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A General Stance Stability Test Based on Stratified Morse Theory With Application to Quasi-Static Locomotion Planning

Rimon, E. and Mason, R. and Burdick, J. W. and Or, Y. (2008) A General Stance Stability Test Based on Stratified Morse Theory With Application to Quasi-Static Locomotion Planning. IEEE Transactions on Robotics, 24 (3). pp. 626-641. ISSN 1552-3098. doi:10.1109/TRO.2008.919287.

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This paper considers the stability of an object supported by several frictionless contacts in a potential field such as gravity. The bodies supporting the object induce a partition of the object's configuration space into strata corresponding to different contact arrangements. Stance stability becomes a geometric problem of determining whether the object's configuration is a local minimum of its potential energy function on the stratified configuration space. We use Stratified Morse Theory to develop a generic stance stability test that has the following characteristics. For a small number of contacts---less than three in 2-D and less than six in 3-D---stance stability depends both on surface normals and surface curvature at the contacts. Moreover, lower curvature at the contacts leads to better stability. For a larger number of contacts, stance stability depends only on surface normals at the contacts. The stance stability test is applied to quasi-static locomotion planning in two dimensions. The region of stable center-of-mass positions associated with a $k$-contact stance is characterized. Then, a quasi-static locomotion scheme for a three-legged robot over a piecewise linear terrain is described. Finally, friction is shown to provide robustness and enhanced stability for the frictionless locomotion plan. A full maneuver simulation illustrates the locomotion scheme.

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Or, Y.0000-0002-9091-9357
Additional Information:© 2008 IEEE. Reprinted with permission. Manuscript received Auguest 6, 2007. This paper was recommended for publication by Associate Editor O. Brock and Editor K. Lynch upon evaluation of the reviewers’ comments. Color versions of one or more of the figures in this paper are available online at
Subject Keywords:Posture stability, quasistatic locomotion, stance stability, stratified Morse theory
Issue or Number:3
Record Number:CaltechAUTHORS:RIMieeetr08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11107
Deposited By: Archive Administrator
Deposited On:15 Jul 2008 05:08
Last Modified:08 Nov 2021 21:33

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