Modeling dynamic interactions between the support foot and the ground in bipedal walking

This paper presents a new method of dynamics-based synthesis of bipedal, especially human, walking. The motion of the body at a time point is determined by ground reaction force and torque under the support foot and joint torques of the body at that time point. Motion synthesis involves specifying conditions that constrain ground reaction force and torque, and joint torques so that a given desired motion may be achieved. There are conditions on a desired motion which end-users can think of easily, e.g. the goal position and orientation of the swing foot for a single step and the time period of a single step. In this paper, we specify constraints on the motion of the support foot, which end-users would find difficult to specify. They are constraints which enforce non-sliding, non-falling, and non-spinning the support foot. They are specified in terms of joint torques and ground reaction force and torque. To satisfy them, both joint torques and ground reaction force and torque should be determined appropriately. The constraints on the support foot themselves do not give any good clues as to how to determine ground reaction force and torque. For that purpose, we specify desired trajectories of the application point of vertical ground reaction force (ground pressure) and the application point of horizontal ground reaction (friction) force. The application points of vertical pressure and friction force are good control variables, because they are indicators to kinds of walking motions to synthesize. The synthesis of a bipedal walking motion, then, consists of finding a trajectory of joint torques to achieve a given desired motion, so that the constraints are satisfied under the condition of the prescribed center of pressure and center of friction. Our approach is distinguished from many other approaches, e.g. the inverted-pendulum approach, in that it captures and formulates dynamics of the support foot and reasonable constraints on it.