Nonprehensile Manipulation of a Stick Using Impulsive Forces

TL;DR

This paper presents a method for controlling the nonprehensile manipulation of a stick in 3D space using impulsive forces, employing a Poincaré map approach to achieve stable juggling motions.

Contribution

It introduces the Impulse Controlled Poincaré Map method for stabilizing a stick juggling orbit, demonstrating convergence through numerical simulations.

Findings

Successfully stabilizes a juggling orbit from arbitrary initial conditions

Reduces dynamics to steady precession in the limit of close configurations

Demonstrates convergence to desired motion via numerical simulations

Abstract

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.