Effect of gait parameters on energetic cost

Last updated October 05, 2023

The effect of gait parameters on energetic cost is a relationship that describes how changes in step length, cadence, step width, and step variability influence the mechanical work and metabolic cost involved in gait. The source of this relationship stems from the deviation of these gait parameters from metabolically optimal values, with the deviations due to environmental, pathological, and other factors.

Cost of transport [COT]

In human gait, to travel a particular distance, chemical energy must be expended by the body. This relationship can be expressed by the dimensionless term, cost of transport (COT).,^[1] that describes the amount of metabolic energy needed to move a body a unit of distance. Healthy humans walking at self-selected speeds have a cost of transport of approximately 0.8 calorie/meter/kilogram.^[2] Depending on speed, stability conditions, and other internal and external factors,^[3]^[4]^[5] the cost of transport for gait can change. These measured metabolic changes are attributed to variations in step length, step width, and other parameters of gait, which have a direct bearing on COT^[6]^[7]

Preferred Gait

Metabolic cost is naturally optimized by selection of a nominal gait. While external factors such as instability and perceived dangers may temporarily alter the body's priorities,^[3] the primary goal of minimizing a task-dependent energetic expenditure^[8] ultimately dominates the determination of preferred walking gait. As a result, humans tend to select a preferred walking speed that minimizes their cost of transport. The relationship between walking and cost of transport is parabola-like with the preferred walking speed at the minimum, meaning walking at a slower or faster speed can incur a similar increase in energetic cost for a 1-kilometer walk.^[1] Within each walking speed, the step length and cadence are also optimized for metabolic cost. While multiple proportional combinations of step length and cadence can be used to achieve the same walking speed, taking faster and shorter steps or slower and longer steps than the optimal combination leads to increased cost of transport.^[9]

Gait Parameter Definitions

The parameters of gait for a fixed walking speed all vary with the size (e.g. leg length) of different individuals. However, a typical or average self-selected value can be estimated based on average human size. The mechanical work and metabolic cost associated with these parameters can be described by the dynamic walking model.

Step Length

Step length is a measure of the distance, parallel to the direction of travel, between the initial point of contact of one foot and the successive initial point of contact of the opposite foot. The step lengths for left and right are similar in normal gait. Another metric similar to step length is known as stride length, which measures the distance between successive points of initial contact of the same foot, and left and right stride lengths are normally equivalent. At self-selected walking speeds, normal step length is approximately 0.75 meters for men and slightly less for women due to a gender-specific shorter average leg length.^[1]^[9]^[10] For other walking speeds, the preferred step length can be approximately predicted based on the relationship $\textstyle s\;\alpha \;v^{0.42}$ , where $\textstyle s$ is step length and $\textstyle v$ is walking speed.^[11]

Cadence

Cadence is a metric of walking rate, typically measured in number of steps per minute. This parameter is also termed as step frequency. At self-selected walking speeds, the step frequency is approximately 100 steps/min.^[2]^[12]

Step Width

Step width is a measure of the distance, perpendicular to the each foot midline, between the initial point of contact of one foot and the successive initial point of contact of the opposite foot. At self-selected walking speeds, step width is typically around 10 to 12 cm. This is based on the relationship that equates step width to $\textstyle 0.12L$ , where $\textstyle L$ is leg length.^[13]

Step Variability

Step variability is a measure of the standard deviation of step length and step width calculated from all valid steps during a single walking trial. At self-selected walking speeds, step width variability (~2.8 cm) is almost always greater than step length variability (~1.8 cm)^[7]^[14]

Dynamic Walking as a Framework for COT

In dynamic walking, the human body can be modeled as the center of mass (COM) supported by a massless rigid leg in single support and two massless legs during double-support,^[15] which is consistent with passive dynamics of the inverted pendulum, otherwise known as the inverted pendulum theory of gait. In single support, no work is done since the ground reaction force is perpendicular to the COM motion. In double support, the trailing leg works in conjunction with the leading leg to redirect the COM motion upward. During this step-to-step transition period, the trailing leg exerts positive mechanical work on the COM while the leading leg exerts negative mechanical work on the COM. To maintain steady walking gait requires the sum of these work terms, or the net work, to be equal to zero since any changes in system energy would impart different COM velocities between the start and end of transition. While the ideal net mechanical work of this system is zero, muscle contractions are necessary to generate the ground reaction forces, implying that the metabolic energy expended is nonzero.

