Abstract

Juggling a devil-stick can be described as a problem of non-prehensile manipulation. Assuming that the devil-stick remains confined to the vertical plane, the problem of juggling the stick between two symmetric configurations is considered. Impulsive forces are applied to the stick intermittently and the impulse of the force and its point of application are modeled as control inputs to the system. The dynamics of the devil-stick due to the impulsive forces and gravity is described by half-return maps between two Poincaré sections; the symmetric configurations are fixed points of these sections. A coordinate transformation is used to convert the juggling problem to that of stabilization of one of the fixed points. Inclusion of the coordinate transformation in the dynamic model results in a nonlinear discrete-time system. A dead-beat design for one of the inputs simplifies the control problem and results in a linear time-invariant discrete-time system. Standard control techniques are used to show that symmetric juggling can be achieved from arbitrary initial conditions.

Department(s)

Mechanical and Aerospace Engineering

Comments

National Science Foundation, Grant 1462118

Keywords and Phrases

Devil-stick; Dynamics; Impulsive force; Juggling; Non-prehensile manipulation; Poincaré map

International Standard Serial Number (ISSN)

1573-269X; 0924-090X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Springer, All rights reserved.

Publication Date

01 Feb 2021

Download

Full Text Link

Share

 
COinS