Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain

Center of mass work analysis predicts preferred walking speeds for varying walking conditions

This study investigates the role of optimal push-off impulses in minimizing the total mechanical work dissipation per step, aiming to achieve passive single support work performance for a variety of walking conditions. By optimizing push-offs to cover the entire step's energy demands, the single support work may become only storage and release of mechanical energy through tendons and tissues when the soft tissue dissipation is negligible. Our simulations indicate that for each walking speed, there is an optimal push-off impulse that ensures energy balance without the need for additional energy regulation post step transition. The analytical optimal push-off coincided with minimum total step dissipation. The experimentally derived center of mass (COM) work components indicated that net single support work played a role in regulating COM momentum. For each walking condition examined, we identified only one specific walking speed at which the net single support work was zero. This speed also coincided with the minimum total step dissipation (the sum of step collision and net negative single support work). It was 64.2 % of the total step work for young adults walking on smooth surfaces. We defined the minimum total step dissipation as the indicator for mechanically preferred walking speed. For level ground (even terrain), the estimated mechanically preferred walking speeds align closely with literature values for young adult (age: 27.7 ± 5.2, speed: ∼1.2 m.s-1) and older adult (age: 66.1 ± 1.4, speed: ∼ 1.0 m.s-1) self-selected speeds, with a reduction observed for the restricted view of oncoming irregularities in the substrate terrain (15 %). For walking on uneven surfaces, terrain amplitude was shown to impact walking costs quadratically, with optimal speeds declining by approximately 20 % per unit increase in terrain amplitude. We also observed that the preferred speeds for older adults tend to be 12-15 % lower than for younger adults, likely due to biomechanical adaptations. Beyond certain terrain amplitudes, no preferred walking speed allowed fully passive single support work, highlighting a possible biomechanical threshold where ankle push-off alone becomes insufficient and hip torque compensation may be necessary. This approach provides a framework for estimating mechanically preferred walking speeds across varying walking conditions such as different terrain amplitudes when the total step dissipation is minimized.

Hen-durance training-effects of an exercise regimen on laying hen muscle architecture and fracture prevalence

Domestic chickens kept for egg laying navigate inclines such as ramps in some commercial housing systems to aid in transitions between housing tiers. Laying hens use their wings and hindlimbs in a locomotion called wing-assisted incline running (WAIR) to ascend steep inclines. There is a potential relationship between the strength of the main flight muscles and the health of the keel bone from which they originate. We sought to test the effects of a controlled, WAIR-based exercise regimen during rearing on keel bone health and muscle properties of white- and brown-feathered laying hens. The WAIR exercise regimen, which consisted of exercise twice weekly for 16 weeks did not promote increases in muscle mass or physiological cross-sectional area at 21 weeks of age (WOA) and did not provide long-term benefits on keel fracture prevalence at 40 WOA. However, the brown-feathered birds were found to have lower amounts of keel fractures at 40 WOA in comparison with the white-feathered birds. Future studies should test for training that begins before chicks become fully feathered, exercises that emphasize full excursion of the wing during downstroke and different levels of intensity, frequency and duration to optimize flight muscle architecture and promote keel bone health.

Center of mass mechanics during locomotion in the arboreal squirrel monkey (Saimiri sciureus) as a function of speed and substrate

It is thought that the magnitude of center of mass (COM) oscillations can affect stability and locomotor costs in arboreal animals. Previous studies have suggested that minimizing collisional losses and maximizing pendular energy exchange are effective mechanisms to reduce muscular input and energy expenditure during terrestrial locomotion. However, few studies have explored whether these mechanisms are used in an arboreal context, where stability and efficiency often act as trade-offs. This study explores three-dimensional COM mechanics in an arboreal primate - the squirrel monkey (Saimiri sciureus) - moving quadrupedally at various speeds on instrumented arboreal and terrestrial supports. Using kinetic data, values of energy recovery, COM mechanical work and power, potential and kinetic energy congruity, and collision angle and fraction were calculated for each stride. Saimiri sciureus differed from many other mammals by having lower energy recovery. Although few differences were observed in COM mechanics between substrates at low or moderate speeds, as speed increased, COM work was done at a much greater range of rates on the pole. Collision angles were higher, whereas collision fractions and energy recovery values were lower on the pole, indicating less moderation of collisional losses during arboreal versus terrestrial locomotion. These data support the idea that the energetic demands of arboreal and terrestrial locomotion differ, suggesting that arboreal primates likely employ different locomotor strategies compared with their terrestrial counterparts - an important factor in the evolution of arboreal locomotion.

An approximate solution of the SLIP model under the regime of linear angular dynamics during stance and the stability of symmetric periodic running gaits

Terrestrial locomotion is a complex phenomenon that is often linked to the survival of an individual and of an animal species. Mathematical models seek to express in quantitative terms how animals move, but this is challenging because the ways in which the nervous and musculoskeletal systems interact to produce body movement is not completely understood. Models with many variables tend to lack biological interpretability and describe the motion of an animal with too many independent degrees of freedom. Instead, reductionist models aim to describe the essential features of a gait with the smallest number of variables, often concentrating on the center of mass dynamics. In particular, spring-mass models have been successful in extracting and describing important characteristics of running. In this paper, we consider the spring loaded inverted pendulum model under the regime of constant angular velocity, small compression, and small angle swept during stance. We provide conditions for the asymptotic stability of periodic trajectories for the full range of parameters. The hypothesis of linear angular dynamics during stance is successfully tested on publicly available human data of individuals running on a treadmill at different velocities. Our analysis highlights a novel bifurcation phenomenon for varying Froude number: there are periodic trajectories of the spring loaded inverted pendulum model that are stable only in a restricted range of Froude numbers, while they become unstable for smaller or larger Froude numbers.

Rethinking the four-wing problem in plesiosaur swimming using bio-inspired decentralized control

A locomotor system that can function across different environmental conditions and produce a range of performances is one of the most critical abilities needed for extant and extinct animals in order to survive and maximise their competitive fitness. Recent engineering-inspired paleontological studies have reconstructed feasible locomotor patterns in extinct animals. However, it is still challenging to describe how extinct animals successfully adjust their locomotor patterns to new situations (e.g., changes in locomotor speed and morphology). In this study, we develop a novel reconstruction method based on a bio-inspired control system. We focus on plesiosaurs, an extinct aquatic reptile group which has two pairs of flipper-shaped limbs, and demonstrate that a highly optimised, flexible locomotor pattern for all four flippers can be reconstructed based on a decentralized control scheme formulated from extant animals' locomotion. The results of our robotic experiments show that a simple, local sensory feedback mechanism allows the plesiosaur-like robot to exploit the fluid flow between the flippers and generate efficient swimming patterns in response to changes in locomotor conditions. Our new method provides further evidence how decentralized control systems can produce a pathway between extinct and extant animals in order to understand the how extinct animals moved and how these movement patterns may have evolved.

