Stability in skipping gaits

Skipping without and with hurdles in bipedal macaque: global mechanics

Macaques trained to perform bipedally used running gaits across a wide range of speeds. At higher speeds they preferred unilateral skipping (galloping). The same asymmetric stepping pattern was used while hurdling across two low obstacles placed at the distance of a stride within our experimental track. In bipedal macaques during skipping, we expected a differential use of the trailing and leading legs. The present study investigated global properties of the effective and virtual leg, the location of the virtual pivot point (VPP), and the energetics of the center of mass (CoM), with the aim of clarifying the differential leg operation during skipping in bipedal macaques. When skipping, macaques displayed minor double support and aerial phases during one stride. Asymmetric leg use was indicated by differences in leg kinematics. Axial damping and tangential leg work did not influence the indifferent peak ground reaction forces and impulses, but resulted in a lift of the CoM during contact of the leading leg. The aerial phase was largely due to the use of the double support. Hurdling amplified the differential leg operation. Here, higher ground reaction forces combined with increased double support provided the vertical impulse to overcome the hurdles. Following CoM dynamics during a stride, skipping and hurdling represented bouncing gaits. The elevation of the VPP of bipedal macaques resembled that of human walking and running in the trailing and leading phases, respectively. Because of anatomical restrictions, macaque unilateral skipping differs from that of humans, and may represent an intermediate gait between grounded and aerial running.

Reduced gravity effects on gait coordinative structures

Humans have stepped on the Lunar surface for less than 80 h of Extravehicular Activity, providing a narrow understanding of Lunar gait patterns. NASA's Human-crewed Artemis missions are quickly approaching; understanding how fractional gravity affects gait patterns will be critical for the Moon's and Mars' long-term habitation. This study examined gait patterns under 1.0 g (Earth), simulated 0.38 g (Martian), and 0.17 g (Lunar). Participants walked and ran on a treadmill supported by ARGOS (Active Response Gravity Offload System), simulating fractional gravity. Vicon motion capture data and principal component analysis software were used to capture and quantify coordinated gait structures. There were found to be significant differences (p < 0.05) in the coordinative gait structures for ambulation between fractional gravity conditions. Additionally, there were significantly higher asymmetric gait components for Lunar conditions. Finally, a skipping coordinative structure was identified within Lunar and Martian running.

Reducing cost of transport in asymmetrical gaits: lessons from unilateral skipping

PURPOSE

Unilateral skipping is an asymmetrical gait only exceptionally used by humans, due to high energetic demands. In skipping, the cost of transport decreases as speed increases, and the spring-mass model coexists with the vaulting pendular one. However, the mechanisms of energy transfers and recovery between the vaulting and the bouncing steps are still unclear in this gait. The objective of this work is to study how spatiotemporal and spring-mass asymmetries impact on metabolic cost, lowering it despite speed augmentation.

METHODS

Kinematics and metabolic rates of healthy subjects were measured during running and skipping on a treadmill at controlled speeds.

RESULTS

Metabolic power in skipping and running increased with similar slope but different intercepts. This fact determined the different behaviour of the cost of transport: constant in running, decreasing in skipping. In skipping the step time asymmetry remained constant, while the step length asymmetry decreased with speed, almost disappearing at 2.5 m/s^-1. Leg stiffness in trailing limb increased with higher slope than in leading limb and running; however, the relative leg stiffness asymmetry remained constant.

CONCLUSIONS

Slow skipping presents short bouncing steps, even shorter than the vaulting, impacting the stride mechanics and the metabolic cost. Faster speeds were achieved by taking longer bouncing steps and a stiffer trailing limb, allowing to improve the effectiveness of the spring-mass mechanism. The step asymmetries' trends with respect to speed in skipping open the possibility to use this gait as an experimental paradigm to study mechanisms of metabolic cost reduction in locomotion.

Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

Locomotory behaviour of the intertidal marble crab (Pachygrapsus marmoratus) supports the underwater spring-loaded inverted pendulum as a fundamental model for punting in animals

In aquatic pedestrian locomotion the dynamics of terrestrial and aquatic environments are coupled. Here we study terrestrial running and aquatic punting locomotion of the marine-living crab Pachygrapsus marmoratus. We detected both active and passive phases of running and punting through the observation of crab locomotory behaviour in standardized settings and by three-dimensional kinematic analysis of its dynamic gaits using high-speed video cameras. Variations in different stride parameters were studied and compared. The comparison was done based on the dimensionless parameter the Froude number (Fr) to account for the effect of buoyancy and size variability among the crabs. The underwater spring-loaded inverted pendulum (USLIP) model better fitted the dynamics of aquatic punting. USLIP takes account of the damping effect of the aquatic environment, a variable not considered by the spring-loaded inverted pendulum (SLIP) model in reduced gravity. Our results highlight the underlying principles of aquatic terrestrial locomotion by comparing it with terrestrial locomotion. Comparing punting with running, we show and increased stride period, decreased duty cycle and orientation of the carapace more inclined with the horizontal plane, indicating the significance of fluid forces on the dynamics due to the aquatic environment. Moreover, we discovered periodicity in punting locomotion of crabs and two different gaits, namely, long-flight punting and short-flight punting, distinguished by both footfall patterns and kinematic parameters. The generic fundamental model which belongs to all animals performing both terrestrial and aquatic legged locomotion has implications for control strategies, evolution and translation to robotic artefacts.

