scholarly journals A simple model of a quadruped discovers single-foot walking and trotting as energy optimal strategies

2019 ◽  
Author(s):  
Delyle T. Polet ◽  
John E. A. Bertram
Keyword(s):  
Simple Model ◽  
Trajectory Optimization ◽  
Animal Movement ◽  
Reaction Force ◽  
Energetic Cost ◽  
Global Optimality ◽  
Canis Lupus Familiaris ◽  
Cost Of Transport ◽  
Transition Speed ◽  
Movement Strategies

AbstractIt is widely held that quadrupeds choose steady gaits that minimize their energetic cost of transport, but it is difficult to explore the entire range of possible footfall sequences empirically. We present a simple model of a quadruped that can spontaneously produce any of the 2300+ planar footfall sequences available to quadrupeds. Through trajectory optimization of a work and force-rate cost, and a large sample of random initial guesses, we provide stronger evidence towards the global optimality of symmetrical four-beat walking at low speeds and two beat running (trotting) at intermediate speeds. Using input parameters based on measurements in dogs (Canis lupus familiaris), the model predicts the correct phase offset in walking and a realistic walk-trot transition speed. It also spontaneously reproduces the double-hump ground reaction force profile observed in walking, and the smooth single-hump profile observed in trotting, despite the model’s lack of springs. However, the model incorrectly predicts duty factor at the slowest speeds, and does not choose galloping as globally optimal at high speeds. These limitations might point to missing levels of complexity that could be added to future quadrupedal models, but the present results suggest that massive legs, elastic components, head-neck oscillations and even multi-linked legs are not critical determiners for the optimality of natural quadrupedal walking and trotting.Author summaryWhy do quadrupedal mammals move in consistent ways, when so many options are available? We tackled this problem by determining energetically-optimal gaits using a simple computational model of a four-legged animal. The model can use virtually any pattern of movement (physics-permitting!) but selects natural movement strategies as energetically optimal. The similarities between the computer-based predictions and natural animal movement are striking, and suggest mammals utilize movement strategies that optimize energy use when they move.

Speed, stride frequency and energy cost per stride: how do they change with body size and gait?

1988 ◽  
Vol 138 (1) ◽  
pp. 301-318 ◽  
Author(s):  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Body Size ◽  
Body Mass ◽  
Energy Cost ◽  
Reaction Force ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Published Data ◽  
Frequency Change ◽  
Cost Of Locomotion ◽  
The Cost

In this study we investigate how speed and stride frequency change with body size. We use this information to define ‘equivalent speeds’ for animals of different size and to explore the factors underlying the six-fold difference in mass-specific energy cost of locomotion between mouse- and horse-sized animals at these speeds. Speeds and stride frequencies within a trot and a gallop were measured on a treadmill in 16 species of wild and domestic quadrupeds, ranging in body size from 30 g mice to 200 kg horses. We found that the minimum, preferred and maximum sustained speeds within a trot and a gallop all change in the same rather dramatic manner with body size, differing by nine-fold between mice and horses (i.e. all three speeds scale with about the 0.2 power of body mass). Although the absolute speeds differ greatly, the maximum sustainable speed was about 2.6-fold greater than the minimum within a trot, and 2.1-fold greater within a gallop. The frequencies used to sustain the equivalent speeds (with the exception of the minimum trotting speed) scale with about the same factor, the −0.15 power of body mass. Combining this speed and frequency data with previously published data on the energetic cost of locomotion, we find that the mass-specific energetic cost of locomotion is almost directly proportional to the stride frequency used to sustain a constant speed at all the equivalent speeds within a trot and a gallop, except for the minimum trotting speed (where it changes by a factor of two over the size range of animals studied). Thus the energy cost per kilogram per stride at five of the six equivalent speeds is about the same for all animals, independent of body size, but increases with speed: 5.0 J kg-1 stride-1 at the preferred trotting speed; 5.3 J kg-1 stride-1 at the trot-gallop transition speed; 7.5 J kg-1 stride-1 at the preferred galloping speed; and 9.4 J kg-1 stride-1 at the maximum sustained galloping speed. The cost of locomotion is determined primarily by the cost of activating muscles and of generating a unit of force for a unit of time. Our data show that both these costs increase directly with the stride frequency used at equivalent speeds by different-sized animals. The increase in cost per stride with muscles (necessitating higher muscle forces for the same ground reaction force) as stride length increases both in the trot and in the gallop.

