GRAVITATIONAL STABILITY OF FRICTIONLESS ASSEMBLIES

Citation
R. Mattikalli et al., GRAVITATIONAL STABILITY OF FRICTIONLESS ASSEMBLIES, IEEE transactions on robotics and automation, 11(3), 1995, pp. 374-388
Citations number
17
Categorie Soggetti
Computer Application, Chemistry & Engineering","Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
ISSN journal
1042296X
Volume
11
Issue
3
Year of publication
1995
Pages
374 - 388
Database
ISI
SICI code
1042-296X(1995)11:3<374:GSOFA>2.0.ZU;2-2
Abstract
The stability of an assemblage of contacting rigid bodies without fric tion is investigated, A method is presented for finding an orientation of the assembly so that the assembly remains motionless under gravity . If no stable orientation exists for an assembly, the method finds th e ''least'' unstable orientation. The metric used to measure stability is based on the second time-rate of change of the gravitational poten tial energy, and the desired orientation for an assembly is expressed in terms of an optimization problem involving changes in potential ene rgy. The problem of finding stable or maximally-stable orientations is formulated as a constrained maximin problem. The maximin problem is s hown to be a variant of standard zero-sum matrix games, and can be sol ved using linear programming. The method is the first general method f or automatically determining stable orientations. Example assemblies a re presented.