Muscle-controlled physics simulations of bird locomotion resolve the grounded running paradox

Humans and birds use very different running styles. Unlike humans, birds adopt "grounded running" at intermediate speeds-a running gait where at least one foot always maintains ground contact. Avian grounded running is a paradox: Animals usually minimize locomotor energy expenditure, but birds prefer grounded running despite incurring higher energy costs. Using predictive gait simulations of the emu (Dromaius novaehollandiae), we resolve this paradox by demonstrating that grounded running represents an optimal gait for birds, from both energetics and muscle excitations perspectives. Our virtual experiments decoupled effects of posture and tendon elasticity, biomechanically relevant anatomical features that cannot be isolated in real birds. The avian body plan prevents (near) vertical leg postures, making the running style used by humans impossible. Under this anatomical constraint, grounded running is optimal if the muscles produce the highest forces in crouched postures, as is true in most birds. Shared anatomical features suggest that, as a behavior, avian grounded running first evolved within non-avian dinosaurs.

Why animals can outrun robots

Animals are much better at running than robots. The difference in performance arises in the important dimensions of agility, range, and robustness. To understand the underlying causes for this performance gap, we compare natural and artificial technologies in the five subsystems critical for running: power, frame, actuation, sensing, and control. With few exceptions, engineering technologies meet or exceed the performance of their biological counterparts. We conclude that biology's advantage over engineering arises from better integration of subsystems, and we identify four fundamental obstacles that roboticists must overcome. Toward this goal, we highlight promising research directions that have outsized potential to help future running robots achieve animal-level performance.

The effect of attentional cues on mechanical efficiency and movement smoothness in running gait: An interdisciplinary investigation

The aim was to examine the effect of focus of attention cues on foot angle for retraining movement purposes. Twenty (females: 8) rearfoot-striking recreational runners (mass: 72.5 ± 11.8 kg; height: 1.73 ± 0.09 m; age: 32.9 ± 11.3 years) were randomly assigned to an internal focus (IF) (n = 10) or external focus (EF) (n = 10) verbal cue group. Participants performed 5 × 6 minute blocks of treadmill running (control run, 3 × cued running, retention run) at a self-selected running velocity (9.4 ± 1.1 km∙h-1) during a single laboratory visit. Touchdown foot angle, mechanical efficiency, internal and external work were calculated and, centre of mass (COM) and foot movement smoothness was quantified. Linear-mixed effect models showed an interaction for foot angle (p < 0.001, ηp2 = 0.35) and mechanical efficiency (p < 0.001, ηp2 = 0.40) when comparing the control to the cued running. Only the IF group reduced foot angle and mechanical efficiency during cued running, but not during the retention run. The IF group produced less external work during the 1st cued run than the control run. COM and foot smoothness were unaffected by cueing. Only an IF produced desired technique changes but at the cost of reduced mechanical efficiency. Movement smoothness was unaffected by cue provision. Changes to foot angle can be achieved within 6 minutes of gait retraining.

Neuromechanical stabilisation of the centre of mass during running

BACKGROUND

Stabilisation of the centre of mass (COM) trajectory is thought to be important during running. There is emerging evidence of the importance of leg length and angle regulation during running, which could contribute to stability in the COM trajectory The present study aimed to understand if leg length and angle stabilises the vertical and anterior-posterior (AP) COM displacements, and if the stability alters with running speeds.

METHODS

Data for this study came from an open-source treadmill running dataset (n = 28). Leg length (m) was calculated by taking the resultant distance of the two-dimensional sagittal plane leg vector (from pelvis segment to centre of pressure). Leg angle was defined by the angle subtended between the leg vector and the horizontal surface. Leg length and angle were scaled to a standard deviation of one. Uncontrolled manifold analysis (UCM) was used to provide an index of motor abundance (IMA) in the stabilisation of the vertical and AP COM displacement.

RESULTS

IMAAP and IMAvertical were largely destabilising and always stabilising, respectively. As speed increased, the peak destabilising effect on IMAAP increased from -0.66(0.18) at 2.5 m/s to -1.12(0.18) at 4.5 m/s, and the peak stabilising effect on IMAvertical increased from 0.69 (0.19) at 2.5 m/s to 1.18 (0.18) at 4.5 m/s.

CONCLUSION

Two simple parameters from a simple spring-mass model, leg length and angle, can explain the control behind running. The variability in leg length and angle helped stabilise the vertical COM, whilst maintaining constant running speed may rely more on inter-limb variation to adjust the horizontal COM accelerations.

Assessing the effects of foot strike patterns and shoe types on the control of leg length and orientation in running

This research investigates the stabilization of leg length and orientation during the landing phase of running, examining the effects of different footwear and foot strike patterns. Analyzing kinematic data from twenty male long-distance runners, both rearfoot and forefoot strikers, we utilized the Uncontrolled Manifold approach to assess stability. Findings reveal that both leg length and orientation are indeed stabilized during landing, challenging the hypothesis that rearfoot strikers exhibit less variance in deviations than forefoot strikers, and that increased footwear assistance would reduce these deviations. Surprisingly, footwear with a lower minimalist index enhanced post-landing stability, suggesting that cushioning contributes to both force dissipation and leg length stability. The study indicates that both foot strike patterns are capable of effectively reducing task-relevant variance, with no inherent restriction on flexibility for rearfoot strikers. However, there is an indication of potential reliance on footwear for stability. These insights advance our understanding of the biomechanics of running, highlighting the role of footwear in stabilizing leg length and orientation, which has significant implications for running efficiency and injury prevention.

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates

Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems.

Muscle force-length dynamics during walking over obstacles indicates delayed recovery and a shift towards more 'strut-like' function in birds with proprioceptive deficit

Recent studies of in vivo muscle function in guinea fowl revealed that distal leg muscles rapidly modulate force and work to stabilize running in uneven terrain. Previous studies focused on running only, and it remains unclear how muscular mechanisms for stability differ between walking and running. Here, we investigated in vivo function of the lateral gastrocnemius (LG) during walking over obstacles. We compared muscle function in birds with intact (iLG) versus self-reinnervated LG (rLG). Self-reinnervation results in proprioceptive feedback deficit due to loss of monosynaptic stretch reflex. We tested the hypothesis that proprioceptive deficit results in decreased modulation of EMG activity in response to obstacle contact, and a delayed obstacle recovery compared with that for iLG. We found that total myoelectric intensity (Etot) of iLG increased by 68% in obstacle strides (S 0) compared with level terrain, suggesting a substantial reflex-mediated response. In contrast, Etot of rLG increased by 31% in S 0 strides compared with level walking, but also increased by 43% in the first post-obstacle (S +1) stride. In iLG, muscle force and work differed significantly from level walking only in the S 0 stride, indicating a single-stride recovery. In rLG, force increased in S 0, S +1 and S +2 compared with level walking, indicating three-stride obstacle recovery. Interestingly, rLG showed little variation in work output and shortening velocity in obstacle terrain, indicating a shift towards near-isometric strut-like function. Reinnervated birds also adopted a more crouched posture across level and obstacle terrains compared with intact birds. These findings suggest gait-specific control mechanisms in walking and running.

