Breaking symmetries and constraints : Transitions from 2D to 3D in passive walkers

• The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.

Keyword

passive bipedal mechanisms

periodic motion

symmetries

center manifold

bifurcations

nonlinear dynamics

multibody modeling

dynamical systems

dynamic walking

Publication and Content Type

ref (subject category)

art (subject category)