Passive dynamic turning in 3D biped locomotion: an extension to passive dynamic walking

Dynamic Walking Analysis of an Underactuated Biped Robot with Asymmetric Structure

Owing to their nonlinear structures and dynamics, bipedal walking robots are commonly used as appropriate case studies for nonlinear modeling and control. In this study, the dynamics of a point-feet 4-link biped robot having asymmetric structure is studied. This asymmetry appears on the robot’s legs such that one leg of the robot does have an active knee while the other is knee-less. In this way, the style and analysis of each step depends on which leg is the stance leg. Although the stable steady state behavior of the system is purely periodic, the gait cycle does consist of two sequential steps. Since each step includes a continuous phase followed by an impact phase, hence, we need to model the system as a multiphase (4-phase) hybrid system. The main purpose of this research is to find stable gating pattern and employ appropriate controller to make sure that the gating is accomplished in an asymptotically stable manner. A combination of feedback linearization and finite-time controllers is used to control the walking posture, and the stability of the whole behavior is investigated by analysis of a one-dimensional Poincaré map. Simulation results successfully support the modeling and control approach.

Existence and stability of limit cycles in the model of a planar passive biped walking down a slope

We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9, 62-82. (doi:10.1177/027836499000900206)). Following the fundamental work by Garcia (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi:10.1115/1.2798313)), we view the slope of the ground as a small parameter γ ≥ 0. When γ = 0, the system can be solved in closed form and the existence of a family of cycles (i.e. potential walking cycles) can be computed in closed form. As observed in Garcia et al. (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi:10.1115/1.2798313)), the family of cycles disappears when γ increases and only isolated asymptotically stable cycles (walking cycles) persist. However, no mathematically complete proofs of the existence and stability of walking cycles have been reported in the literature to date. The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps. In particular, we derive a perturbation theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences.

From a 3D Passive Biped Walker to a 3D Passivity-Based Controlled Robot

Asymptotically stable control of biped robots, especially based on reproducing passive periodic motions, have become of interest nowadays. In this paper, firstly, a three-dimensional (3D) stable passive biped walker which is a compass gait one with flat feet, compliant ankles and particular arrangement of moments of inertia has been presented. Then, a passivity-based control of the related biped robot based on elaborating 3D form of potential energy shaping method has been applied. In other words, by adding minimal actuations to the aforementioned passive walker, its passive periodic gait that belongs to a particular slope has been reproduced on any arbitrary surface such as the level ground. Simulation results support the effectiveness of the proposed approach.