Acoustics, Dynamics, and Controls Commons^™

Derivation And Application Of A Conserved Orbital Energy For The Inverted Pendulum Bipedal Walking Model, Jerry E. Pratt, Sergey V. Drakunov

Publications

We present an analysis of a point mass, point foot, planar inverted pendulum model for bipedal walking. Using this model, we derive expressions for a conserved quantity, the “Orbital Energy”, given a smooth Center of Mass trajectory. Given a closed form Center of Mass Trajectory, the equation for the Orbital Energy is a closed form expression except for an integral term, which we show to be the first moment of area under the Center of Mass path. Hence, given a Center of Mass trajectory, it is straightforward and computationally simple to compute phase portraits for the system. In fact, for …