Humans plan for the near future to walk economically on uneven terrain

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking and have no obvious organization. But humans often look ahead when they walk, and could potentially plan anticipatory fluctuations for the terrain. Such planning is only sensible if it serves some an objective purpose, such as maintaining constant speed or reducing energy expenditure, that is also attainable within finite planning capacity. Here, we show that humans do plan and perform optimal control strategies on uneven terrain. Rather than maintaining constant speed, they make purposeful, anticipatory speed adjustments that are consistent with minimizing energy expenditure. A simple optimal control model predicts economical speed fluctuations that agree well with experiments with humans (N = 12) walking on seven different terrain profiles (correlated with model [Formula: see text] , [Formula: see text] all terrains). Participants made repeatable speed fluctuations starting about six to eight steps ahead of each terrain feature (up to ±7.5 cm height difference each step, up to 16 consecutive features). Nearer features matter more, because energy is dissipated with each succeeding step's collision with ground, preventing momentum from persisting indefinitely. A finite horizon of continuous look-ahead and motor working space thus suffice to practically optimize for any length of terrain. Humans reason about walking in the near future to plan complex optimal control sequences.

Optimism persists when walking in unpredictable environments

Humans continuously modulate their control strategies during walking based on their ability to anticipate disturbances. However, how people adapt and use motor plans to create stable walking in unpredictable environments is not well understood. Our purpose was to investigate how people adapt motor plans when walking in a novel and unpredictable environment. We evaluated the whole-body center of mass (COM) trajectory of participants as they performed repetitions of a discrete goal-directed walking task during which a laterally-directed force field was applied to the COM. The force field was proportional in magnitude to forward walking velocity and randomly directed towards either the right or left each trial. We hypothesized that people would adapt a control strategy to reduce the COM lateral deviations created by the unpredictable force field. In support of our hypothesis, we found that with practice the magnitude of COM lateral deviation was reduced by 28% (force field left) and 44% (force field right). Participants adapted two distinct unilateral strategies, implemented regardless of if the force field was applied to the right or to the left, that collectively created a bilateral resistance to the unpredictable force field. These strategies included an anticipatory postural adjustment to resist against forces applied to the left, and a more lateral first step to resist against forces applied to the right. In addition, during catch trials when the force field was unexpectedly removed, participants exhibited trajectories similar to baseline trials. These findings were consistent with an impedance control strategy that provides a robust resistance to unpredictable perturbations. However, we also found evidence that participants made predictive adaptations in response to their immediate experience that persisted for three trials. Due to the unpredictable nature of the force field, this predictive strategy would sometimes result in greater lateral deviations when the prediction was incorrect. The presence of these competing control strategies may have long term benefits by allowing the nervous system to identify the best overall control strategy to use in a novel environment.

The bumpy road ahead: the role of substrate roughness on animal walking and a proposed comparative metric

Outside laboratory conditions and human-made structures, animals rarely encounter flat surfaces. Instead, natural substrates are uneven surfaces with height variation that ranges from the microscopic scale to the macroscopic scale. For walking animals (which we define as encompassing any form of legged movement across the ground, such as walking, running, galloping, etc.), such substrate 'roughness' influences locomotion in a multitude of ways across scales, from roughness that influences how each toe or foot contacts the ground, to larger obstacles that animals must move over or navigate around. Historically, the unpredictability and variability of natural environments has limited the ability to collect data on animal walking biomechanics. However, recent technical advances, such as more sensitive and portable cameras, biologgers, laboratory tools to fabricate rough terrain, as well as the ability to efficiently store and analyze large variable datasets, have expanded the opportunity to study how animals move under naturalistic conditions. As more researchers endeavor to assess walking over rough terrain, we lack a consistent approach to quantifying roughness and contextualizing these findings. This Review summarizes existing literature that examines non-human animals walking on rough terrain and presents a metric for characterizing the relative substrate roughness compared with animal size. This framework can be applied across terrain and body scales, facilitating direct comparisons of walking over rough surfaces in animals ranging in size from ants to elephants.

How human runners regulate footsteps on uneven terrain

Running stably on uneven natural terrain takes skillful control and was critical for human evolution. Even as runners circumnavigate hazardous obstacles such as steep drops, they must contend with uneven ground that is gentler but still destabilizing. We do not know how footsteps are guided based on the uneven topography of the ground and how those choices influence stability. Therefore, we studied human runners on trail-like undulating uneven terrain and measured their energetics, kinematics, ground forces, and stepping patterns. We find that runners do not selectively step on more level ground areas. Instead, the body's mechanical response, mediated by the control of leg compliance, helps maintain stability without requiring precise regulation of footsteps. Furthermore, their overall kinematics and energy consumption on uneven terrain showed little change from flat ground. These findings may explain how runners remain stable on natural terrain while devoting attention to tasks besides guiding footsteps.

Adaptive multi-objective control explains how humans make lateral maneuvers while walking

To successfully traverse their environment, humans often perform maneuvers to achieve desired task goals while simultaneously maintaining balance. Humans accomplish these tasks primarily by modulating their foot placements. As humans are more unstable laterally, we must better understand how humans modulate lateral foot placement. We previously developed a theoretical framework and corresponding computational models to describe how humans regulate lateral stepping during straight-ahead continuous walking. We identified goal functions for step width and lateral body position that define the walking task and determine the set of all possible task solutions as Goal Equivalent Manifolds (GEMs). Here, we used this framework to determine if humans can regulate lateral stepping during non-steady-state lateral maneuvers by minimizing errors consistent with these goal functions. Twenty young healthy adults each performed four lateral lane-change maneuvers in a virtual reality environment. Extending our general lateral stepping regulation framework, we first re-examined the requirements of such transient walking tasks. Doing so yielded new theoretical predictions regarding how steps during any such maneuver should be regulated to minimize error costs, consistent with the goals required at each step and with how these costs are adapted at each step during the maneuver. Humans performed the experimental lateral maneuvers in a manner consistent with our theoretical predictions. Furthermore, their stepping behavior was well modeled by allowing the parameters of our previous lateral stepping models to adapt from step to step. To our knowledge, our results are the first to demonstrate humans might use evolving cost landscapes in real time to perform such an adaptive motor task and, furthermore, that such adaptation can occur quickly-over only one step. Thus, the predictive capabilities of our general stepping regulation framework extend to a much greater range of walking tasks beyond just normal, straight-ahead walking.

Limb, joint and pelvic kinematic control in the quail coping with steps upwards and downwards

Small cursorial birds display remarkable walking skills and can negotiate complex and unstructured terrains with ease. The neuromechanical control strategies necessary to adapt to these challenging terrains are still not well understood. Here, we analyzed the 2D- and 3D pelvic and leg kinematic strategies employed by the common quail to negotiate visible steps (upwards and downwards) of about 10%, and 50% of their leg length. We used biplanar fluoroscopy to accurately describe joint positions in three dimensions and performed semi-automatic landmark localization using deep learning. Quails negotiated the vertical obstacles without major problems and rapidly regained steady-state locomotion. When coping with step upwards, the quail mostly adapted the trailing limb to permit the leading leg to step on the elevated substrate similarly as it did during level locomotion. When negotiated steps downwards, both legs showed significant adaptations. For those small and moderate step heights that did not induce aerial running, the quail kept the kinematic pattern of the distal joints largely unchanged during uneven locomotion, and most changes occurred in proximal joints. The hip regulated leg length, while the distal joints maintained the spring-damped limb patterns. However, to negotiate the largest visible steps, more dramatic kinematic alterations were observed. There all joints contributed to leg lengthening/shortening in the trailing leg, and both the trailing and leading legs stepped more vertically and less abducted. In addition, locomotion speed was decreased. We hypothesize a shift from a dynamic walking program to more goal-directed motions that might be focused on maximizing safety.

