Receding horizon viability radius for stability of humanoid robot under external perturbation

Abstract

In this paper, a new approach that uses the rate of change of the angular momentum about the center of mass (COM) to improve the balance of a humanoid robot is proposed. This approach is motivated by how humans balance themselves when standing, walking, and running by making use of their upper body and swinging legs. Human movements such as lunging forward or backward and rotating arms make use of angular momentum to maintain balance. As the external perturbation increases, a human instinctively decides when and where to take a step to avoid a fall. In the same manner, a humanoid robot subjected to an external perturbation can determine whether to remain standing or to take a step with a swinging leg to maintain balance using RHVR conditions obtained from the proposed linear inverted dumbbell model. The rotation of a dumbbell model with mass inertia is an easy expression of the angular momentum of an upper body, arms, and legs. A zero-moment point (ZMP) outside the support polygon indicates an unbalanced gait and cannot represent a physical point related to the sole of the robot foot, which is defined as pseudo-ZMP (PZMP) in this paper. PZMP located outside the support area provides useful information for balancing the gait. PZMP from the foot edge provides a measure of the unbalanced moment that tends to rotate the humanoid robot around the supporting foot and causes it to fall. It is shown that PZMP is determined by the Gauss’s principle within mechanical constraints of the rate of change of angular momentum about COM. In fact, the actual angular acceleration about COM is determined by the Gauss’s principle. Additionally, RHVRs is defined, that is, viability regions to keep the balance that indicate the essential range of stability implemented to a real system. RHVRs are divided into the real ZMP (RZMP), PZMP and stepping PZMP (SPZMP). Hence, the regions of RHVR and the actual angular acceleration about COM determine which of the three control strategies is used.