Computation and Graphical Characterization of Robust Multiple-Contact Postures in Two-Dimensional Gravitational Environments

Quasistatic multi-legged locomotion consists of a series of postures where the mechanism supports itself against gravity while moving free limbs to new positions. A posture is robust if the contacts can passively support the mechanism against gravity as well as disturbance forces generated by moving limbs of the mechanism. This paper is concerned with identifying and computing robust postures of planar mechanisms supported by frictional contacts in two-dimensional gravitational environments. The complex kinematic structure of the mechanism is lumped into a single rigid body B having the same contacts with the environment and a variable center of mass. Inertial forces generated by moving parts of the mechanism are lumped into a neighborhood of wrenches centered at the nominal gravitational wrench. The robust equilibrium postures associated with a given set of contacts become the center-of-mass locations of B that maintain equilibrium with respect to all wrenches in the given neighborhood. The paper formulates the set of robust center-of-mass locations as a linear programming problem. It provides a graphical characterization of the robust center-ofmass locations, and gives a geometric algorithm for computing these center-of-mass locations. The paper reports experiments validating the equilibrium criterion on a 2-legged prototype. Finally, it describes initial progress associated with computation of robust equilibrium postures in three-dimensions.