Departmental Papers (ESE)


The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for running in numerous animal species. Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits can be found in the SLIP with both linear and "air" springs, controlled by a simple fixed-leg reset policy. We first derive touchdown-to-touchdown Poincaré maps under the common assumption of negligible gravitational effects during the stance phase. We subsequently include and assess these effects and briefly consider coupling to pitching motions. We investigate the domains of attraction of symmetric periodic gaits and bifurcations from the branches of stable gaits in terms of nondimensional parameters.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version

May 2003


Reprinted from SIAM Journal on Applied Dynamical Systems, Volume 2, Issue 2, May 8 2004, pages 187-218.
Publisher URL:

NOTE: At the time of publication the author, Daniel Koditschek, was affiliated with the University of Michigan. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania.


legged locomotion, spring-loaded inverted pendulum, periodic gaits, bifurcation, stability



Date Posted: 03 April 2008

This document has been peer reviewed.