Journal
SIAM REVIEW
Volume 47, Issue 3, Pages 519-549Publisher
SIAM PUBLICATIONS
DOI: 10.1137/050626594
Keywords
legged locomotion; spring-loaded inverted pendulum; periodic gaits; bifurcation; stability
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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 Poincare 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.
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