Effects of animal movement strategies and costs on the distribution of active subsidies across simple landscapes

2014 ◽  
Vol 283 ◽  
pp. 45-52 ◽  
Author(s):  
Julia E. Earl ◽  
Patrick A. Zollner
Keyword(s):  
Animal Movement ◽  
Movement Strategies

Efficiency of uphill locomotion in nocturnal and diurnal lizards

1996 ◽  
Vol 199 (3) ◽  
pp. 587-592 ◽  
Author(s):  
C Farley ◽  
M Emshwiller
Keyword(s):  
Body Mass ◽  
Low Cost ◽  
Minimum Cost ◽  
Mechanical Work ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
Unit Distance ◽  
Cost Of Locomotion ◽  
Average Body Mass ◽  
Average Body

Nocturnal geckos can walk on level ground more economically than diurnal lizards. One hypothesis for why nocturnal geckos have a low cost of locomotion is that they can perform mechanical work during locomotion more efficiently than other lizards. To test this hypothesis, we compared the efficiency of the nocturnal gecko Coleonyx variegatus (average body mass 4.2 g) and the diurnal skink Eumeces skiltonianus (average body mass 4.8 g) when they performed vertical work during uphill locomotion. We measured the rate of oxygen consumption when each species walked on the level and up a 50 slope over a range of speeds. For Coleonyx variegatus, the energetic cost of traveling a unit distance (the minimum cost of transport, Cmin) increased from 1.5 to 2.7 ml O2 kg-1 m-1 between level and uphill locomotion. For Eumeces skiltonianus, Cmin increased from 2.5 to 4.7 ml O2 kg-1 m-1 between level and uphill locomotion. By taking the difference between Cmin for level and uphill locomotion, we found that the efficiency of performing vertical work during locomotion was 37 % for Coleonyx variegatus and 19 % for Eumeces skiltonianus. The similarity between the 1.9-fold difference in vertical efficiency and the 1.7-fold difference in the cost of transport on level ground is consistent with the hypothesis that nocturnal geckos have a lower cost of locomotion than other lizards because they can perform mechanical work during locomotion more efficiently.

scholarly journals The rising cost of warming waters: effects of temperature on the cost of swimming in fishes

2011 ◽  
Vol 8 (2) ◽  
pp. 266-269 ◽  
Author(s):  
Andrew M. Hein ◽  
Katrina J. Keirsted
Keyword(s):  
Water Temperature ◽  
Fish Species ◽  
Global Climate ◽  
Swimming Performance ◽  
Metabolic Cost ◽  
Quantitative Model ◽  
The Body ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
The Cost

Understanding the effects of water temperature on the swimming performance of fishes is central in understanding how fish species will respond to global climate change. Metabolic cost of transport (COT)—a measure of the energy required to swim a given distance—is a key performance parameter linked to many aspects of fish life history. We develop a quantitative model to predict the effect of water temperature on COT. The model facilitates comparisons among species that differ in body size by incorporating the body mass-dependence of COT. Data from 22 fish species support the temperature and mass dependencies of COT predicted by our model, and demonstrate that modest differences in water temperature can result in substantial differences in the energetic cost of swimming.

scholarly journals Terrain-blind walking of planar underactuated bipeds via velocity decomposition-enhanced control

2019 ◽  
Vol 38 (10-11) ◽  
pp. 1307-1323 ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P Schmiedeler
Keyword(s):  
Feedback Control ◽  
Biped Robot ◽  
Rate Of Change ◽  
Energetic Cost ◽  
Practical Implementation ◽  
Leg Length ◽  
Cost Of Transport ◽  
Velocity Decomposition ◽  
Novel Approach ◽  
Hybrid Zero Dynamics

In this article, we develop and assess a novel approach for the control of underactuated planar bipeds that is based on velocity decomposition. The new controller employs heuristic rules that mimic the functionality of transverse linearization feedback control and that can be layered on top of a conventional hybrid zero dynamics (HZD)-based controller. The heuristics sought to retain HZD-based control’s simplicity and enhance disturbance rejection for practical implementation on realistic biped robots. The proposed control strategy implements a feedback on the time rate of change of the decomposed uncontrolled velocity and is compared with conventional HZD-based control and transverse linearization feedback control for both vanishing and non-vanishing disturbances. Simulation studies with a point-foot, three-link biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. For the non-vanishing case, the velocity decomposition-enhanced controller outperforms HZD-based control, but takes fewer steps on average before failure than transverse linearization feedback control when walking on uneven terrain without visual perception of the ground. The findings were validated experimentally on a planar, five-link biped robot for eight different uneven terrains. The velocity decomposition-enhanced controller outperformed HZD-based control while maintaining a relatively low specific energetic cost of transport (~0.45). The biped robot “blindly” traversed uneven terrains with changes in terrain height accumulating to 5% of its leg length using the stand-alone low-level controller.

