Designing multi-link robot arms in a convex polygon

Ichiro Suzuki, Masafumi Yamashita

Research output: Contribution to journalArticle

Abstract

The problem of designing a k-link robot arm confined in a convex polygon that can reach any point in the polygon starting from a fixed initial configuration is considered. The links of an arm are assumed to be all of the same length. We present a necessary condition and a sufficient condition on the shape of the given polygon for the existence of such a k-link arm for various values of k, as well as necessary and sufficient conditions for rectangles, triangles and diamonds to have such an arm. We then study the case k = 2, and show that, for an arbitrary n-sided convex polygon, in O(n2) time we can decide whether there exists a 2-link arm that can reach all inside points, and construct such an arm if it exists. Finally, we prove a lower bound and an upper bound on the number of links needed to construct an arm that can reach every point in a general n-sided convex polygon, and show that the two bounds can differ by at most one. The constructive proof of the upper bound thus provides a simple method for designing a desired arm having at most k+1 links when a minimum of k links are necessary, for any k ≥ 3. The method can be implemented to run in O(n2) time.

Original languageEnglish
Pages (from-to)461-486
Number of pages26
JournalInternational Journal of Computational Geometry and Applications
Volume6
Issue number4
DOIs
Publication statusPublished - Jan 1 1996

Fingerprint

Convex polygon
Diamonds
Robot
Robots
Polygon
Upper bound
Necessary Conditions
Sufficient Conditions
Strombus or kite or diamond
Rectangle
Triangle
Lower bound
Configuration
Necessary
Arbitrary

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Designing multi-link robot arms in a convex polygon. / Suzuki, Ichiro; Yamashita, Masafumi.

In: International Journal of Computational Geometry and Applications, Vol. 6, No. 4, 01.01.1996, p. 461-486.

Research output: Contribution to journalArticle

Suzuki, Ichiro ; Yamashita, Masafumi. / Designing multi-link robot arms in a convex polygon. In: International Journal of Computational Geometry and Applications. 1996 ; Vol. 6, No. 4. pp. 461-486.
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