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This paper applies geometric reduction-based control to derive a set of asymptotically stable dynamic walking gaits for a 3-D bipedal robot, each corresponding to walking along a nominal arc of constant curvature for a fixed number of steps. We show that any such set of asymptotically stable gait primitives may be composed in arbitrary order without causing the robot to fall, so any walking path that is a sequence of these gaits may be followed by the robot. This result enables motion planning for bipedal dynamic walkers, which are fast and energetically efficient, in a similar manner to what is already possible for biped locomotion based on Zero Moment Point (ZMP) equilibrium constraints.
Gregg et al. (Sat,) studied this question.