Geometric Phases, Control Theory, and Robotics
Richard M. Murray
Proceedings of the Board on Mathematical Sciences, Science and Technology Symposium, Washington DC, 12 April 1994
Differential geometry and nonlinear control theory provide essential
tools for studying motion generation in robot systems. Two areas
where progress is being made are motion planning for mobile robots on
the factory floor (or on the surface of Mars), and control of highly
articulated robots---such as multifingered robot hands and robot
``snakes''---for medical inspection and manipulation inside the
gastrointestinal tract. A common feature of these systems is the role
of constraints on the behavior of the system. Typically, these
constraints force the instantaneous velocities of the system to lie in
a restricted set of directions, but do not actually restrict the
reachable configurations of the system. A familiar example in which
this geometric structure can be exploited is parallel parking of an
automobile, where periodic motion in the driving speed and steering
angle can be used to achieve a net sideways motion. By studying the
geometric nature of velocity constraints in a more general setting, it
is possible to synthesize gaits for snake-like robots, generate
parking and docking maneuvers for automated vehicles, and study the
effects of rolling contacts on multifingered robot hands. As in
parallel parking, rectification of periodic motions in the control
variables plays a central role in the techniques which are used to
generation motion in this broad class of robot systems.
Preprint
(PDF, 826K, 23 pages)
Slides from my talk (PDF, 1.7M compressed)
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Richard Murray (murray@cds.caltech.edu)
Last modified: Tue Aug 30 07:42:21 2005