A Limit Cycle Analysis of the Simplest Passive Dynamic Walker

Passive dynamic walkers (PDWs) are simple dynamical systems that have been used to study the fundamentals of normal human walking. In essence, they are a collection of links and joints capable of “walking” down shallow slopes with a surprisingly human-like gait. PDWs have no active motors or control system, rather they are “powered” by gravity. With judicious choice of model parameters and initial conditions, PDWs can exhibit stable limit cycles. The goals of this project are twofold: (1) to create a general limit cycle analysis and simulation tool using Python and (2) explores some aspects of the limit cycle behavior of a PDW. In order to test the accuracy of the Python code, I recreated some of the results of by Garcia's et al., (1998) simplest passive dynamic walking model. Specifically, I verified the author's reported range of stable limit cycles. My calculations agree that this model does possess stable limit cycles for ground slopes less than about 0.015 radians.