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Studies of biped control including standing, walking, hopping and running on humanoid robots are reviewed in this survey paper. Model-based approaches standing upon reduced-order dynamics are focused. It begins with revisiting the centroidal dynamics and the zero-moment point, which leads to the linear inverted pendulum (LIP) model and some of its variations. Then, some representative standing and walking control techniques based on the LIP model are reviewed, where the concept of capturability is also discussed. It is followed by consideration of height variation of the center of mass. Enhancement to hopping and running motions, which include aerial phases, is also addressed. Ideas to deal with complex nature as a hybrid system underlying discontinuously varying mechanics mainly due to unilateral constraints on contact forces are concisely explained.
Yamamoto et al. (Mon,) studied this question.