Limb dynamics in agility jumps of beginner and advanced dogs

A considerable body of work has examined the dynamics of different dog gaits, but there are no studies that have focused on limb dynamics in jumping. Jumping is an essential part of dog agility, a dog sport in which handlers direct their dogs through an obstacle course in a limited time. We hypothesized that limb parameters like limb length and stiffness indicate the skill level of dogs. We analyzed global limb parameters in jumping for 10 advanced and 10 beginner dogs. In experiments, we collected 3D kinematics and ground reaction forces during dog jumping at high forward speeds. Our results revealed general strategies of limb control in jumping and highlighted differences between advanced and beginner dogs. In take-off, the spatially leading forelimb was 75% (P<0.001) stiffer than the trailing forelimb. In landing, the trailing forelimb was 14% stiffer (P<0.001) than the leading forelimb. This indicates a strut-like action of the forelimbs to achieve jumping height in take-off and to transfer vertical velocity into horizontal velocity in landing (with switching roles of the forelimbs). During landing, the more (24%) compliant forelimbs of beginner dogs (P=0.005) resulted in 17% (P=0.017) higher limb compression during the stance phase. This was associated with a larger amount of eccentric muscle contraction, which might in turn explain the soft tissue injuries that frequently occur in the shoulder region of beginner dogs. For all limbs, limb length at toe-off was greater for advanced dogs. Hence, limb length and stiffness might be used as objective measures of skill.

Effects of hip torque during step-to-step transition on center-of-mass dynamics during human walking examined with numerical simulation

Besides the leg force actuator, humans also use a hip torque actuator during the step-to-step transition to redirect the velocity of CoM (Center of Mass). Although the leg force actuator has been widely studied, few researches analyze the hip torque actuator during the step-to-step transition. In this paper, we build a powered walking model which consists of a point mass linked with two compliant legs. Each leg has a spring and a damper in parallel. Two types of active actuators, the force actuator on the leg and the torque actuator at the hip, are added to simulate the leg force and hip torque actuator during the step-to-step transition. The cycle walk is solved by numerical simulations under different hip torque strength, and the energetics and stability are evaluated. The simulation results show that the hip torque actuator can reduce the energy cost and improve the stability of walking. Further analysis shows that the hip torque actuator can reduce mechanical works of both legs with small extra energy cost. To understand the principle of hip torque actuator, the CoM dynamics is analyzed. It is shown that the hip torque actuator is efficient on the redirection of CoM. Thus, it can improve the stability and reduce required forces of both legs, which decreases the energy cost. Our work provides a fundamental understanding of the hip torque during the step-to-step transition, and may help improve the design of bipedal robots and prosthesis.

Bipedal gait versatility in the Japanese macaque (Macaca fuscata)

It was previously believed that, among primates, only humans run bipedally. However, there is now growing evidence that at least some non-human primates can not only run bipedally but can also generate a running gait with an aerial phase. Japanese macaques trained for bipedal performances have been known to exhibit remarkable bipedal locomotion capabilities, but no aerial-phase running has previously been reported. In the present study, we investigated whether Japanese macaques could run with an aerial phase by collecting bipedal gait sequences from three macaques on a level surface at self-selected speeds (n = 188). During our experiments, body kinematics and ground reaction forces were recorded by a motion-capture system and two force plates installed within a wooden walkway. Our results demonstrated that macaques were able to utilize a variety of bipedal gaits including grounded running, skipping, and even running with an aerial phase. The self-selected bipedal locomotion speed of the macaques was fast, with Froude speed ranging from 0.4 to 1.3. However, based on congruity, no single trial that could be categorized as a pendulum-like walking gait was observed. The parameters describing the temporal, kinematic, and dynamic characteristics of macaque bipedal running gaits follow the patterns previously documented for other non-human primates and terrestrial birds that use running gaits, but are different from those of humans and from birds' walking gaits. The present study confirmed that when a Japanese macaque engages in bipedal locomotion, even without an aerial phase, it generally utilizes a spring-like running mechanism because the animals have a limited ability to stiffen their legs. That limitation is due to anatomical restrictions determined by the morphology and structure of the macaque musculoskeletal system. The general adoption of grounded running in macaques and other non-human primates, along with its absence in human bipedal locomotion, suggests that abandonment of compliant gait was a critical transition in the evolution of human obligatory bipedalism.

All common bipedal gaits emerge from a single passive model

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.

Skipping on uneven ground: trailing leg adjustments simplify control and enhance robustness

It is known that humans intentionally choose skipping in special situations, e.g. when descending stairs or when moving in environments with lower gravity than on Earth. Although those situations involve uneven locomotion, the dynamics of human skipping on uneven ground have not yet been addressed. To find the reasons that may motivate this gait, we combined experimental data on humans with numerical simulations on a bipedal spring-loaded inverted pendulum model (BSLIP). To drive the model, the following parameters were estimated from nine subjects skipping across a single drop in ground level: leg lengths at touchdown, leg stiffness of both legs, aperture angle between legs, trailing leg angle at touchdown (leg landing first after flight phase), and trailing leg retraction speed. We found that leg adjustments in humans occur mostly in the trailing leg (low to moderate leg retraction during swing phase, reduced trailing leg stiffness, and flatter trailing leg angle at lowered touchdown). When transferring these leg adjustments to the BSLIP model, the capacity of the model to cope with sudden-drop perturbations increased.