  This paper studies bipedal locomotion as a nonlinear optimization problem
based on continuous and discrete dynamics, by simultaneously optimizing the
remaining step duration, the next step duration and the foot location to
achieve robustness. The linear inverted pendulum as the motion model captures
the center of mass dynamics and its low-dimensionality makes the problem more
tractable. We first formulate a holistic approach to search for optimality in
the three-dimensional parametric space and use these results as baseline. To
further improve computational efficiency, our study investigates a sequential
approach with two stages of customized optimization that first optimizes the
current step duration, and subsequently the duration and location of the next
step. The effectiveness of both approaches is successfully demonstrated in
simulation by applying different perturbations. The comparison study shows that
these two approaches find mostly the same optimal solutions, but the latter
requires considerably less computational time, which suggests that the proposed
sequential approach is well suited for real-time implementation with a minor
trade-off in optimality.
