Humans as bipeds enjoy certain advantages over other terrestrial systems, which motivate us to study and develop biped robots. Underactuated biped robots adopt the energy efficient gait of the biological counterparts and passive walkers. However, the control design for such robots is challenging due to lesser controllable joints, non-linear hybrid system dynamics and the goal of utilizing the natural dynamics. This paper summarizes various designs, models and control strategies used to enable stable walking and running for the underactuated biped robots. It gives a brief about how the mechanism of such bipeds evolved to incorporate the design variations which significantly improved the system performance. The few basic mathematical models which are used to simulate, analyze and predict the system dynamics and test control designs, are described, highlighting the difference in walking and running models. An introduction to the various stability criteria and control methods, successful in enabling stable walking for the robots on flat or uneven terrains, is provided. This paper gives a brief of the significant achievements in this field and ends with the highlights of the abilities inherent to humans but lacking in underactuated bipeds, and adopting or improving which should be the focus of the future research.
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