Active Dynamic Walking Research Articles

3-D Passive Dynamic Bipedal Walking and its Extension to Active Dynamic Walking

3-D Passive Dynamic Bipedal Walking and its Extension to Active Dynamic Walking

Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics

In this paper, we investigate the mathematical structures and mechanisms of bipedal walking from a dynamical viewpoint. Especially, we focus on the basin of attraction since it determines the stability of bipedal walking. We treat two similar but different bipedal walking models (passive and active dynamic walking models) and examine common mathematical structure between these models. We find that the saddle hyperbolicity and hybrid system play important roles for the shape of the basin of attraction in both models, which are quite common for more general bipedal models and important for understanding the stability mechanism of bipedal walking.

A Passive 2-DOF Walker: Hunting for Gaits Using Virtual Holonomic Constraints

A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.

The simplest passive dynamic walking model with toed feet: a parametric study

This paper presents a passive dynamic walking model with toed feet that can walk down a gentle slope under the action of gravity alone. The model is the simplest of its kind with a point mass at the hip and two rigid legs each hinged at the hip on the one end and equipped with toed foot on the other end. We investigate two cases of the model, one with massless legs and another with infinitesimal leg masses. Rotation of the stance foot about the toe joint is initiated by ankle-strike, which is caused by the inelastic collision of the stance leg with a stop mounted on the stance foot. Numerical simulations of walking show that larger step lengths, higher speeds, stability, and energy efficiency can be achieved than what is achievable by a point-feet walker of same hip mass and leg lengths. Period-two gait of a point-feet walker is compared with period-one gait of the toed-feet walker and the mechanism responsible for achieving longer step lengths is described. It is shown that the advantage of the proposed walker comes from its relation to arc-feet walker. The characteristics of deterministic gait with infinitesimal leg masses is compared with that of nondeterministic gait with zero leg masses. It is shown that deterministic gait does not give maximum speed and efficiency compared to nondeterministic gait with swing leg control. Finally, active dynamic walking of the proposed walker is discussed.

The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective

We examine two prevailing, yet surprisingly contradictory, theories of human walking. The six determinants of gait are kinematic features of gait proposed to minimize the energetic cost of locomotion by reducing the vertical displacement of the body center of mass (COM). The inverted pendulum analogy proposes that it is beneficial for the stance leg to behave like a pendulum, prescribing a more circular arc, rather than a horizontal path, for the COM. Recent literature presents evidence against the six determinants theory, and a simple mathematical analysis shows that a flattened COM trajectory in fact increases muscle work and force requirements. A similar analysis shows that the inverted pendulum fares better, but paradoxically predicts no work or force requirements. The paradox may be resolved through the dynamic walking approach, which refers to periodic gaits produced almost entirely by the dynamics of the limbs alone. Demonstrations include passive dynamic walking machines that descend a gentle slope, and active dynamic walking robots that walk on level ground. Dynamic walking takes advantage of the inverted pendulum mechanism, but requires mechanical work to transition from one pendular stance leg to the next. We show how the step-to-step transition is an unavoidable energetic consequence of the inverted pendulum gait, and gives rise to predictions that are experimentally testable on humans and machines. The dynamic walking approach provides a new perspective, focusing on mechanical work rather than the kinematics or forces of gait. It is helpful for explaining human gait features in a constructive rather than interpretive manner.

Biped gait generation and control based on a unified property of passive dynamic walking

Principal mechanisms of passive dynamic walking are studied from the mechanical energy point of view, and novel gait generation and control methods based on passive dynamic walking are proposed. First, a unified property of passive dynamic walking is derived, which shows that the walking system's mechanical energy increases proportionally with respect to the position of the system's center of mass. This yields an interesting indeterminate equation that determines the relation between the system's control torques and its center of mass. By solving this indeterminate equation for the control torque, active dynamic walking on a level can then be realized. In addition, the applications to the robust energy referenced control are discussed. The effectiveness and control performances of the proposed methods have been investigated through numerical simulations.

受動歩行を規範とした２足ロボットの歩容生成と制御

This paper studies basic mechanisms of passive dynamic walking from the mechanical energy point of view, and proposes novel gait generation and control methods based on the passive dynamic walking. Firstly, we show the uniform property of passive dynamic walking that, the walking system's mechanical energy increases proportionally with respect to the position of the system's center of gravity, which results in an interesting indeterminate equation that determines the relation between the system's control torques and its center of gravity. We then show that active dynamic walking on a level can be realized by solving this equation for the control torques. Furthermore, the applications to robust energy referenced control, as well as the extension for controlling a kneed biped system are discussed. The effectiveness of the proposed methods have been investigated through numerical simulations.

From passive to active dynamic walking

AbstractThis paper is concerned with a walking robot with knees on level ground imitating the passive walking on a given slope. Basic principle of a proposed control method is that dynamics of the active walking robot is matched to that of the passive walking one. However, since it is hard for the knee‐jointed walking robot to successively or robustly realize a stable passive walking on the downhill slope, the passive walking robot is first actively controlled to continue to walk with an actuator at the hip. Then the dynamics of the walking robot on the level grand is matched to that of the stabilized passive walking robot on the slope by implementing actuators at the ankles as well as at the hip. Copyright © 2001 John Wiley & Sons, Ltd.