  Dynamic walking on bipedal robots has evolved from an idea in science fiction
to a practical reality. This is due to continued progress in three key areas: a
mathematical understanding of locomotion, the computational ability to encode
this mathematics through optimization, and the hardware capable of realizing
this understanding in practice. In this context, this review article outlines
the end-to-end process of methods which have proven effective in the literature
for achieving dynamic walking on bipedal robots. We begin by introducing
mathematical models of locomotion, from reduced order models that capture
essential walking behaviors to hybrid dynamical systems that encode the full
order continuous dynamics along with discrete footstrike dynamics. These models
form the basis for gait generation via (nonlinear) optimization problems.
Finally, models and their generated gaits merge in the context of real-time
control, wherein walking behaviors are translated to hardware. The concepts
presented are illustrated throughout in simulation, and experimental
instantiation on multiple walking platforms are highlighted to demonstrate the
ability to realize dynamic walking on bipedal robots that is agile and
efficient.