The spring-mass model and other reductionist models of bipedal locomotion on inclines

The spring-mass model is a model of locomotion aimed at giving the essential mathematical laws of the trajectory of the center of mass of an animal during bouncing gaits, such as hopping (one-dimensional) and running (two-dimensional). This reductionist mechanical system has been extensively investigated for locomotion over horizontal surfaces, whereas it has been largely neglected on other ecologically relevant surfaces, including inclines. For example, how the degree of inclination impacts the dynamics of the center of mass of the spring-mass model has not been investigated thoroughly. In this work, we derive a mathematical model which extends the spring-mass model to inclined surfaces. Among our results, we derive an approximate solution of the system, assuming a small angular sweep of the limb and a small spring compression during stance, and show that this approximation is very accurate, especially for small inclinations of the ground. Furthermore, we derive theoretical bounds on the difference between the Lagrangian and Lagrange equations of the true and approximate system, and discuss locomotor stability questions of the approximate solutions. We test our models through a sensitivity analysis using parameters relevant to the locomotion of bipedal animals (quail, pheasant, guinea fowl, turkey, ostrich, and humans) and compare our approximate solution to the numerically derived solution of the exact system. We compare the two-dimensional spring-mass model on inclines with the one-dimensional spring-mass model to which it reduces under the limit of no horizontal velocity; we compare the two-dimensional spring-mass model on inclines with the inverted-pendulum model on inclines towards which it converges in the case of high stiffness-to-mass ratio. We include comparisons with historically prevalent no-gravity approximations of these models, as well. The insights we have gleaned through all these comparisons and the ability of our approximation to replicate some of the kinematic changes observed in animals moving on different inclines (e.g. reduction in vertical oscillation of the center of mass and decreased stride length) underlines the valuable and reasonable contributions that very simple, reductionist models, like the spring-mass model, can provide.

Kinematic trajectories in response to speed perturbations in walking suggest modular task-level control of leg angle and length

Navigating complex terrains requires dynamic interactions between the substrate, musculoskeletal and sensorimotor systems. Current perturbation studies have mostly used visible terrain height perturbations, which do not allow us to distinguish among the neuromechanical contributions of feedforward control, feedback-mediated and mechanical perturbation responses. Here, we use treadmill belt speed perturbations to induce a targeted perturbation to foot speed only, and without terrain-induced changes in joint posture and leg loading at stance onset. Based on previous studies suggesting a proximo-distal gradient in neuromechanical control, we hypothesized that distal joints would exhibit larger changes in joint kinematics, compared to proximal joints. Additionally, we expected birds to use feedforward strategies to increase the intrinsic stability of gait. To test these hypotheses, seven adult guinea fowl were video recorded while walking on a motorized treadmill, during both steady and perturbed trials. Perturbations consisted of repeated exposures to a deceleration and acceleration of the treadmill belt speed. Surprisingly, we found that joint angular trajectories and center of mass fluctuations remain very similar, despite substantial perturbation of foot velocity by the treadmill belt. Hip joint angular trajectories exhibit the largest changes, with the birds adopting a slightly more flexed position across all perturbed strides. Additionally, we observed increased stride duration across all strides, consistent with feedforward changes in the control strategy. The speed perturbations mainly influenced the timing of stance and swing, with the largest kinematic changes in the strides directly following a deceleration. Our findings do not support the general hypothesis of a proximo-distal gradient in joint control, as distal joint kinematics remain largely unchanged. Instead, we find that leg angular trajectory and the timing of stance and swing are most sensitive to this specific perturbation, and leg length actuation remains largely unchanged. Our results are consistent with modular task-level control of leg length and leg angle actuation, with different neuromechanical control and perturbation sensitivity in each actuation mode. Distal joints appear to be sensitive to changes in vertical loading but not foot fore-aft velocity. Future directions should include in vivo studies of muscle activation and force-length dynamics to provide more direct evidence of the sensorimotor control strategies for stability in response to belt speed perturbations.

Ostrich-Inspired Soft Robotics: A Flexible Bipedal Manipulator for Aggressive Physical Interaction

In this letter, ostrich-inspired soft robotics, an approach to intelligent robots that can achieve dexterous manipulation and locomotion without hesitating to collide with the surrounding environment, is proposed. The rationale behind the approach is described from the history of bio-inspired mechanisms, biology, and the theory of robot control. This letter focuses on the manipulator. The first prototype of an ostrich-inspired manipulator was developed to investigate its feasibility. This prototype is a serial chain of 18 rigid links connected with rotation joints moving in a vertical plane and driven through two asymmetric antagonistic wire systems connected to two levers that are directly operated by a human operator playing the role of the controller. Therefore, this manipulator is a highly underactuated mechanism that is flexible against external forces. The experimental results show that a human operator can control this manipulator so that its tip (i.e., the head) can reach several positions, including an upper position against gravity, indicating the potential of ostrich-inspired manipulators.

BirdBot achieves energy-efficient gait with minimal control using avian-inspired leg clutching

Designers of legged robots are challenged with creating mechanisms that allow energy-efficient locomotion with robust and minimalistic control. Sources of high energy costs in legged robots include the rapid loading and high forces required to support the robot's mass during stance and the rapid cycling of the leg's state between stance and swing phases. Here, we demonstrate an avian-inspired robot leg design, BirdBot, that challenges the reliance on rapid feedback control for joint coordination and replaces active control with intrinsic, mechanical coupling, reminiscent of a self-engaging and disengaging clutch. A spring tendon network rapidly switches the leg's slack segments into a loadable state at touchdown, distributes load among joints, enables rapid disengagement at toe-off through elastically stored energy, and coordinates swing leg flexion. A bistable joint mediates the spring tendon network's disengagement at the end of stance, powered by stance phase leg angle progression. We show reduced knee-flexing torque to a 10th of what is required for a nonclutching, parallel-elastic leg design with the same kinematics, whereas spring-based compliance extends the leg in stance phase. These mechanisms enable bipedal locomotion with four robot actuators under feedforward control, with high energy efficiency. The robot offers a physical model demonstration of an avian-inspired, multiarticular elastic coupling mechanism that can achieve self-stable, robust, and economic legged locomotion with simple control and no sensory feedback. The proposed design is scalable, allowing the design of large legged robots. BirdBot demonstrates a mechanism for self-engaging and disengaging parallel elastic legs that are contact-triggered by the foot's own lever-arm action.

