Title :
Stability of coupled hybrid oscillators
Author :
Klavins, Eric ; Koditschek, Daniel
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA
Abstract :
We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled system exhibiting the desired phase difference. This extends our previous work wherein the application of the method to two individually deadbeat-stabilized oscillators (paddle juggling mechanisms) was shown to yield the desired result. Central to this method is the idea that cyclic systems may be composed into a larger, aggregate, cyclic system. Its application entails moving from physical coordinates (for example, the position and velocity of each constituent mechanism) to the coordinates of phase and phase velocity. Within this canonical coordinate system we construct a model dynamical system, called a reference field, which encodes the desired behavior of each cyclic system as well as the phase relationships between them. We then force the actual composite system to behave like the model.
Keywords :
asymptotic stability; interconnected systems; limit cycles; oscillators; asymptotically stable limit cycle; canonical coordinate system; composite system; coupled hybrid oscillator stability; cyclic system composition; deadbeat-stabilized oscillators; decentralized phase regulation; hopping robots; model dynamical system; paddle juggling mechanisms; phase coordinates; phase relationships; phase velocity coordinates; physical coordinates; reference field; synchronization method; Interconnected systems; Leg; Legged locomotion; Oscillators; Production facilities; Robot control; Robot kinematics; Robotic assembly; Robotics and automation; Stability;
Conference_Titel :
Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on
Print_ISBN :
0-7803-6576-3
DOI :
10.1109/ROBOT.2001.933274