1282 A Study of the Passive Gait of a Compass - Like Biped Robot : Symmetry and Chaos

The focus of this work is a systematic study of the passive gait of a compass-like, planar, biped robot on inclined slopes. The robot is kinematically equivalent to a double pendulum, possessing two kneeless legs with point masses and a third point mass at the "hip" joint. Three parameters, namely, the ground-slope angle and the normalized mass and length of the robot describe its gait. We show that in response to a continuous change in any one of its parameters, the symmetric and steady stable gait of the unpowered robot gradually evolves through a regime of bifurcations characterized by progressively complicated asymmetric gaits, eventually arriving at an apparently chaotic gait where no two steps are identical. The robot can maintain this gait indefinitely. A necessary (but not sufficient) condition for the stability of such gaits is the contraction of the "phase-fluid" volume. For this frictionless robot, the volume contraction, which we compute, is caused by the dissipative effects of the ground-impact model. In the chaotic regime, the fractal dimension of the robot’s strange attractor (2.07) compared to its state-space dimension (4) also reveals strong