Development of a Complete Multi-phase Dynamics Model for a Biped Robot

Human walking is quite an efficient and smooth movement involving multiple successive phases. But for biped robots, most current dynamic walking models are simplified to some extent, with some phases neglected. This paper addresses the development of a complete multi-phase dynamics model for a biped robot. To achieve this, both the single support phase and double support phase are divided into two sub-phases by taking into consideration the rotation of stance foot around its toe and the rotation of swing foot around its heel. Therefore, a more human-like robotic gait is achieved, with transitions occurring at toe-off, heel-off, heel-strike, and toe-strike. Comparing the numbers of degrees of freedom with independent actuators of the biped robot, the whole gait cycle can also be represented by fully-actuated phase, under-actuated phase, and over-actuated phase. On this basis, the detailed dynamics model of each phase is derived using Euler-Lagrange method. And the validity of the dynamics model is demonstrated by simulation.