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Licentiate seminar

Passive Walking: Transition from 2D to 3D


Defendant Main Advisor Extra Advisor Date
Petri Piiroinen Harry Dankowicz 2000-08-22

Opponent
Viktor Berbyuk, Dept of machine and Vehicle Systems, Chalmers

Evaluation committee

Abstract

The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional planes and those free to move in a three-dimensional 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. Symmetry properties of such mechanism are discussed and a few special symmetries are defined. Using these symmetries, we classify a number of different gaits. The results indicate the limitations of a two-dimensional analysis to predict the dynamics in the three-dimensional 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. A center-manifold technique is implemented to arrive at a normal-form for the natural dynamics of a passive, bipedal rigid-body mechanism in the vicinity of infinite foot width and near-symmetric body geometry. In particular, numerical schemes are developed for finding approximate forms of the relevant invariant manifolds and the near-singular dynamics on these manifolds. The normal-form approximations are found to be highly accurate for relative large foot widths with a range of validity extending to widths on the order of the mechanisms` height.