Gait cycles of passive walking biped robot model with flexible legs

Abstract

Passive dynamic walking of bipeds exhibits a new concept of robot locomotion that is well- known for its success in human mimicry. Many efforts have been devoted in the literature to implement flexible and anthropomorphic passive bipeds. However, utilization of flexible characteristics of elastic structures has not been considered yet. This paper presents a modified simplest passive walking model with flexible legs which are a pair of elastic beams with small deflections instead of usual rigid links. The main contributions of this paper lie in modeling the impulsive hybrid dynamics of the flexible passive biped and applying a numerical technique based on finite difference formula to seek for appropriate initial conditions of walking gait cycles. Extended Hamilton's principle and assumed mode method along with Euler–Bernoulli's beam theory and updated transition rules at impact are used to derive the mathematical model of this biped. Numerical simulations reveal non-periodic patterns of motion for small slope angles due to vibrations of elastic legs. It is also shown that the period-one gait cycles with quicker steps can be generated on slower slopes for different values of elasticity and damping coefficients compared to the rigid model.