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Dynamic Stability of Open-Loop Hopping

Cham, Jorge G. and Cutkosky, Mark R. (2007) Dynamic Stability of Open-Loop Hopping. Journal of Dynamic Systems, Measurement, and Control, 129 (3). pp. 275-284. ISSN 0022-0434. doi:10.1115/1.2718237.

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Simulations and physical robots have shown that hopping and running are possible without sensory feedback. However, stable behavior is often limited to a certain range of the parameters of the open-loop system. Even the simplest of hopping systems can exhibit unstable behavior that results in unpredictable nonperiodic motion as system parameters are adjusted. This paper analyzes the stability of a simplified vertical hopping model driven by an open-loop, feedforward motor pattern. Periodic orbits of the resulting hybrid system are analyzed through a generalized formula for the system's Poincare Map and Jacobian. The observed behavior is validated experimentally in a physical pneumatically actuated hopping machine. This approach leads to observations on the stability of this and similar systems, revealing inherent limitations of open-loop hopping and providing insights that can inform the design and control of dynamic legged robots capable of rapid and robust locomotion.

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Additional Information:© 2007 American Society of Mechanical Engineers. Received 8 September 2004; revised 21 September 2006. We have been fortunate to collaborate with Professor Robert J. Full at the U.C. Berkeley Polypedal Laboratory. Thanks especially to Jonathan Karpick and the other members of the Biomimetics lab at CDR. Funding was provided by the Office of Naval Research under Grant No. N00014-98-1-0669.
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Office of Naval Research (ONR)N00014-98-1-0669
Subject Keywords: robot dynamics, mechanical stability, Poincare mapping, Jacobian matrices, legged locomotion, robust control
Issue or Number:3
Classification Code:PACS: # 45.40.Ln (Robotics (dynamics/kinematics)) # 02.30.Uu (Integral transforms) # 02.10.Yn (Matrix theory)
Record Number:CaltechAUTHORS:20100311-145248231
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Official Citation:Dynamic Stability of Open-Loop Hopping Jorge G. Cham and Mark R. Cutkosky, J. Dyn. Sys., Meas., Control 129, 275 (2007), DOI:10.1115/1.2718237
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17727
Deposited By: Tony Diaz
Deposited On:15 Mar 2010 17:17
Last Modified:08 Nov 2021 23:38

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