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Due to their morphology and mechanical design, bipedal robots have the ability to traverse over a wide range of terrain including those with discrete footholds like stepping stones. This work addresses the challenge of dynamic robotic walking over stochastically generated stepping stones with significant variations in step length and step height, and where the robot has knowledge about the location of the next discrete foothold only one step ahead. Specifically, our approach utilizes a 2-step periodic gait optimization technique to build a library of gaits parametrized by their resulting step lengths and step heights, as well as the initial configuration of the robot. By doing so, we address the problems involved during step transition when switching between the different walking gaits. We then use gait interpolation in real-time to obtain the desired gait. The proposed method is successfully validated on ATRIAS, an underactuated, human-scale bipedal robot, to achieve precise footstep placement. With no change in step height, step lengths are varied in the range of [23:78] cm. When both step length and step height are changed, their variation are within [30:65] cm and [-22:22] cm respectively. The average walking speed of both these experiments is 0.6 m/s.
