Journal
INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
Volume 24, Issue 8, Pages 657-674Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/0278364905056194
Keywords
legged locomotion; spring loaded inverted pendulum; three-dimensional motions; Poincare mapping; stability; periodic gaits
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We analyze a simple model for running: a three-dimensional spring-loaded inverted pendulum carrying a point mass (3D-SLIP). Our formulation reduces to the sagittal plane SLIP and horizontal plane lateral leg spring (LLS) models in the appropriate limits. Using the intrinsic geometry and symmetries and appealing to the case of stiff springs, in which gravity may be neglected during stance, we derive an explicit approximate mapping describing stride-to-stride behavior. We thereby show that all left-right symmetric periodic gaits are unstable, deriving a particularly simple mapping for sagittal plane dynamics. Continuation to fixed points for the exact mapping confirms instability of these gaits, and we describe a simple feedback stabilization scheme for leg placement at touchdown.
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