Humans optimally anticipate and compensate for an uneven step during walking

The simple task of walking up a sidewalk curb is actually a dynamic prediction task. The curb is a disturbance that could cause a loss of momentum if not anticipated and compensated for. It might be possible to adjust momentum sufficiently to ensure undisturbed time of arrival, but there are infinite possible ways to do so. Much of steady, level gait is determined by energy economy, which should be at least as important with terrain disturbances. It is, however, unknown whether economy also governs walking up a curb, and whether anticipation helps. Here, we show that humans compensate with an anticipatory pattern of forward speed adjustments, predicted by a criterion of minimizing mechanical energy input. The strategy is mechanistically predicted by optimal control for a simple model of bipedal walking dynamics, with each leg’s push-off work as input. Optimization predicts a triphasic trajectory of speed (and thus momentum) adjustments, including an anticipatory phase. In experiment, human subjects ascend an artificial curb with the predicted triphasic trajectory, which approximately conserves overall walking speed relative to undisturbed flat ground. The trajectory involves speeding up in a few steps before the curb, losing considerable momentum from ascending it, and then regaining speed in a few steps thereafter. Descending the curb entails a nearly opposite, but still anticipatory, speed fluctuation trajectory, in agreement with model predictions that speed fluctuation amplitudes should scale linearly with curb height. The fluctuation amplitudes also decrease slightly with faster average speeds, also as predicted by model. Humans can reason about the dynamics of walking to plan anticipatory and economical control, even with a sidewalk curb in the way.

Does posture explain the kinematic differences in a grounded running gait between male and female Svalbard rock ptarmigan (Lagopus muta hyperborea) moving on snow?

The majority of locomotor research is conducted on treadmills and few studies attempt to understand the differences between this and animals moving in the wild. For example, animals may adjust their gait kinematics or limb posture, to a more compliant limb, to increase stability of locomotion to prevent limb failure or falling on different substrates. Here, using video recordings, we compared locomotor parameters (speed range, stride length, stride frequency, stance duration, swing duration and duty factor) of female Svalbard rock ptarmigan (Lagopus muta hyperborea) moving in the wild over snow to previous treadmill-based research. We also compared the absolute and body size (body mass and limb length)-corrected values of kinematic parameters to published data from males to look for any sex differences across walking and grounded running gaits. Our findings indicate that the kinematics of locomotion are largely conserved between the field and laboratory in that none of the female gaits were drastically affected by moving over snow, except for a prolonged swing phase at very slow walking speeds, likely due to toe dragging. Comparisons between the sexes indicate that the differences observed during a walking gait are likely due to body size. However, sexual dimorphism in body size could not explain the disparate grounded running kinematics of the female and male ptarmigan, which might be linked to a more crouched posture in females. Our findings provide insight into how males and females moving in situ may use different strategies to alleviate the effects of a variable substrate.

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic "Spring-mass" computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

The menisci are not shock absorbers: A biomechanical and comparative perspective

The lateral and medial menisci are fibrocartilaginous structures in the knee that play a crucial role in normal knee biomechanics. However, one commonly cited role of the menisci is that they function as "shock absorbers." Here we provide a critique of this notion, drawing upon a review of comparative anatomical and biomechanical data from humans and other tetrapods. We first review those commonly, and often exclusively, cited studies in support of a shock absorption function and show that evidence for a shock absorptive function is dubious. We then review the evolutionary and comparative evidence to show that (1) the human menisci are unremarkable in morphology compared with most other tetrapods, and (2) "shock" during locomotion is uncommon, with humans standing out as one of the only tetrapods that regularly experiences high levels of shock during locomotion. A shock-absorption function does not explain the origin of menisci, nor are human menisci specialized in any way that would explain a unique shock-absorbing function during human gait. Finally, we show that (3) the material properties of menisci are distinctly poorly suited for energy dissipation and that (4) estimations of meniscal energy absorption based on published data are negligible, both in their absolute amount and in comparison to other well-accepted structures which mitigate shock during locomotion. The menisci are evolutionarily ancient structures crucial for joint congruity, load distribution, and stress reduction, among a number of other functions. However, the menisci are not meaningful shock absorbers, neither in tetrapods broadly, nor in humans.

Metric variation in the postcranial skeleton of ostriches, Struthio (Aves: Palaeognathae), with new data on extinct subspecies

As a result of numerous fossil and subfossil finds of ostriches, there is great demand for a comprehensive osteometric dataset for the living species and subspecies of the genus Struthio. We meet this demand by providing a set of &gt; 100 measurements for a sample of 18 sexed skeletons, including all living and recently extinct species and subspecies of ostriches. We provide the first mensural data for two extinct subspecies, the hitherto questioned Struthio camelus spatzi from north-western Africa and the Arabian ostrich, Struthio camelus syriacus. The unique skeletal proportions of S. c. spatzi, with a relatively short wing, broad pelvis, short tarsometatarsus and big third toe, confirm the validity of this taxon and suggest an increased stability at the expense of cursoriality, which might have contributed to its extermination by humans. Our biometric analysis of the entire sample suggests a subtle sexual dimorphism in the ostrich skeleton, with females having more robust limb bones (especially wider and/or deeper at the ends) despite being on average smaller than males. If confirmed by further research, this size-independent dimorphism might reflect the independent regulation of the longitudinal and transverse dimensions of bones as revealed by several independent studies of morphological integration (covariance among morphological traits) in the avian skeleton.

Locomotor transitions in the potential energy landscape-dominated regime

To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor-terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.

Boron Supplementation Promotes Osteogenesis of Tibia by Regulating the Bone Morphogenetic Protein-2 Expression in African Ostrich Chicks

The present study aimed to explore the effects of supplemental boron on osteogenesis of tibia and to investigate the possible relationship between additional boron and the expression of bone morphogenetic protein-2 (BMP-2) in tibia of ostrich chicks. Therefore, forty-eight African ostrich chicks (15 days old) were supplemented with 0 mg/L, 40 mg/L, 80 mg/L, 160 mg/L, 320 mg/L, and 640 mg/L of boron in drinking water for 75 days. The paraffin sections of tibia used to measure histomorphometric parameters by hematoxylin and eosin (HE) staining, Masson's staining, and immunohistochemistry (IHC). Enzyme-linked immunosorbent assay was performed to assess the level of BMP-2, osteocalcin (BGP), glucocorticoids (GCs), osteoprotegerin (OPG), and receptor activator of nuclear factor kappa-B ligand (RANKL) in serum. TUNEL (terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling) technique was performed to detect the cell apoptosis. The results indicated that low dose of supplemental boron (40 mg/L-160 mg/L) in drinking water promotes bone development by increasing the mature ossein. The expression of BMP2 on 45 days was higher than 90 days. Serum level of BMP-2, BGP, and GCs changed significantly in groups with low dosage of boron, and OPG/RANKL ratio was upregulated from 0 to 160 mg/L. Cell apoptosis was least in 40 mg/L and 160 mg/L groups. Taken together, low dose of boron supplemented in drinking water could promote osteogenesis and growth and development of tibia by regulating the expression and secretion of BMP-2 and providing a dynamically balanced environment for tibia growth, development, and reconstruction by regulating the concentrations of BGP, GCs, and OPG/RANKL ratio in serum.

