Stability Analysis of a Flexible Biped Robot in Periodic Walking

Abstract

The stability of a flexible biped robot during periodic walking is studied. Firstly, the Spring-Loaded Inverted Pendulum (SLIP) model with variable leg length is used as a model for the robot, and the dynamics equation is derived using the Euler-Lagrange method. Secondly, the feedback linearization method is applied to design the controller, by controlling the length of the legs, the system converges to desired gaits. Finally, Newton-Raphson iteration method and Poincaré mapping are adopted to analyze the stability of the robot. On the basis of theoretical analysis, the control method is simulated. The simulation result shows that the robot has settled down to a periodic gait by the variable leg length and feedback linearization method. The stable limit cycle of the system has been formed. all the eigenvalues of the Jacobian matrix are located inside the unit circle, so the stability condition of the biped robot system is satisfied.