STABILITY ANALYSIS FOR WALKING OF PASSIVE DYNAMIC BIPED ROBOT

The focus of this work is the modeling and analyzing the stability of walk of a passive dynamic knee-less biped robot on an inclined ramp. The main objective of this paper is to study robustness of a passive biped robot. The biped robot is designed with three point masses, two masses at two knee-less legs and a third mass at the hip. The kinematics of knee-less passive biped robot, which is powered only by the gravity, is equivalent to the double inverted pendulum. The biped robot will possess a stable gait after the multiple steps when it walks on the inclined ramp, so there is no need to stabilize the biped in each of its steps. A necessary condition for the stable walk is that the walker should begin its walk inside the basin of attraction. The basin of attraction is a measure for computing the area of allowable initial states for which the bipedal robot can walk stably.

We describe the cell mapping method to compute the basin of attraction of a fixed point attractor of a Poincare map. The stability of periodic motion is described in the form of fixed point of Poincare map. Additionally, we find the feasible region of initial states for which robot can walk successfully. This paper presents the 2D and 3D graphical techniques based on the Poincare map that efficiently explain the complete development of the symmetric gait.