Accidents alter animal fitness landscapes

Animals alter their habitat use in response to the energetic demands of movement ('energy landscapes') and the risk of predation ('the landscape of fear'). Recent research suggests that animals also select habitats and move in ways that minimise their chance of temporarily losing control of movement and thereby suffering slips, falls, collisions or other accidents, particularly when the consequences are likely to be severe (resulting in injury or death). We propose that animals respond to the costs of an 'accident landscape' in conjunction with predation risk and energetic costs when deciding when, where, and how to move in their daily lives. We develop a novel theoretical framework describing how features of physical landscapes interact with animal size, morphology, and behaviour to affect the risk and severity of accidents, and predict how accident risk might interact with predation risk and energetic costs to dictate movement decisions across the physical landscape. Future research should focus on testing the hypotheses presented here for different real-world systems to gain insight into the relative importance of theorised effects in the field.

Frictional performance of ostrich (Struthio camelus) foot sole on sand in all directions

To study the ostrich (Struthio camelus) foot sole with an irregular surface and papillae, we designed a multi-angle device to measure its friction properties on sand. The observed macro- and micro-structures of the ostrich foot sole intensified friction by tightly gripping sand particles. The sliding friction of the ostrich foot on a single-layer sand board increased with the enlarging particle size. A loose sand all-direction test showed that the coefficient of friction (COF) of the ostrich foot sole was higher than that of the nonpapillary foot. The COF of the ostrich foot sole minimized to 0.30 at 0° and maximized to 0.61 at 180°, and that of the nonpapillary foot minimized to 0.23 at 300° and maximized to 0.54 at 180°, suggesting the ostrich papillae exerted a friction effect. Significant differences in COF were observed among the ranges 10°-40°, 90° and 120°-350°, indicating the papillae can steadily enhance the frictional performance. This study provides an important theoretical basis for the design of frictional robots for deep space exploration and other soft media.

Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds

Quadrupedal animal locomotion is energetically costly. We explore two forms of mechanical work that may be relevant in imposing these physiological demands. Limb work, due to the forces and velocities between the stance foot and the centre of mass, could theoretically be zero given vertical limb forces and horizontal centre of mass path. To prevent pitching, skewed vertical force profiles would then be required, with forelimb forces high in late stance and hindlimb forces high in early stance. By contrast, joint work-the positive mechanical work performed by the limb joints-would be reduced with forces directed through the hip or shoulder joints. Measured quadruped kinetics show features consistent with compromised reduction of both forms of work, suggesting some degree of, but not perfect, inter-joint energy transfer. The elbows-back, knees-forward design reduces the joint work demand of a low limb-work, skewed, vertical force profile. This geometry allows periods of high force to be supported when the distal segment is near vertical, imposing low moments about the elbow or knee, while the shoulder or hip avoids high joint power despite high moments because the proximal segment barely rotates-translation over this period is due to rotation of the distal segment.

Postural stability in human running with step-down perturbations: an experimental and numerical study

Postural stability is one of the most crucial elements in bipedal locomotion. Bipeds are dynamically unstable and need to maintain their trunk upright against the rotations induced by the ground reaction forces (GRFs), especially when running. Gait studies report that the GRF vectors focus around a virtual point above the centre of mass (VPA), while the trunk moves forward in pitch axis during the stance phase of human running. However, a recent simulation study suggests that a virtual point below the centre of mass (VPB) might be present in human running, because a VPA yields backward trunk rotation during the stance phase. In this work, we perform a gait analysis to investigate the existence and location of the VP in human running at 5 m s-1, and support our findings numerically using the spring-loaded inverted pendulum model with a trunk. We extend our analysis to include perturbations in terrain height (visible and camouflaged), and investigate the response of the VP mechanism to step-down perturbations both experimentally and numerically. Our experimental results show that the human running gait displays a VPB of ≈-30 cm and a forward trunk motion during the stance phase. The camouflaged step-down perturbations affect the location of the VPB. Our simulation results suggest that the VPB is able to encounter the step-down perturbations and bring the system back to its initial equilibrium state.

Vision does not impact walking performance in Argentine ants

Many walking insects use vision for long-distance navigation, but the influence of vision on rapid walking performance that requires close-range obstacle detection and directing the limbs towards stable footholds remains largely untested. We compared Argentine ant (Linepithema humile) workers in light versus darkness while traversing flat and uneven terrain. In darkness, ants reduced flat-ground walking speeds by only 5%. Similarly, the approach speed and time to cross a step obstacle were not significantly affected by lack of lighting. To determine whether tactile sensing might compensate for vision loss, we tracked antennal motion and observed shifts in spatiotemporal activity as a result of terrain structure but not illumination. Together, these findings suggest that vision does not impact walking performance in Argentine ant workers. Our results help contextualize eye variation across ants, including subterranean, nocturnal and eyeless species that walk in complete darkness. More broadly, our findings highlight the importance of integrating vision, proprioception and tactile sensing for robust locomotion in unstructured environments.

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of 'stable' or 'unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

An energy landscape approach to locomotor transitions in complex 3D terrain

Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Despite this, far more mechanistic understanding of terrestrial locomotion has been on how to generate and stabilize around near-steady-state movement in a single mode. We still know little about how locomotor transitions emerge from physical interaction with complex terrain. Consequently, robots largely rely on geometric maps to avoid obstacles, not traverse them. Recent studies revealed that locomotor transitions in complex three-dimensional (3D) terrain occur probabilistically via multiple pathways. Here, we show that an energy landscape approach elucidates the underlying physical principles. We discovered that locomotor transitions of animals and robots self-propelled through complex 3D terrain correspond to barrier-crossing transitions on a potential energy landscape. Locomotor modes are attracted to landscape basins separated by potential energy barriers. Kinetic energy fluctuation from oscillatory self-propulsion helps the system stochastically escape from one basin and reach another to make transitions. Escape is more likely toward lower barrier direction. These principles are surprisingly similar to those of near-equilibrium, microscopic systems. Analogous to free-energy landscapes for multipathway protein folding transitions, our energy landscape approach from first principles is the beginning of a statistical physics theory of multipathway locomotor transitions in complex terrain. This will not only help understand how the organization of animal behavior emerges from multiscale interactions between their neural and mechanical systems and the physical environment, but also guide robot design, control, and planning over the large, intractable locomotor-terrain parameter space to generate robust locomotor transitions through the real world.

Tuning of feedforward control enables stable muscle force-length dynamics after loss of autogenic proprioceptive feedback

Animals must integrate feedforward, feedback and intrinsic mechanical control mechanisms to maintain stable locomotion. Recent studies of guinea fowl (Numida meleagris) revealed that the distal leg muscles rapidly modulate force and work output to minimize perturbations in uneven terrain. Here we probe the role of reflexes in the rapid perturbation responses of muscle by studying the effects of proprioceptive loss. We induced bilateral loss of autogenic proprioception in the lateral gastrocnemius muscle (LG) using self-reinnervation. We compared in vivo muscle dynamics and ankle kinematics in birds with reinnervated and intact LG. Reinnervated and intact LG exhibit similar steady state mechanical function and similar work modulation in response to obstacle encounters. Reinnervated LG exhibits 23ms earlier steady-state activation, consistent with feedforward tuning of activation phase to compensate for lost proprioception. Modulation of activity duration is impaired in rLG, confirming the role of reflex feedback in regulating force duration in intact muscle.