Leg Swing Mechanics

The massless leg assumption in the inverted pendulum theory omits the amount of work required to swing the contralateral leg during single support. Due to the similarity of leg swing with the hanging pendulum paradigm, the work performed is dominated by gravity.^[16] In the case that the leg is swung at a rate outside of the natural frequency, the hip torque generated by muscle action becomes significantly larger. For typical steady gait, it is approximated that the energy expended to perform leg swing accounts for 10% to 30% of the total metabolic energy consumed.^[17]^[18]

Gait Parameters and Energetic Cost

Changes to each individual gait parameter affects the energetic cost of walking. However, these same changes also affect other gait parameters, leading to trade offs that require the human body to apply optimizations that minimize energetic cost.

Step Length

Energetic cost increases with longer step lengths due to increased ground reaction forces during double-support and more hip torque during the swing phase. According to the dynamic walking model, mechanical work in the step-to-step transitions increases proportional to step length and can be described by $\textstyle {\dot {W}}\;\alpha \;l^{4}$ , where $\textstyle {\dot {W}}$ is mechanical work rate and $\textstyle l$ is step length, which equates to a proportional increase in net metabolic rate.^[19] This relationship is due to reduced vertical force contribution for redirecting the COM at the wider step angles associated with longer step lengths. Larger step lengths also require additional hip torque during the swing phase to travel a wider angle, which contributes to the rate of metabolic cost by a factor of leg length squared^[15]

Cadence

Increase in cadence yields more instances of leg swings and step-to-step transitions within a unit of time, leading to an increase in the rate of energetic cost. The relationship between mechanical work and step frequency can be described by $\textstyle {\dot {W}}\;\alpha \;f^{3}$ for the step-to-step transitions, where $\textstyle {\dot {W}}$ is the mechanical work rate and $\textstyle f$ is the step frequency.^[19] Rate of metabolic cost also follows this relationship. The impact of cadence on leg swing metabolic cost is approximated as $\textstyle {\dot {E}}\;\alpha \;f^{4}$ , where $\textstyle {\dot {E}}$ is the rate of metabolic cost and $\textstyle f$ is the step frequency^[17]

Step Width

Similar to selection of stride length and frequency, humans also select for a metabolically optimal step width.^[6] Adopting a wider stance increases the stability of a passive dynamic system, as well as increases the lateral clearance of the swing leg from the stance leg.^[20] According to the dynamic walking model, the mediolateral "rocking" of the legs can be also described by the inverted pendulum paradigm, and a wider stance would similarly require increased ground reaction force to redirect the COM, and thus increase the metabolic demand. For a narrower stance, due to insufficient clearance, hip torque may be increased to project the swing leg out laterally, leading to increased metabolic cost as well.^[6] The relationship between step width and energetic cost for the step-to-step transitions can be described as $\textstyle {\dot {E}}\;\alpha \;{\dot {W}}\;\alpha \;w^{2}$ , where $\textstyle {\dot {E}}$ is the rate of metabolic cost, $\textstyle {\dot {W}}$ is the mechanical work rate, and $\textstyle w$ is the step width.

Step Variability

Step width variability is associated with the active control of the nervous system for walking stability, and is reduced in the presence of external stabilizers^[4]^[21] while increased with exposure to balance perturbations.^[7] Step length variability is similarly attributed due to a coupling that exists between medio-lateral and fore-aft motion in walking, but to a diminished degree.^[13] Step width variability is positively correlated with rate of metabolic cost, and with respect to the variability associated with mediolateral balance, accounts for about 6% of metabolic cost in preferred gait.^[13] While some of the energetic cost encountered with step variability may arise due to the net changes in step width and step length, there exists a portion of the cost that can be attributed to the effort of stability control during walking.

Constrained Optimization

Since multiple distinct gait parameters have a significant impact on the energetic cost of walking, each of these parameters have to be considered when examining the primary goal of metabolic cost optimization. The visualization of such an optimization for walking speed, cadence, and step length can be expressed in the form of a contour map, in which parameter combinations that lie on the same contour line share the same cost of transport (cal/kg/m).^[2]^[22] The green, red, and blue, dotted lines represent values where cadence, walking speed, and step length are constrained, respectively. These lines can be formed by finding the tangent points that lines representative of several constant parameter values form with the constant COT contours. For example, the optimal COT's for constrained walking speeds (red) can be found by drawing vertical lines and noting where they form a tangent with a contour, as seen with point B in the diagram. A series of these intersections can then form the curve for optimal COT under constrained walking speed. These constrained optimization values not only reflect the naturally selected preferred gait parameters that are observed by fixing a single parameter at different values, but also form part of a predictive map that allows for the identification of the cost of transport for a multivariate system.

