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Volume 24 Issue 8 - Publication Date: 1 August 2005
 
Running in Three Dimensions: Analysis of a Point-mass Sprung-leg Model
 
J.E. Seipel Department of Mechanical and Aerospace Engineering, Princeton University. Princeton, NJ 08544, USA and P. Holmes Department of Mechanical and Aerospace Engineering, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
 
We analyze a simple model for running: a three-dimensional springloaded 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 con-firms instability of these gaits, and we describe a simple feedback stabilization scheme for leg placement at touchdown.
 
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