Low leg compliance permits grounded running at speeds where the inverted pendulum model gets airborne

Animals typically switch from grounded (no flight phases) to aerial running at dimensionless speeds u^ < 1. But some birds use grounded running far above u^ = 1, which puzzles biologists because the inverted pendulum becomes airborne at this speed. Here, we combine computer experiments using the spring-mass model with locomotion data from small birds, macaques and humans to understand the relationship between leg function (stiffness, angle of attack), locomotion speed and gait. With our model, we found three-humped ground reaction force profiles for slow grounded running speeds. The minimal single-humped grounded running speed is u^ = 0.4. This speed value roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Maximal grounded running speed in the model is not limited. In experiments, animals changed from grounded to aerial running at dimensionless contact time around 1. Considering these real-world contact times reduces the solution space drastically, but experimental data fit well. The model still predicts maximal grounded running speed  u^ > 1 for low stiffness values used by birds but decreases below u^ = 1 for increasing stiffness. For stiffer legs used in human walking and running, periodic grounded running vanishes. At speeds at which birds and macaques change to aerial running, we found periodic aerial running to intersect grounded running. This could explain why animals can alternate between grounded and aerial running at the same speed and identical leg parameters. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations.

The fast and the frugal: Divergent locomotory strategies drive limb lengthening in theropod dinosaurs

Limb length, cursoriality and speed have long been areas of significant interest in theropod paleobiology, since locomotory capacity, especially running ability, is critical in the pursuit of prey and to avoid becoming prey. The impact of allometry on running ability, and the limiting effect of large body size, are aspects that are traditionally overlooked. Since several different non-avian theropod lineages have each independently evolved body sizes greater than any known terrestrial carnivorous mammal, ~1000kg or more, the effect that such large mass has on movement ability and energetics is an area with significant implications for Mesozoic paleoecology. Here, using expansive datasets that incorporate several different metrics to estimate body size, limb length and running speed, we calculate the effects of allometry on running ability. We test traditional metrics used to evaluate cursoriality in non-avian theropods such as distal limb length, relative hindlimb length, and compare the energetic cost savings of relative hindlimb elongation between members of the Tyrannosauridae and more basal megacarnivores such as Allosauroidea or Ceratosauridae. We find that once the limiting effects of body size increase is incorporated there is no significant correlation to top speed between any of the commonly used metrics, including the newly suggested distal limb index (Tibia + Metatarsus/ Femur length). The data also shows a significant split between large and small bodied theropods in terms of maximizing running potential suggesting two distinct strategies for promoting limb elongation based on the organisms’ size. For small and medium sized theropods increased leg length seems to correlate with a desire to increase top speed while amongst larger taxa it corresponds more closely to energetic efficiency and reducing foraging costs. We also find, using 3D volumetric mass estimates, that the Tyrannosauridae show significant cost of transport savings compared to more basal clades, indicating reduced energy expenditures during foraging and likely reduced need for hunting forays. This suggests that amongst theropods, hindlimb evolution was not dictated by one particular strategy. Amongst smaller bodied taxa the competing pressures of being both a predator and a prey item dominant while larger ones, freed from predation pressure, seek to maximize foraging ability. We also discuss the implications both for interactions amongst specific clades and Mesozoic paleobiology and paleoecological reconstructions as a whole.

Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots

Bipedal animals have diverse morphologies and advanced locomotion abilities. Terrestrial birds, in particular, display agile, efficient, and robust running motion, in which they exploit the interplay between the body segment masses and moment of inertias. On the other hand, most legged robots are not able to generate such versatile and energy-efficient motion and often disregard trunk movements as a means to enhance their locomotion capabilities. Recent research investigated how trunk motions affect the gait characteristics of humans, but there is a lack of analysis across different bipedal morphologies. To address this issue, we analyze avian running based on a spring-loaded inverted pendulum model with a pronograde (horizontal) trunk. We use a virtual point based control scheme and modify the alignment of the ground reaction forces to assess how our control strategy influences the trunk pitch oscillations and energetics of the locomotion. We derive three potential key strategies to leverage trunk pitch motions that minimize either the energy fluctuations of the center of mass or the work performed by the hip and leg. We suggest how these strategies could be used in legged robotics.

Can skeletal surface area predict in vivo foot surface area?

The surface area of feet in contact with the ground is a key morphological feature that influences animal locomotion. Underfoot pressures (and consequently stresses experienced by the foot), as well as stability of an animal during locomotion, depend on the size and shape of this area. Here we tested whether the area of a skeletal foot could predict in vivo soft tissue foot surface area. Computed tomography scans of 29 extant tetrapods (covering mammals, reptiles, birds and amphibians) were used to produce models of both the soft tissues and the bones of their feet. Soft tissue models were oriented to a horizontal plane, and their outlines projected onto a surface to produce two-dimensional silhouettes. Silhouettes of skeletal models were generated either from bones in CT pose or with all autopodial bones aligned to the horizontal plane. Areas of these projections were calculated using alpha shapes (mathematical tight-fitting outline). Underfoot area of soft tissue was approximately 1.67 times that of skeletal tissue area (~ 2 times for manus, ~ 1.6 times for pes, if analysed separately). This relationship between skeletal foot area and soft tissue area, while variable in some of our study taxa, could provide information about the size of the organisms responsible for fossil trackways, suggest what size of tracks might be expected from potential trackmakers known only from skeletal remains, and aid in soft tissue reconstruction of skeletal remains for biomechanical modelling.

Humans Optimize Ground Contact Time and Leg Stiffness to Minimize the Metabolic Cost of Running

Trained endurance runners appear to fine-tune running mechanics to minimize metabolic cost. Referred to as self-optimization, the support for this concept has primarily been collated from only a few gait (e.g., stride frequency, length) and physiological (e.g., oxygen consumption, heart rate) characteristics. To extend our understanding, the aim of this study was to examine the effect of manipulating ground contact time on the metabolic cost of running in trained endurance runners. Additionally, the relationships between metabolic cost, and leg stiffness and perceived effort were examined. Ten participants completed 5 × 6-min treadmill running conditions. Self-selected ground contact time and step frequency were determined during habitual running, which was followed by ground contact times being increased or decreased in four subsequent conditions whilst maintaining step frequency (2.67 ± 0.15 Hz). The same self-selected running velocity was used across all conditions for each participant (12.7 ± 1.6 km · h^-1). Oxygen consumption was used to compute the metabolic cost of running and ratings of perceived exertion (RPE) were recorded for each run. Ground contact time and step frequency were used to estimate leg stiffness. Identifiable minimums and a curvilinear relationship between ground contact time and metabolic cost was found for all runners (r ² = 0.84). A similar relationship was observed between leg stiffness and metabolic cost (r ² = 0.83). Most (90%) runners self-selected a ground contact time and leg stiffness that produced metabolic costs within 5% of their mathematical optimal. The majority (n = 6) of self-selected ground contact times were shorter than mathematical optimals, whilst the majority (n = 7) of self-selected leg stiffness' were higher than mathematical optimals. Metabolic cost and RPE were moderately associated (r _s = 0.358 p = 0.011), but controlling for condition (habitual/manipulated) weakened this relationship (r _s = 0.302, p = 0.035). Both ground contact time and leg stiffness appear to be self-optimized characteristics, as trained runners were operating at or close to their mathematical optimal. The majority of runners favored a self-selected gait that may rely on elastic energy storage and release due to shorter ground contact times and higher leg stiffness's than optimal. Using RPE as a surrogate measure of metabolic cost during manipulated running gait is not recommended.

