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Finding Stable Orientations of Assemblies with Linear Programming
D. Baraff, R. Mattikalli, B. Repetto, and P. Khosla
tech. report CMU-RI-TR-93-13, Robotics Institute, Carnegie Mellon University, June, 1993.

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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.

Grant ID: MDA972-92-J-1010

Number of pages: 16

D. Baraff, R. Mattikalli, B. Repetto, and P. Khosla, Finding Stable Orientations of Assemblies with Linear Programming, tech. report CMU-RI-TR-93-13, Robotics Institute, Carnegie Mellon University, June, 1993.

@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",
   institution = "Robotics Institute, Carnegie Mellon University",
   month = "June",
   year = "1993",
   number = "CMU-RI-TR-93-13",
   address = "Pittsburgh, PA"
}