Walking and steering control for a 3D biped robot considering ground contact and stability

The walking of a bipedal robot is composed of different phases such as single support (SS) with flat foot, SS with foot rotation around the metatarsal axis and double support. During every walking phase there is a dynamic model and a contact with the ground. Thus, an appropriated control law has to be implemented for each phase. Generally, the type of contact with the ground is imposed but it is obtained only if the conditions on ground reaction forces, friction cone and zero moment point (ZMP) are satisfied. The ZMP, firstly introduced by Vukobratovic [1], is the most important factor in achieving stable walking of an humanoid robot. The ZMP is defined as a point where the resulting horizontal reaction moment generated by the ground reaction forces equals to zero. If this point is inside of the support polygon, the robot will not rotate around the edges of its stance foot so it remains flat on the ground. The ZMP can be used to measure instantaneous balance at each time step but it does not contain notion of stability in the future [2]. In earlier studies many bipedal robots adopted a control strategy in which the desired trajectories of joint angles are firstly designed based on the ZMP condition and after that a feedback control tracks the desired trajectories [1]. However, contact conditions could not be satisfied in presence of perturbations.