Effective locomotion at multiple stride frequencies using proprioceptive feedback on a legged microrobot

Limitations in actuation, sensing, and computation have forced small legged robots to rely on carefully tuned, mechanically mediated leg trajectories for effective locomotion. Recent advances in manufacturing, however, have enabled in such robots the ability for operation at multiple stride frequencies using multi-degree-of-freedom leg trajectories. Proprioceptive sensing and control is key to extending the capabilities of these robots to a broad range of operating conditions. In this work, we use concomitant sensing for piezoelectric actuation with a computationally efficient framework for estimation and control of leg trajectories on a quadrupedal microrobot. We demonstrate accurate position estimation (<16[Formula: see text] root-mean-square error) and control (<16[Formula: see text] root-mean-square tracking error) during locomotion across a wide range of stride frequencies (10 Hz-50 Hz). This capability enables the exploration of two bioinspired parametric leg trajectories designed to reduce leg slip and increase locomotion performance (e.g. speed, cost-of-transport (COT), etc). Using this approach, we demonstrate high performance locomotion at stride frequencies (10 Hz-30 Hz) where the robot's natural dynamics result in poor open-loop locomotion. Furthermore, we validate the biological hypotheses that inspired the trajectories and identify regions of highly dynamic locomotion, low COT (3.33), and minimal leg slippage (<10%).

Is conservation of center of mass mechanics a priority in human walking? Insights from leg-length asymmetry experiments

Center of mass (COM) control has been proposed to serve economy- and stability-related locomotor task objectives. However, given the lack of evidence supporting direct sensing and/or regulation of the COM, it remains unclear whether COM mechanics are prioritized in the control scheme of walking. We posit that peripheral musculoskeletal structures, e.g. muscle, are more realistic control targets than the COM, given their abundance of sensorimotor receptors and ability to influence whole-body energetics. As a first test of this hypothesis, we examined whether conservation of stance-phase joint mechanics is prioritized over COM mechanics in a locomotor task where simultaneous conservation of COM and joint mechanics is not feasible: imposed leg-length asymmetry. Positive joint mechanical cost of transport (work per distance traveled; COT_JNT) was maintained at values closer to normal walking than COM mechanical cost of transport (COT_COM; P<0.05, N=15). Furthermore, compared with our measures of COM mechanics (COT_COM, COM displacement), joint-level variables (COT_JNT, integrated total support moment) also displayed stronger conservation (less change from normal walking) when the participants' self-selected gait was assessed against other possible gait solutions. We conclude that when walking humans are exposed to an asymmetric leg-length perturbation, control of joint mechanics is prioritized over COM mechanics. Our results suggest that mechanical and metabolic effort is likely regulated via control of peripheral structures and not directly at the level of the COM. Joint mechanics may provide a more accurate representation of the underlying locomotor control targets and may prove advantageous in informing predictive models of human walking.

Dynamics and stability of running on rough terrains

Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope also varies randomly. The orientational instability is significantly mitigated by minimizing the tangential collision, which typically requires sensory information and anticipatory strategies such as leg retraction. By analysing the propagation of perturbations, we derive a single dimensionless parameter that governs stability. This parameter provides guidelines for the design and control of both biological and robotic runners.

Compliant legs enable lizards to maintain high running speeds on complex terrains

Substrate variations are likely to compel animal performance in natural environments, as running over complex terrains challenges the dynamic stability of the body differently in each step. Yet, being able to negotiate complex terrains at top speed is a strong advantage for animals that have to deal with predators and evasive prey. Only little is known on how animals negotiate such terrain variability at high speed. We investigated this in fast running Acanthodactylus boskianus lizards, by measuring their 3D kinematics using four synchronized high-speed video cameras (325Hz) on an adaptable racetrack. This racetrack was covered with four different substrates, representing increasing levels of terrain complexity. We found that the lizards deal with this complexity gradient by gradually adopting more erect parasagittal leg postures. More erected legs enable, in turn, more compliant legs use which are highly adjustable on complex terrains. Additionally, the lizards stabilise their head, which facilitates vestibular and visual perception. Together, compliant legs and head stabilisation enable the lizards to minimise movements of the body centre of mass, even when running on highly irregular terrains. This suggests that the head and the centre of mass are the priority targets for running on uneven terrains. As a result, running performance (mean forward speed) decreases only slightly, and only on the most challenging substrate under investigation.

An Overview on Principles for Energy Efficient Robot Locomotion

Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied.

The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11-18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1-4.7 years) required to locomote at a range of speeds but free to select their own gaits.

Understanding the Agility of Running Birds: Sensorimotor and Mechanical Factors in Avian Bipedal Locomotion

Birds are a diverse and agile lineage of vertebrates that all use bipedal locomotion for at least part of their life. Thus birds provide a valuable opportunity to investigate how biomechanics and sensorimotor control are integrated for agile bipedal locomotion. This review summarizes recent work using terrain perturbations to reveal neuromechanical control strategies used by ground birds to achieve robust, stable, and agile running. Early experiments in running guinea fowl aimed to reveal the immediate intrinsic mechanical response to an unexpected drop ("pothole") in terrain. When navigating the pothole, guinea fowl experience large changes in leg posture in the perturbed step, which correlates strongly with leg loading and perturbation recovery. Analysis of simple theoretical models of running has further confirmed the crucial role of swing-leg trajectory control for regulating foot contact timing and leg loading in uneven terrain. Coupling between body and leg dynamics results in an inherent trade-off in swing leg retraction rate for fall avoidance versus injury avoidance. Fast leg retraction minimizes injury risk, but slow leg retraction minimizes fall risk. Subsequent experiments have investigated how birds optimize their control strategies depending on the type of perturbation (pothole, step, obstacle), visibility of terrain, and with ample practice negotiating terrain features. Birds use several control strategies consistently across terrain contexts: (1) independent control of leg angular cycling and leg length actuation, which facilitates dynamic stability through simple control mechanisms, (2) feedforward regulation of leg cycling rate, which tunes foot-contact timing to maintain consistent leg loading in uneven terrain (minimizing fall and injury risks), (3) load-dependent muscle actuation, which rapidly adjusts stance push-off and stabilizes body mechanical energy, and (4) multi-step recovery strategies that allow body dynamics to transiently vary while tightly regulating leg loading to minimize risks of fall and injury. In future work, it will be interesting to investigate the learning and adaptation processes that allow animals to adjust neuromechanical control mechanisms over short and long timescales.