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.

Nyckelord

passive bipedal mechanisms

periodic motion

symmetries

center manifold

bifurcations

nonlinear dynamics

multibody modeling

dynamical systems

dynamic walking

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