Controllability Analysis of a Standing Bipedal Robot with Active Toe-Joints

In this paper capability of a simplified bipedal robot model having active toe-joint to keep standing balance is investigated. The model consists of a rigid link as the upper body considering the ankle strategy for standing balance maintenance, and a foot, which contains two segments as heel link and toe link, hinged together at a toe joint. To ensure contact between foot and ground, COP constraints are defined and exerted to the dynamical equations. Applying constraints to the model, imposes bounds on the control torques of the joints. In this work, the joint torque bounds, which are important for control, are determined by numerical solution of equations. It is found that angular orientation and velocity of the upper body play a significant role in such allowed control torques. Accordingly, there exists a region in phase plane named controllable region beyond which constraints cannot be satisfied regardless of the control torques. The controllable regions are determined and plotted in phase plane.