Differentially Flat Design of Bipeds Ensuring Limit-Cycles

Abstract

In bipedal walking, a trajectory is acceptable as long as it is repetitive and allows the foot to clear the ground, while allowing the biped to move forward. Since the actual trajectory followed by a biped is not as important, a biped having more than one passive joints can also meet the motion requirements. Due to physical constraints, a biped is under-actuated at the ground contact with the feet. A biped should exhibit limit cycles when moving continuously in an environment. In general, it is difficult to prove existence of limit cycles for nonlinear systems. In this work, we generate limit cycles for a class of nonlinear under-actuated bipeds using differential flatness. A specific inertia distribution renders the biped design differentially flat. Differential Flatness allows generation of a family of limit cycles amenable to numerical optimization. The results are illustrated by two DOF biped.

Modeling, stability and walking pattern generators of biped robots: a review

“…This sagittal plane model has 5-DOF. 25 r 5-link model: A sagittal plane model consisting of a trunk and two legs with knees, but without feet. This model is frequently used, since it is considered a reasonable trade-off between simplicity and leg anatomy.…”

“…The under-actuation during the swing phase poses particular difficulty for the control of biped robot. Four state-of-the-art control methods are used to solve this problem: the time scaling method, 12,39 hybrid zero dynamics, 40 the differentially flatness-based approach 25 and the port-Hamiltonian method. 41 Further elaboration of these methods is left for subsequent papers.…”