Probabilistic algorithms for efficient grasping and fixturing

M. Teichmann, Bhubaneswar Mishra

Research output: Contribution to journalArticle

Abstract

Given an object with n points on its boundary where fingers can be placed, we give algorithms to select a "strong" grasp with the least number c of fingers (up to a logarithmic factor) using several measures of goodness. Along similar lines, given an integer c, we find the "best" κc log c finger grasp for a small constant κ. In addition, we generalize existing measures for the case of frictionless assemblies of many objects in contact. We also give an approximation scheme which guarantees a grasp quality close to the overall optimal value where fingers are not restricted to preselected points. These problems translate into a collection of convex set covering problems where we either minimize the cover size or maximize the scaling factor of an inscribed geometric object L. We present an algorithmic framework which handles these problems in a uniform way and give approximation algorithms for specific instances of L including convex polytopes and balls. The framework generalizes an algorithm for polytope covering and approximation by Clarkson [Cla] in two different ways. Let γ = 1/[d/2], where d is the dimension of the Euclidean space containing L. For both types of problems, when L is a polytope, we get the same expected time bounds (with a minor improvement), and for a ball, the expected running time is O(n 1+δ + (nc) 1/(1+γ/(1+δ)) + c log(n/c)(c log c) [d/2] for fixed d, and arbitrary positive δ. We improve this bound if we allow in addition a different kind of approximation for the optimal radius. We also give bounds when d is not a constant.

Original languageEnglish (US)
Pages (from-to)345-363
Number of pages19
JournalAlgorithmica (New York)
Volume26
Issue number3-4
StatePublished - 2000

Fingerprint

Probabilistic Algorithms
Grasping
Polytope
Ball
Approximation algorithms
Set Covering Problem
Convex Polytopes
Generalise
Geometric object
Scaling Factor
Approximation
Approximation Scheme
Convex Sets
Euclidean space
Approximation Algorithms
Minor
Logarithmic
Covering
Maximise
Radius

Keywords

  • Approximate geometric algorithms
  • Closure grasps
  • Fixturing
  • Grasp metrics
  • Grasping
  • Multifinger robot hands
  • Polytope covering

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics

Cite this

Probabilistic algorithms for efficient grasping and fixturing. / Teichmann, M.; Mishra, Bhubaneswar.

In: Algorithmica (New York), Vol. 26, No. 3-4, 2000, p. 345-363.

Research output: Contribution to journalArticle

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