Motion analysis of passive dynamic walking with a rigorously constraint model: A necessary condition for maintaining period-1 gait

The friction force is an important environmental factor that influences dynamic walking. While most of the related works simply assume static friction or Coulomb friction, we use the LuGre friction, which accounts for both static and dynamic effects, to model the horizontal ground reaction force of passive dynamic walking. We present a detailed mathematical modeling method and perform numerical simulations using it. Furthermore, we analyze the ground surface cases of the Coulomb friction condition and static friction condition to verify the model’s generalization. We discover the required condition for the existence of the period-1 gait through investigation. Our mathematical model and theoretical analysis add to our understanding of passive dynamic walking, which helps to positively utilize the natural dynamics of the legged locomotion system in control design.