Stability regions for standing balance of biped humanoid robots

Abstract

Based on the liner inverted pendulum model (LIPM) for the dynamics of biped humanoid robots, an analytical method for computing stability regions relevant to standing balance of the biped humanoid robots is introduced in this paper. More precisely, two types of the stability regions are discussed in this paper with the consideration of that the zero moment point (ZMP) should be located in the supporting region to guarantee stable standing of the biped humanoid robots. First, assuming no external disturbances affecting the motion of the biped humanoid robots, the set of the initial values of the center of mass (CoM) position and velocity with which the location of the ZMP is limited to be inside the supporting region can be explicitly obtained by solving a finite number of linear inequalities. Second, two admissible sets of external force disturbances (impulse and finite energy) with which the ZMP does not deviate from the supporting region are characterized by solving finite number of linear inequalities or the discrete-time Lyapunov equation, respectively. The validity and effectiveness of the analytical method proposed in this paper are verified through a simulation result.