3D model of a simple hipped bipedal robot and its stable walking

For the further research on 3D passive walking, a hybrid model for a 3D bipedal robot consisting of 3-links and passive point-feet is represented in this article. The robot has 4-DOF in the single support phase and four actuators. Utilizing techniques from a variant of Routhian reduction termed functional Routhian reduction, to effectively decouple the dynamics of the three-dimensional biped into its sagittal and lateral components, a feedback control law is used on the model that makes the robot walk stably on flat ground. Furthermore, on the sagittal plane, passivity-based and energy-based controls is added as for the 2D robot model, this makes the robot can walk stably with slope change. And at last, as the hip width is an evident difference the 3D model and the 2D, some simulation is made to analyze the relation between hip width and the stability.