All common bipedal gaits emerge from a single passive model

Abstract

<jats:p>In this paper, we systematically investigate passive gaits that emerge from the natural mechanical dynamics of a bipedal system. We use an energetically conservative model of a simple spring-leg biped that exhibits well-defined swing leg dynamics. Through a targeted continuation of periodic motions of this model, we systematically identify different gaits that emerge from simple bouncing in place. We show that these gaits arise along one-dimensional manifolds that bifurcate into different branches with distinctly different motions. The branching is associated with repeated breaks in symmetry of the motion. Among others, the resulting passive dynamic gaits include walking, running, hopping, skipping and galloping. Our work establishes that the most common bipedal gaits can be obtained as different oscillatory motions (or nonlinear modes) of a single mechanical system with a single set of parameter values. For each of these gaits, the timing of swing leg motion and vertical motion is matched. This work thus supports the notion that different gaits are primarily a manifestation of the underlying natural mechanical dynamics of a legged system. Our results might explain the prevalence of certain gaits in nature, and may provide a blueprint for the design and control of energetically economical legged robots.</jats:p>

Humans use multi-objective control to regulate lateral foot placement when walking

“…Simple mechanical models have successfully elucidated many fundamental aspects of locomotion dynamics (e.g., [ 16 , 75 – 77 ]). These models represent biomechanical “templates” [ 57 – 59 ] for the most basic mechanics and dynamics of any biped (human, robot, model, etc.)…”

“…and reveal how those biomechanics shape locomotor behavior. Similarly, the stepping models presented here and in our previous work [ 9 , 10 ] act as “control templates” that serve as minimal models to describe how movements of those mechanical templates (e.g., [ 16 , 75 – 77 ]) should be regulated from step to step if they are to match human behavior. Our models show how fundamental stepping variables can be regulated to satisfy some particular goal-directed strategy (e.g., “stay in the middle of the path”, “maintain heading”, “maintain step width”, etc.).…”

A Multibody Dynamics Approach to Limit Cycle Walking

“…Recently, Gan propagates one periodic solution to the others by solving a one-dimensional continuation problem and studies different gaits of a single passive walking model. 25 Here, a two-step searching algorithm for the initial value v 0 is proposed to obtain the stable periodic gait for any given models. The second PDW walker is taken as an example to illustrate the implementation of the algorithm.…”

Efficient and Goal-Directed Oscillations in Articulated Soft Robots: The Point-To-Point Case

“…Articulated soft robots have considerable potential for applications involving repetitive motions, e.g. pick and place [5] and locomotion [6]. Among these motions, our work focuses specifically on the efficient execution of end effector point-to-point oscillations, which cover tasks that are widespread in the practice, such as Pick-and-Place actions.…”