scholarly journals Effects of Sex and Fatigue on Biomechanical Measures During the Drop-Jump Task in Children

2017 ◽  
Vol 5 (1) ◽  
pp. 232596711667964 ◽  
Author(s):  
Kristín Briem ◽  
Kolbrún Vala Jónsdóttir ◽  
Árni Árnason ◽  
Þórarinn Sveinsson
Keyword(s):  
Knee Flexion ◽  
Female Athletes ◽  
Cruciate Ligament ◽  
Pearson Correlation ◽  
Reaction Force ◽  
Acl Injury ◽  
Initial Contact ◽  
Drop Jump ◽  
Increased Risk ◽  
Movement Strategies

Background: Female athletes have a higher rate of anterior cruciate ligament (ACL) injury than males from adolescence and into maturity, which is suggested to result from sex-specific changes in dynamic movement patterns with maturation. Few studies have studied movement strategies and response to fatigue in children. Purpose: To evaluate the effect of fatigue on biomechanical variables associated with increased risk for ACL injury during a drop-jump (DJ) performance in children. Study Design: Controlled laboratory study. Methods: A total of 116 children (mean age, 10.4 years) were recruited from local sports clubs and performed 5 repetitions of a DJ task before and after a fatigue protocol. Kinematic and kinetic data from initial contact (IC) to the first peak vertical ground reaction force (vGRF) were analyzed for both limbs, including limb and fatigue as within-subject factors for analyses between boys and girls. Pearson correlation coefficients were calculated to identify associations between variables of interest. Results: Girls demonstrated greater peak vGRF values than boys (by 8.1%; P < .05), there were greater peak vGRF values for the right limb than the left (by 6.2%; P < .001), and fatigue led to slightly greater values ( P < .05). Although weak, the correlation between peak vGRF values and knee flexion excursion was stronger for girls ( r = –0.20) than boys ( r = –0.08) ( P < .006). Fatigue resulted in greater knee flexion angles at IC and less excursion during landing, more so for girls (by 6.1° vs 1.4°; interaction, P < .001), although the knee flexion moment was generally lowered by fatigue ( P < .001). Limb asymmetry in knee flexion moments was more pronounced for boys than for girls (interaction, P < .05), contrary to that seen in frontal plane knee moments, where asymmetry was much greater in girls than boys (interaction, P < .001). Conclusion: Even as young athletes, girls and boys seem to adopt dissimilar movement strategies and are differently affected by fatigue. Clinical Relevance: Injury prevention programs should be considered at an earlier age in an effort to lower the risk of ACL injury in athletes.

scholarly journals Muscle mechanical advantage of human walking and running: implications for energy cost

2004 ◽  
Vol 97 (6) ◽  
pp. 2266-2274 ◽  
Author(s):  
Andrew A. Biewener ◽  
Claire T. Farley ◽  
Thomas J. Roberts ◽  
Marco Temaner
Keyword(s):  
Ground Reaction Force ◽  
Energy Demand ◽  
Muscle Force ◽  
Inverse Dynamics ◽  
Reaction Force ◽  
Knee Extensor ◽  
Metabolic Cost ◽  
Fold Increase ◽  
Cost Of Transport ◽  
Mechanical Advantage

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force ( R) and therefore the effective mechanical advantage (EMA = r/ R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154–176°) during much of the support phase of walking, its flexed position (134–164°) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% ( P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.

scholarly journals Does the Preferred Walk-Run Transition Speed on Steep Inclines Minimize Energetic Cost, Heart Rate or Neither?

