Abstract: The walking stability controller is designed for researching the biped robots in 3D (three-dimensional) space. The 3D dynamics model of biped robot is established. By constructing the almost-cyclic Lagrange function, the biped robot dynamic system is decoupled into sagittal and lateral portions. The potential energy shaping and kinetic energy shaping controller is designed for the sagittal portion of under-actuated robot in 2D space. In order to solve the energy shaping controller, the matching condition is be separated into two sub-conditions which relate to angle and angular velocity respectively. The nonlinear partial differential equation is changed into linear partial differential equation, and the energy controller is solved to regulate sagittal locomotion, so that the stable walking gait and bionic characteristic gait can be obtained. The output zero dynamic controller is applied to control the lateral portion, which satisfies the dynamic decoupling conditions of the system. The simulation experiments are carried out on different step length. The simulation results show that the dynamic walking converges to a stable limit cycle and the gait accord with biomimetic law, the feasibility and effectiveness of the theory is verified.

Key words: Almost-cyclic lagrangians function, Kinetic energy shaping, Potential energy shaping, Zero dynamics control