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All common bipedal gaits emerge from a single passive model.

ABSTRACT: 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.

SUBMITTER: Gan Z

PROVIDER: S-EPMC6170781 | biostudies-literature | 2018 Sep

REPOSITORIES: biostudies-literature

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All common bipedal gaits emerge from a single passive model.

Gan Zhenyu Z Yesilevskiy Yevgeniy Y Zaytsev Petr P Remy C David CD

Journal of the Royal Society, Interface 20180926 146

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 branch ...[more]

PMID: 30257925

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Project description:BackgroundSynergy modules have been used to describe activation of lower limb muscles during locomotion and hence to understand how the system controls movement. Walking and running have been shown shared synergy patterns suggesting common motor control of both symmetrical gaits. Unilateral skipping, an equivalent gait to the quadrupedal gallop in humans, has been defined as the third locomotion paradigm but the use by humans is limited due to its high metabolic cost. Synergies in skipping have been little investigated. In particular, to the best of our knowledge, the joint study of both trailing and leading limbs has never been addressed before.Research questionHow are organized muscle activation patterns in unilateral skipping? Are they organized in the same way that in symmetrical gaits? If yes, which are the muscle activation patterns in skipping that make it a different gait to walking or running? In the present research, we investigate if there are shared control strategies for all gaits in locomotion. Addressing these questions in terms of muscle synergies could suggest possible determinants of the scarce use of unilateral skipping in humans.MethodsElectromyographic data of fourteen bilateral muscles were collected from volunteers while performing walking, running and unilateral skipping on a treadmill. Also, spatiotemporal gait parameters were computed from 3D kinematics. The modular composition and activation timing extracted by non-negative matrix factorization were analyzed to detect similarities and differences among symmetrical gaits and unilateral skipping.ResultsSynergy modules showed high similarity throughout the different gaits and between trailing and leading limbs during unilateral skipping. The synergy associated with the propulsion force operated by calf muscles was anticipated in bouncing gaits. Temporal features of synergies in the leading leg were very similar to those observed for running. The different role of trailing and leading legs in unilateral skipping was reflected by the different timing in two modules. Activation for weight acceptance was anticipated and extended in the trailing leg, preparing the body for landing impact after the flight phase. A different behaviour was detected in the leading leg, which only deals with a pendular weight transference.SignificanceThe evidence gathered in this work supports the hypothesis of shared modules among symmetrical and asymmetrical gaits, suggesting a common motor control despite of the infrequent use of unilateral skipping in humans. Unilateral skipping results from phase-shifted activation of similar muscular groups used in symmetrical gaits, without the need for new muscular groups. The high and anticipated muscle activation in the trailing leg for landing could be the key distinctive event of unilateral skipping.

Project description:Background: Most animal studies of spinal cord injury are conducted in quadrupeds, usually rodents. It is unclear to what extent functional results from such studies can be translated to bipedal species such as humans because bipedal and quadrupedal locomotion involve very different patterns of spinal control of muscle coordination. Bipedalism requires upright trunk stability and coordinated postural muscle control; it has been suggested that peripheral sensory input is less important in humans than quadrupeds for recovery of locomotion following spinal injury. Methods: We used an Australian macropod marsupial, the tammar wallaby (Macropuseugenii), because tammars exhibit an upright trunk posture, human-like alternating hindlimb movement when swimming and bipedal over-ground locomotion. Regulation of their muscle movements is more similar to humans than quadrupeds. At different postnatal (P) days (P7-60) tammars received a complete mid-thoracic spinal cord transection. Morphological repair, as well as functional use of hind limbs, was studied up to the time of their pouch exit. Results: Growth of axons across the lesion restored supraspinal innervation in animals injured up to 3 weeks of age but not in animals injured after 6 weeks of age. At initial pouch exit (P180), the young injured at P7-21 were able to hop on their hind limbs similar to age-matched controls and to swim albeit with a different stroke. Those animals injured at P40-45 appeared to be incapable of normal use of hind limbs even while still in the pouch. Conclusions: Data indicate that the characteristic over-ground locomotion of tammars provides a model in which regrowth of supraspinal connections across the site of injury can be studied in a bipedal animal. Forelimb weight-bearing motion and peripheral sensory input appear not to compensate for lack of hindlimb control, as occurs in quadrupeds. Tammars may be a more appropriate model for studies of therapeutic interventions relevant to humans.

Project description:Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect's neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion.

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All common bipedal gaits emerge from a single passive model.

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All common bipedal gaits emerge from a single passive model.

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