2021 ◽  
pp. jeb.233056
Author(s):  
Jackson W. Brill ◽  
Rodger Kram
Keyword(s):  
Heart Rate ◽  
Linear Regression ◽  
Energetic Cost ◽  
Regression Equations ◽  
Rate Data ◽  
Heart Rate Data ◽  
Transition Speed ◽  
Wide Range ◽  
Incremental Protocol ◽  
Preferred Transition Speed

Humans prefer to walk at slow speeds and to run at fast speeds. In between, there is a speed at which people choose to transition between gaits, the Preferred Transition Speed (PTS). At slow speeds, it is energetically cheaper to walk and at faster speeds, it is cheaper to run. Thus, there is an intermediate speed, the Energetically Optimal Transition Speed (EOTS). Our goals were to determine: 1) how PTS and EOTS compare across a wide range of inclines and 2) if the EOTS can be predicted by the heart rate optimal transition speed (HROTS). Ten healthy, high-caliber, male trail/mountain runners participated. On day 1, subjects completed 0° and 15° trials and on day 2, 5° and 10°. We calculated PTS as the average of the walk-to-run transition speed (WRTS) and the run-to-walk transition speed (RWTS) determined with an incremental protocol. We calculated EOTS and HROTS from energetic cost and heart rate data for walking and running near the expected EOTS for each incline. The intersection of the walking and running linear regression equations defined EOTS and HROTS. We found that PTS, EOTS, and HROTS all were slower on steeper inclines. PTS was slower than EOTS at 0°, 5°, and 10°, but the two converged at 15°. Across all inclines, PTS and EOTS were only moderately correlated. Although EOTS correlated with HROTS, EOTS was not predicted accurately by heart rate on an individual basis.

scholarly journals A Rotating Respirometer to Monitor Voluntary Activity and Associated Exchange of Respiratory Gases in the Land Hermit Crab (Coenobita Compressus)

1985 ◽  
Vol 119 (1) ◽  
pp. 85-101
Author(s):  
MICHÉLE G. WHEATLY ◽  
BRIAN R. MCMAHON ◽  
WARREN W. BURGGREN ◽  
ALAN W. PINDER
Keyword(s):  
Gas Exchange ◽  
Hermit Crab ◽  
Activity Patterns ◽  
Energetic Cost ◽  
Voluntary Activity ◽  
Good Correspondence ◽  
Cost Of Transport ◽  
Comparable Activity ◽  
The Mean ◽  
Respiratory Gases

A rotating respirometer was designed which enabled respiratory gas exchange in the land hermit crab Coenobita compressus to be correlated with voluntary submaximal sustained pedestrian activity. In the laboratory, crabs remained spontaneously active for up to 150 min, maintaining velocities of 0.6cm s−1. Comparable activity patterns were observed in the field. Quiescent O2 uptake (MOO2) increased logarithmically as a function of load rating of the adopted molluscan shell. Steady-state MOO2 and MCOCO2 were measured after 30 min of spontaneous activity and both increased linearly with velocity. There was good correspondence between Y-intercept values and those measured in inactive crabs. At the mean locomotory speed, MOO2 and MCOCO2 were increased 3.4-fold and 2.6-fold respectively above settled rates. Minimum and gross energetic cost of transport were estimated and compared with values in the literature. MOO2 and MCOCO2 returned to settled levels within the first hour of recovery. The activity profile and concomitant changes in gas exchange are discussed in the context of acquisition of the shell-dwelling habit.

scholarly journals Energetic cost of locomotion as a function of ambient temperature and during growth in the marsupial Potorous tridactylus.

1993 ◽  
Vol 174 (1) ◽  
pp. 81-95
Author(s):  
R V Baudinette ◽  
E A Halpern ◽  
D S Hinds
Keyword(s):  
Oxygen Consumption ◽  
Ambient Temperature ◽  
Multiple Regression ◽  
Stride Length ◽  
Energy Use ◽  
Linear Increase ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
Cost Of Locomotion

In the marsupial, the potoroo, multiple regression analysis shows that ambient temperature makes a minor (2%) contribution towards variation in oxygen consumption with speed. This suggests that the heat generated during running is substituted for heat which would otherwise have to be generated for temperature regulation. Maximum levels of oxygen consumption are also temperature-independent over the range 5-25 degrees C, but plasma lactate concentrations at the conclusion of exercise significantly increase with ambient temperature. Adult potoroos show a linear increase in oxygen consumption with speed, and multiple regression indicates that the most significant factor affecting energy use during running is stride length. Juvenile potoroos have an incremental cost of locomotion about 40% lower than that predicted on the basis of body mass. The smaller animals meet the demands of increasing speed by increasing stride length rather than stride frequency, as would be expected in a smaller species. Our results show that juvenile potoroos diverge significantly from models based only on adult animals in incremental changes in stride frequency, length and the cost of transport, suggesting that they are not simply scaled-down adults.

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