Departmental Papers (ESE)


We address the problem of coupling cyclic robotic tasks to produce a specified coordinated behavior. Such coordination tasks are common in robotics, appearing in applications like walking, hopping, running, juggling and factory automation. In this paper we introduce a general methodology for designing controllers for such settings. We introduce a class of dynamical systems defined over n-dimensional tori (the cross product of n oscillator phases) that serve as reference fields for the specified task. These dynamical systems represent the ideal flow and phase couplings of the various cyclic tasks to be coordinated. In particular, given a specification of the desired connections between oscillating subsystems, we synthesize an appropriate reference field and show how to determine whether the specification is realized by the field. In the simplest case that the oscillating components admit a continuous control authority, they are made to track the phases of the corresponding components of the reference field. We further demonstrate that reference fields can be applied to the control of intermittent contact systems, specifically to the task of juggling balls with a paddle and to the task of synchronizing hopping robots.

For more information: Kod*Lab

Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version


Publication Source

International Journal of Robotics Research





Start Page


Last Page





Postprint version. Published in International Journal of Robotics Research, Volume 21, Issue 3, March 2002, pages 257-275. Publisher URL:

Bib Tex

@inproceedings{klavins -ICRR-2002, author = "E. Klavins and D.E. Koditschek", title = "Phase Regulation of Decentralized Cyclic Robotic Systems", booktitle = "International Journal of Robotics Research", year = "2002" month = "March" volume = "21" pages = "257-275" number = "3" }



Date Posted: 19 November 2014

This document has been peer reviewed.