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The International Journal of Robotics Research
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Phase Regulation of Decentralized Cyclic Robotic Systems

E. Klavins

Computer Science Department California Institute of Technology Pasadena, CA 91125, USA klavins{at}caltech.edu

D.E. Koditschek

Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI 48109, USA kod{at}umich.edu

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.

Key Words: coupled oscillators • hopping robots • juggling robots • behavior composition

The International Journal of Robotics Research, Vol. 21, No. 3, 257-275 (2002)
DOI: 10.1177/027836402320556430
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