Abstract
It is empirically known that the stability of limit cycle gaits is dramatically improved by partly applying trajectory tracking control. This paper considers the model of an underactuated biped robot and investigates the stability of the gait strictly controlled to follow the desired-time trajectory of the hip angle using the linearized model. First, we derive the transition function for the state error of the stance phase, and analytically solve the stability condition and optimal solution. Second, we exactly show the stability of the collision phase and derive the sufficient condition for the limit cycle stability. Finally, the validity of the theoretical results is verified through numerical simulations.
