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Finding Stable Orientations of Assemblies with Linear Programming

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journal contribution
posted on 01.01.1993 by David Baraff, Raju Mattikalli, Bruno Repetto, Pradeep Khosla

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.


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