Series: Mathematics Colloquium

Date: Thursday, February 14, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Mark Levi

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Andy Ruina, Cornell University

Title: The Possible Physics (Mechanics) of Walking

Abstract: 

Robots have motors and people have muscles.  What for?  To guide
motions and to make up for lost mechanical energy.  How much guidance
is fundamentally needed for repetitive tasks?  How much energy needs
to be supplied for what losses?  One approach to understanding the
need for motors and controllers is what can be done without them.

Tad McGeer demonstrated (1988-1993) with simple computational models
and with physical devices that uncontrolled human-like walking motions
can be achieved with, to put it simply, sticks and hinges that walk
downhill.  The motions of these toy-like devices are energetically
efficient (low specific transport cost) and stable (limit-cycles with
linearized stability).  We have found that, in principle, some of
these devices can walk on arbitrarily small slopes and thus approach
perfect efficiency and that Robot configurations that have this
efficiency are reminiscent of the human design.  These models can also
limp (period 2), waltz (period 3), and stumble (chaos).  One of our
devices has the unintuitive feature that it has no stable standing
posture, yet can walk stably.

The basic theory is not novel: numerical search for limit cycles and
numerical evaluation of their stability.  However, two morals seem to
be exposed: locomotion efficiency is based on avoidance of impacts,
and stability comes from utilizing non-holonomic constraints.