scholarly journals Virtual Energy Management for Physical Energy Savings in a Legged Robot Hopping on Granular Media

2021 ◽  
Vol 8 ◽  
Author(s):  
Sonia F. Roberts ◽  
Daniel E. Koditschek
Keyword(s):  
Granular Media ◽  
Energy Savings ◽  
Single Step ◽  
Active Damping ◽  
Energetic Cost ◽  
Direct Drive ◽  
Cost Of Transport ◽  
Physical Experiments ◽  
Physical Energy ◽  
Damping Controller

We discuss an active damping controller to reduce the energetic cost of a single step or jump of dynamic locomotion without changing the morphology of the robot. The active damping controller adds virtual damping to a virtual leg spring created by direct-drive motors through the robot’s leg linkage. The virtual damping added is proportional to the intrusion velocity of the robot’s foot, slowing the foot’s intrusion, and thus the rate at which energy is transferred to and dissipated by the ground. In this work, we use a combination of simulations and physical experiments in a controlled granular media bed with a single-leg robot to show that the active damping controller reduces the cost of transport compared with a naive compression-extension controller under various conditions.

scholarly journals Unsteady propulsion by an intermittent swimming gait

2017 ◽  
Vol 834 ◽  
pp. 149-172 ◽  
Author(s):  
Emre Akoz ◽  
Keith W. Moored
Keyword(s):  
Scaling Laws ◽  
Energy Savings ◽  
Leading Edge ◽  
Added Mass ◽  
Energetic Cost ◽  
Scaling Relations ◽  
Power Scaling ◽  
Cost Of Transport ◽  
The Mean ◽  
Jet Structure

Inviscid computational results are presented on a self-propelled swimmer modelled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (Proc. R. Soc. Lond. B, vol. 179, 1971, pp. 125–138) originally proposed that this burst-and-coast behaviour can save fish energy during swimming by taking advantage of the viscous Bone–Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added-mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, $DC$, of locomotion. This mechanism can save intermittent swimmers as much as 60 % of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, $Li$, and switch to an energetic cost above continuous swimming for sufficiently low $DC$. Intermittent swimmers are observed to shed four vortices per cycle that give rise to an asymmetric time-averaged jet structure with both momentum surplus and deficit branches. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3 % and 18 % of their full-scale values by using these relations.

scholarly journals Nucleation barriers at corners for a cubic-to-tetragonal phase transformation

2015 ◽  
Vol 145 (4) ◽  
pp. 715-724 ◽  
Author(s):  
Peter Bella ◽  
Michael Goldman
Keyword(s):  
Phase Transformation ◽  
Tetragonal Phase ◽  
Scaling Law ◽  
Energetic Cost ◽  
Minimal Energy ◽  
Physical Experiments ◽  
Domain With A Corner ◽  
Appl Math ◽  
Good Agreement

We are interested in the energetic cost of a martensitic inclusion of volume V in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of Knüpfer, Kohn and Otto (Commun. Pure Appl. Math.66 (2013), 867–904), we consider a domain with a corner and obtain a better scaling law for the minimal energy (Emin ∼ min(V2/3, V7/9)). Our predictions are in good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

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

2021 ◽  
Vol 17 (11) ◽  
pp. e1009608
Author(s):  
Ryan T. Schroeder ◽  
Arthur D. Kuo
Keyword(s):  
Elastic Energy ◽  
Energy Cost ◽  
Energy Savings ◽  
Mechanical Energy ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Mass Model ◽  
Human 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.

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 Evidence for energy savings from aerial running in the Svalbard rock ptarmigan ( Lagopus muta hyperborea )

2011 ◽  
Vol 278 (1718) ◽  
pp. 2654-2661 ◽  
Author(s):  
R. L. Nudds ◽  
L. P. Folkow ◽  
J. J. Lees ◽  
P. G. Tickle ◽  
K.-A. Stokkan ◽  
...  
Keyword(s):  
Energy Expenditure ◽  
Energy Savings ◽  
Metabolic Energy ◽  
Current Evidence ◽  
Cost Of Transport ◽  
Walking Gait ◽  
High Speeds ◽  
Lagopus Muta ◽  
Metabolic Energy Expenditure ◽  
First Time

Svalbard rock ptarmigans were walked and run upon a treadmill and their energy expenditure measured using respirometry. The ptarmigan used three different gaits: a walking gait at slow speeds (less than or equal to 0.75 m s −1 ), grounded running at intermediate speeds (0.75 m s −1 < U < 1.67 m s −1 ) and aerial running at high speeds (greater than or equal to 1.67 m s −1 ). Changes of gait were associated with reductions in the gross cost of transport (COT; J kg −1 m −1 ), providing the first evidence for energy savings with gait change in a small crouched-postured vertebrate. In addition, for the first time (excluding humans) a decrease in absolute metabolic energy expenditure (rate of O 2 consumption) in aerial running when compared with grounded running was identified. The COT versus U curve varies between species and the COT was cheaper during aerial running than grounded running, posing the question of why grounded running should be used at all. Existing explanations (e.g. stability during running over rocky terrain) amount to just so stories with no current evidence to support them. It may be that grounded running is just an artefact of treadmill studies. Research investigating the speeds used by animals in the field is sorely needed.

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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