; A. Frank Van Der Stappen; Jules Vleugels

doi:10.1007/BFb0054357

Models and motion planning

Mark De Berg, Matthew J. Katz, Mark Overmars, A. Frank Van Der Stappen, Jules Vleugels

Institute for the Theory of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simplecover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(n^f/2) in the plane, and O(n^2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(n^f) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments.

Original language	English
Title of host publication	Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings
Editors	Stefan Arnborg, Lars Ivansson
Publisher	Springer Verlag
Pages	83-94
Number of pages	12
ISBN (Print)	3540646825, 9783540646822
DOIs	https://doi.org/10.1007/BFb0054357
State	Published - 1 Jan 1998
Event	6th Scandinavian Workshop on Algorithm Theory, SWAT 1998 - Stockholm, Sweden Duration: 8 Jul 1998 → 10 Jul 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1432
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th Scandinavian Workshop on Algorithm Theory, SWAT 1998
Country/Territory	Sweden
City	Stockholm
Period	8/07/98 → 10/07/98

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/BFb0054357

Cite this

De Berg, M., Katz, M. J., Overmars, M., Frank Van Der Stappen, A., & Vleugels, J. (1998). Models and motion planning. In S. Arnborg, & L. Ivansson (Eds.), Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings (pp. 83-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1432). Springer Verlag. https://doi.org/10.1007/BFb0054357

De Berg, Mark ; Katz, Matthew J. ; Overmars, Mark et al. / Models and motion planning. Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings. editor / Stefan Arnborg ; Lars Ivansson. Springer Verlag, 1998. pp. 83-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Models and motion planning",

abstract = "We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simplecover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(nf/2) in the plane, and O(n2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(nf) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments.",

author = "\{De Berg\}, Mark and Katz, \{Matthew J.\} and Mark Overmars and \{Frank Van Der Stappen\}, A. and Jules Vleugels",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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De Berg, M, Katz, MJ, Overmars, M, Frank Van Der Stappen, A & Vleugels, J 1998, Models and motion planning. in S Arnborg & L Ivansson (eds), Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1432, Springer Verlag, pp. 83-94, 6th Scandinavian Workshop on Algorithm Theory, SWAT 1998, Stockholm, Sweden, 8/07/98. https://doi.org/10.1007/BFb0054357

Models and motion planning. / De Berg, Mark; Katz, Matthew J.; Overmars, Mark et al.
Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings. ed. / Stefan Arnborg; Lars Ivansson. Springer Verlag, 1998. p. 83-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1432).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Models and motion planning

AU - De Berg, Mark

AU - Katz, Matthew J.

AU - Overmars, Mark

AU - Frank Van Der Stappen, A.

AU - Vleugels, Jules

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simplecover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(nf/2) in the plane, and O(n2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(nf) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments.

AB - We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simplecover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(nf/2) in the plane, and O(n2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(nf) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments.

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U2 - 10.1007/BFb0054357

DO - 10.1007/BFb0054357

M3 - Conference contribution

AN - SCOPUS:84957657031

SN - 3540646825

SN - 9783540646822

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 83

EP - 94

BT - Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings

A2 - Arnborg, Stefan

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PB - Springer Verlag

T2 - 6th Scandinavian Workshop on Algorithm Theory, SWAT 1998

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De Berg M, Katz MJ, Overmars M, Frank Van Der Stappen A, Vleugels J. Models and motion planning. In Arnborg S, Ivansson L, editors, Algorithm Theory — SWAT 1998 - 6th Scandinavian Workshop on Algorithm Theory, Proceedings. Springer Verlag. 1998. p. 83-94. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0054357

Models and motion planning

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