## Computing 3-legged equilibrium stances in three-dimensional gravitational environments (1984)

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Venue: | In IEEE Int. Conf. on Robotics and Automation |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Or84computing3-legged,

author = {Yizhar Or and Elon Rimon},

title = {Computing 3-legged equilibrium stances in three-dimensional gravitational environments},

booktitle = {In IEEE Int. Conf. on Robotics and Automation},

year = {1984}

}

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### Abstract

Quasistatic multi-legged locomotion consists of a sequence of equilibrium postures where the mechanism supports itself against gravity while moving free limbs to new positions. A posture maintains equilibrium if the contacts can passively support the mechanism against gravity. This paper is concerned with identifying and computing equilibrium postures for mechanisms supported by frictional contacts in a threedimensional gravitational field. The complex kinematic structure of the mechanism is lumped into a single rigid body having the same contacts with the environment and a variable center of mass. The identification of equilibrium postures associated with a given set of contacts is reduced to the identification of center-of-mass locations that maintain equilibrium while all nonlinear frictional constraints are satisfied. This work is mainly a continuation of two previous works- the work of Mason et. al. [1] who computed stable equilibrium stances in frictionless environments, and the work of Or and Rimon [2], who computed frictional equilibrium stances 2D. In the three-dimensional frictional case, Han et. al. [3] formulated the problem as linear matrix inequalities (LMI) for finding optimal frictional grasps, and Bretl et. al. [4]

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