SCIENTIFIC PROGRAMS AND ACTIVITIES

2010-11 Schedule

The coordination of robotic and natural walking and running is often treated as a complex control problem. In contrast, I will mention some things that can be inferred from simple mechanical analysis. As promoted early on by Tom McMahon and then Tad McGeer, walking gaits can be generated by machines with no control. These machines use relatively little energy and, like many bicycles, can have a measure of self-stability. However, the hypothesis that natural gaits might be largely passive is close in some ways, but not identical to, the stronger and more biologically interesting hypothesis that natural gaits minimize energy use. The talk includes videos of robots, some heuristic explanations, and a few equations.

Bio: Andy Ruina got three degrees from Brown University in Engineering. He studied friction, fracture, collisions, bicycles and the mechanics of walking. His lab made the most energy stingy walking robot and also a robot that walked 14.3 miles without human contact or refueling. He spends his summers in on an island in SouthWest Finland near Stockholm where is wife studies wasps that lay eggs in baby butterflies. Google ruina.

It is well known that a system with zero angular momentum can, by appropriate deformations, rotate while always maintaining the condition of zero angular momentum. This effect explains how a cat that is dropped while upside down can turn over and of how certain gymnastic maneuvers are performed. These rotations are taken as a demonstration of the "non-integrability" of a "non-holonomic" constraint. There is a simple demonstration of this rotation-with-zero-angular-momentum effect with a rotating platform. But the demonstration often doesn't work because most floors are not perfectly flat. I found a simple better demonstration experiment. Unfortunately, the experiment came out all wrong for different reasons. But I figured out why and did a second demonstration experiment. And that came out wrong exactly in the opposite way.

The talk presents the four puzzles: a) how can you turn while having zero angular momentum? b) Why does a rotating platform demonstration often not work. c) Why does a simple demonstration not work? d) Why does almost exactly the same demonstration not work in the opposite way?

The talk starts with various personal stories about non-holonomic constraints and their relation to locomotion --- that's bikes, skates, driving on ice and walking --- and then gets into the 4 rotation puzzles.

Bio: Andy Ruina got three degrees from Brown University in Engineering. He studied friction, fracture, collisions, bicycles and the mechanics of walking. His lab made the most energy stingy walking robot and also a robot that walked 14.3 miles without human contact or refueling. He spends his summers in on an island in SouthWest Finland near Stockholm where is wife studies wasps that lay eggs in baby butterflies. Google ruina.

Previous Seminars

Cinema uses computers to animate physics. Special effects such as explosions and lifelike depictions of imaginary characters are made possible by mathematical and computational models that capture qualitative, characteristic behavior of a mechanical system. This is scientific computing with a twist. I will describe the process by which we derive and compute models of physics, and show actual examples of resulting technologies in film, consumer products, physics, and medicine.

Our research group develops scientific computing tools by focusing on the underlying geometry of the mechanical system. I will describe a process in which we build a discrete picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting. I will survey the problems we address using this methodology, such as computing the motion of flexible surfaces, cloth, hair, honey, and solids experiencing mechanical contact. Industry and academia has adopted these methods to improve products such as Adobe Photoshop, films such as Disney's Tangled (whose release date coincides with this talk), train surgeons, and understand nonlinear soft-matter phenomena.

BIO

Eitan Grinspun is Associate Professor of Computer Science at Columbia University in the City of New York. He was Professeur d'Universite Invite at l'Universite Pierre et Marie Curie in 2009, a Research Scientist at the Courant Institute of Mathematical Sciences from 2003-2004, and a graduate student at the California Institute of Technology from 1997-2003. He was an NVIDIA Fellow in 2001, an Everhart Distinguished Lecturer in 2003, an NSF CAREER Award recipient in 2007, and is currently an Alfred P. Sloan Research Fellow.

Many physical phenomena can explained by geometric principles that underly and govern them. For example, the fascinating curved shapes taken on by thin elastic rods (such as ropes, knots, or DNA strands), which can be physically explained by the nonlinear interaction between bending and twisting potentials, have a geometric interpretation in terms of moving adapted frames. The computation of these phenomena benefits from explicit attention to this geometric viewpoint.

Computer-based simulations of solid rods and fluid threads necessarily rely on reducing the continuous description to a discrete (finite) one. Using notions of discrete framed curves and discrete parallel transport we develop a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Using Raleigh's analogy enables a time-discretized transition to a model of viscous fluid threads. The resulting computations of elastic rods and viscous threads are validated via comparison of buckling, stability, and coupled-mode numerical, analytical, and empirical experiments.

This is joint work with Basile Audoly, Miklós Bergou, Etienne Vouga and Max Wardetzky.

BIO

Eitan Grinspun is Associate Professor of Computer Science at Columbia University in the City of New York. He was Professeur d'Universite Invite at l'Universite Pierre et Marie Curie in 2009, a Research Scientist at the Courant Institute of Mathematical Sciences from 2003-2004, and a graduate student at the California Institute of Technology from 1997-2003. He was an NVIDIA Fellow in 2001, an Everhart Distinguished Lecturer in 2003, an NSF CAREER Award recipient in 2007, and is currently an Alfred P. Sloan Research Fellow.