Related Research Articles

Walking is one of the main gaits of terrestrial locomotion among legged animals. Walking is typically slower than running and other gaits. Walking is defined by an 'inverted pendulum' gait in which the body vaults over the stiff limb or limbs with each step. This applies regardless of the usable number of limbs—even arthropods, with six, eight, or more limbs, walk. In humans, walking has health benefits including improved mental health and reduced risk of cardiovascular disease and death.

Gait is the pattern of movement of the limbs of animals, including humans, during locomotion over a solid substrate. Most animals use a variety of gaits, selecting gait based on speed, terrain, the need to maneuver, and energetic efficiency. Different animal species may use different gaits due to differences in anatomy that prevent use of certain gaits, or simply due to evolved innate preferences as a result of habitat differences. While various gaits are given specific names, the complexity of biological systems and interacting with the environment make these distinctions "fuzzy" at best. Gaits are typically classified according to footfall patterns, but recent studies often prefer definitions based on mechanics. The term typically does not refer to limb-based propulsion through fluid mediums such as water or air, but rather to propulsion across a solid substrate by generating reactive forces against it.

A gait is a manner of limb movements made during locomotion. Human gaits are the various ways in which humans can move, either naturally or as a result of specialized training. Human gait is defined as bipedal forward propulsion of the center of gravity of the human body, in which there are sinuous movements of different segments of the body with little energy spent. Varied gaits are characterized by differences such as limb movement patterns, overall velocity, forces, kinetic and potential energy cycles, and changes in contact with the ground.

Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in On Growth and Form and by Julian Huxley in 1932.

Locomotor effects of shoes are the way in which the physical characteristics or components of shoes influence the locomotion neuromechanics of a person. Depending on the characteristics of the shoes, the effects are various, ranging from alteration in balance and posture, muscle activity of different muscles as measured by electromyography (EMG), and the impact force. There are many different types of shoes that exist, such as running, walking, loafers, high heels, sandals, slippers, work boots, dress shoes, and many more. However, a typical shoe will be composed of an insole, midsole, outsole, and heels, if any. In an unshod condition, where one is without any shoes, the locomotor effects are primarily observed in the heel strike patterns and resulting impact forces generated on the ground.

Parkinsonian gait is the type of gait exhibited by patients with Parkinson's disease (PD). It is often described by people with Parkinson's as feeling like being stuck in place, when initiating a step or turning, and can increase the risk of falling. This disorder is caused by a deficiency of dopamine in the basal ganglia circuit leading to motor deficits. Gait is one of the most affected motor characteristics of this disorder although symptoms of Parkinson's disease are varied.

Sprinting involves a quick acceleration phase followed by a velocity maintenance phase. During the initial stage of sprinting, the runners have their upper body tilted forward in order to direct ground reaction forces more horizontally. As they reach their maximum velocity, the torso straightens out into an upright position. The goal of sprinting is to reach and maintain high top speeds to cover a set distance in the shortest possible time. A lot of research has been invested in quantifying the biological factors and mathematics that govern sprinting. In order to achieve these high velocities, it has been found that sprinters have to apply a large amount of force onto the ground to achieve the desired acceleration, rather than taking more rapid steps.

Running energetics is the study of the energy cost of running. It is clear in the vast majority of species that as running speed increases the energetic cost of running increases. It also has long been known that between and within species variability exists in the energy cost of running a given speed. This variability has led to the study of biomechanical or physiological factors that may be predictive of the energy cost to run both between and within species.

The preferred walking speed is the speed at which humans or animals choose to walk. Many people tend to walk at about 1.42 metres per second. Individuals find slower or faster speeds uncomfortable.

Human locomotion is considered to take two primary forms: walking and running. In contrast, many quadrupeds have three distinct forms of locomotion: walk, trot, and gallop. Walking is a form of locomotion defined by a double support phase when both feet are on the ground at the same time. Running is a form of locomotion that does not have this double support phase.

