Nonprehensile Manipulation of a Stick Using Impulsive Forces
This addresses a specific robotics manipulation problem, but it appears incremental as it builds on existing Poincaré map methods for juggling tasks.
The paper tackles the problem of nonprehensile manipulation of a stick in 3D space using impulsive forces to juggle it between rotationally symmetric configurations, achieving stabilization of the desired motion via an Impulse Controlled Poincaré Map approach and demonstrating convergence in simulations.
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 Poincaré 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 Poincaré map. The Impulse Controlled Poincaré 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.