Underactuated bipedal walking has been intensively studied for the past few decades and several methods have been proposed to design trajectories; however, quickly generating trajectories with varying speeds remains a challenge. One solution is to have a library of trajectories precomputed from which a new one can be picked or constructed quickly based on specific requirements. For this to become feasible one needs to develop a good understanding of the solution space. This is non-trivial for a non-linear hybrid system such as a walking robot. The goal of this study is to explore a two parameter solution space of simple underactuated biped, under a specific virtual constraint, used in literature, to enforce a symmetric gait. The family of feasible walking solutions identified is further evaluated for performance and energy efficiency. This analysis can potentially facilitate quick selection of walking trajectories for meeting specific walking speed and efficiency requirements.
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