Joel Burdick
Department of Mechanical Engineering
Caltech
"Biomimetic locomotion" is the movement of robotic mechanisms in ways
that are
analogous to the patterns of movement found in nature. Practically
speaking,
it is movement that does not rely upon wheels, jets, thrusters, or
propellers.
Biomimetic locomotion is typically generated by a coupling of periodic
internal body deformations to an external constraint.
A significant body of research has been developed in the area of robotic
locomotion. Prior studies have often focused either on a particular set
of
assumptions (such as quasi-static motion) or a particular robot
morphology
(such as a biped or quadruped). To date there exists no unifying
methodology
for analyzing or controlling robotic locomotion. Ultimately, we seek a
"mechanics theory" and a "control theory" for robotic locomotion which
is both
rigorous and uniformly applicable to a broad class of locomotory
problems.
This talk summarizes some recent work on the development of unifying
principles for a broad class of locomotion problems.
In order to establish notation and key ideas, the talk will begin with a
review of the basic mechanics underlying biomimetic locomotion. In
particular, ideas from the geometric mechanics literature, such as
principal
fiber bundles and their associated connections, will be stressed.
A biomimetic locomotion mechanism is "controllable" if there exists an
admissible set of controls which drives the system from its current
configuration to any nearby configuration. Controllability is a key
issue
that must be addressed by any comprehensive theory of biomimetic
locomotion
engineering. Unfortunately, standard controllability methods from
nonlinear
control theory, such as Chow's theorem, are not well suited to the
analysis of
biomimetic locomotors. Extensions to controllability theory that are
adapted to biomimetic locomotion systems will be reviewed.
While controllability is a key issue in the design and analysis of
biomimetic
locomotion systems, trajectory generation is a primary practical problem
for
the deployment of complex biomimetic locomotors. Using the new
controllability framework, the second part of the
talk will describe trajectory generation methods.