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 kine matically equivalent to a double pendulum, possessing two kneeless leg s with point masses and a third point mass at the ''hip'' joint. Three parameters, namely, the ground-slope angle and the normalized mass an d 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 ste ady stable gait of the unpowered robot gradually evolves through a reg ime of bifurcations characterized by progressively complicated asymmet ric 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 fric tionless robot, the volume contraction, which we compute, is caused by the dissipative effects of the ground-impact model In the chaotic reg ime, the fractal dimension of the robot's strange attractor (2.07) com pared to its state-space dimension (4) also reveals strong contraction . We present a novel graphical technique based on the first return map that compactly captures the entire evolution of the gait, from symmet ry to chaos. Additional passive dissipative elements in the robot join t result in a significant improvement in the stability and the versati lity of the gait, and provide a rich repertoire for simple control law s.