Finding Stable Orientations of Assemblies with Linear Programming

David Baraff, Raju Mattikalli, Bruno Repetto, and Pradeep Khosla
tech. report CMU-RI-TR-93-13, Robotics Institute, Carnegie Mellon University, June, 1993


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Abstract
In the paper by Mattikalli et al.[5], the stability of an assemblage of frictionless contacting bodies with uniform gravity was considered. The problem of finding a stable orientation for such an assembly was formulated as a constrained maximin problem. A solution to the maximin problem yielded an orientation of the assembly that was stable under gravity; however, if no such orientation existed, then the solution to the maximin problem yielded the most stable orientation possible for the assembly. The maximin problem was solved using a numerical iteration procedure that solved a linear program for each step of the iteration. In this paper, we show that the stability problem can be considered a variant of standard zero-sum matrix games. A solution to the maximin problem can be found by solving a single linear program.

Notes
Grant ID: MDA972-92-J-1010
Number of pages: 16

Text Reference
David Baraff, Raju Mattikalli, Bruno Repetto, and Pradeep Khosla, "Finding Stable Orientations of Assemblies with Linear Programming," tech. report CMU-RI-TR-93-13, Robotics Institute, Carnegie Mellon University, June, 1993

BibTeX Reference
@techreport{Baraff_1993_304,
   author = "David Baraff and Raju Mattikalli and Bruno Repetto and Pradeep Khosla",
   title = "Finding Stable Orientations of Assemblies with Linear Programming",
   booktitle = "",
   institution = "Robotics Institute",
   month = "June",
   year = "1993",
   number= "CMU-RI-TR-93-13",
   address= "Pittsburgh, PA",
}