  The problem of nonprehensile manipulation of a stick in three-dimensional
space using intermittent impulsive forces is considered. The objective is to
juggle the stick between a sequence of configurations that are rotationally
symmetric about the vertical axis. The dynamics of the stick is described by
five generalized coordinates and three control inputs. Between two consecutive
configurations where impulsive inputs are applied, the dynamics is conveniently
represented by a Poincar\'e map in the reference frame of the juggler.
Stabilization of the orbit associated with a desired juggling motion is
accomplished by stabilizing a fixed point on the Poincar\'e map. The Impulse
Controlled Poincar\'e Map approach is used to stabilize the orbit, and
numerical simulations are used to demonstrate convergence to the desired
juggling motion from an arbitrary initial configuration. In the limiting case,
where consecutive rotationally symmetric configurations are chosen arbitrarily
close, it is shown that the dynamics reduces to that of steady precession of
the stick on a hoop.

Systems and Control;Robotics;Systems and Control