Frictional dynamics, hybrid dynamics, and stability of planar two-contact stances under gravity

Yizhar Or, Dept. of Mechanical Engineering, Technion – Israel
Institute of Technology

Automated planning for quasistatic legged locomotion on rough terrains requires tools for computing stable equilibrium postures. Lumping the complex kinematic structure of the robot into a single rigid body with variable center-of-mass, the problem reduces to finding the region of center-of-mass locations that generate stable equilibrium stances for a given set of frictional contacts. Focusing on planar two-contact stances, this talk analyzes the dynamics under initial perturbations that include contact separation, rolling or sliding, and defines the new notion of frictional stability. The constrained dynamics is then formulated under Coulomb's friction model. The phenomena of dynamic ambiguity and dynamic inconsistency are reviewed, and their relation with frictional stability is established.  Accounting for separation and collision at the contacts, a hybrid dynamical system, composed of phases of continuous dynamics interleaved by discrete impact events, is then formulated. Two types of collision sequences, namely, bouncing and clattering, are analyzed, and conditions for their convergence are derived using Poincaré map.

Finally, frictional stability is addressed, by concatenating the phases of constrained dynamics with the phases of hybrid dynamics. A novel criterion that guarantees frictional stability is presented. The criterion, which depends on mass distribution and center-of-mass location, is demonstrated
in graphical examples.

The work is part of Yizhar's Ph.D. thesis under the supervision of Prof. Elon Rimon.

Biography:
Yizhar graduated two B.Sc. degrees, in Mechanical Engineering and Computer Science Education at the Technion, Israel, in 2001.  Then he studied in the direct doctoral track at the ME Dept, Technion, under the supervision of Prof. Elon Rimon, and has just recently submitted his Ph.D. thesis.  Yizhar was awarded the Fulbright Posdtoctoral Fellowship and the Bikura Postdoctoral Scholarship of the Israeli Science Foundation (ISF) for year 2007-2008. He is a currently a postdoctoral fellow at the Technion, supported by the Russel Berrie Nanotechnology Institute (RBNI), Technion. His research interests include hybrid dynamical systems and nonlinear control theory, with applications to robotic locomotion with intermittent contacts.