Obesity and walking describes how the locomotion of walking differs between an obese individual and a non-obese individual. The prevalence of obesity is a worldwide problem. In 2007–2008, prevalence rates for obesity among adult American men were approximately 32% and over 35% amongst adult American women. According to the Johns Hopkins Bloomberg School of Public Health, 66% of the American population is either overweight or obese and this number is predicted to increase to 75% by 2015. Obesity is linked to health problems such as decreased insulin sensitivity and diabetes, cardiovascular disease, cancer, sleep apnea, and joint pain such as osteoarthritis. It is thought that a major factor of obesity is that obese individuals are in a positive energy balance, meaning that they are consuming more calories than they are expending. Humans expend energy through their basal metabolic rate, the thermic effect of food, non-exercise activity thermogenesis (NEAT), and exercise. While many treatments for obesity are presented to the public, exercise in the form of walking is an easy, relatively safe activity. Walking may initially result in reduced weight, but adopting the habit over the long term may not result in additional weight loss.

Terrestrial locomotion by means of a running gait can be accomplished on level surfaces. However, in most outdoor environments an individual will experience terrain undulations requiring uphill running. Similar conditions can be mimicked in a controlled environment on a treadmill also. Additionally, running on inclines is used by runners, both distance and sprinter, to improve cardiovascular conditioning and lower limb strength.

<span class="mw-page-title-main">Arm swing in human locomotion</span>

Arm swing in human bipedal walking is a natural motion wherein each arm swings with the motion of the opposing leg. Swinging arms in an opposing direction with respect to the lower limb reduces the angular momentum of the body, balancing the rotational motion produced during walking. Although such pendulum-like motion of arms is not essential for walking, recent studies point that arm swing improves the stability and energy efficiency in human locomotion. Those positive effects of arm swing have been utilized in sports, especially in racewalking and sprinting.

Neuromechanics of orthoses refers to how the human body interacts with orthoses. Millions of people in the U.S. suffer from stroke, multiple sclerosis, postpolio, spinal cord injuries, or various other ailments that benefit from the use of orthoses. Insofar as active orthoses and powered exoskeletons are concerned, the technology to build these devices is improving rapidly, but little research has been done on the human side of these human-machine interfaces.

A (bipedal) gait cycle is the time period or sequence of events or movements during locomotion in which one foot contacts the ground to when that same foot again contacts the ground, and involves propulsion of the centre of gravity in the direction of motion. A gait cycle usually involves co-operative movements of both the left and right legs and feet. A single gait cycle is also known as a stride.

Robotic prosthesis control is a method for controlling a prosthesis in such a way that the controlled robotic prosthesis restores a biologically accurate gait to a person with a loss of limb. This is a special branch of control that has an emphasis on the interaction between humans and robotics.

Gait deviations are nominally referred to as any variation of standard human gait, typically manifesting as a coping mechanism in response to an anatomical impairment. Lower-limb amputees are unable to maintain the characteristic walking patterns of an able-bodied individual due to the removal of some portion of the impaired leg. Without the anatomical structure and neuromechanical control of the removed leg segment, amputees must use alternative compensatory strategies to walk efficiently. Prosthetic limbs provide support to the user and more advanced models attempt to mimic the function of the missing anatomy, including biomechanically controlled ankle and knee joints. However, amputees still display quantifiable differences in many measures of ambulation when compared to able-bodied individuals. Several common observations are whole-body movements, slower and wider steps, shorter strides, and increased sway.

Gait variability seen in Parkinson's Disorders arise due to cortical changes induced by pathophysiology of the disease process. Gait rehabilitation is focused to harness the adapted connections involved actively to control these variations during the disease progression. Gait variabilities seen are attributed to the defective inputs from the Basal Ganglia. However, there is altered activation of other cortical areas that support the deficient control to bring about a movement and maintain some functional mobility.

<span class="mw-page-title-main">Charles Richard Taylor</span>

Charles Richard Taylor was an American biologist whose career focused on animal physiology. After conducting work in east Africa, Taylor became the Charles P. Lyman professor of biology at Harvard University and was named first director the University's Concord Field Station. Taylor was elected to the American National Academy of Sciences in 1985.

The study of animal locomotion is a branch of biology that investigates and quantifies how animals move.

References

1 2 3 Ralston, H. J. (1958). Energy-speed relation and optimal speed during level walking. Internationale Zeitschrift für Angewandte Physiologie Einschliesslich Arbeitsphysiologie, 17(4), 277-283.
1 2 3 Zarrugh, M. Y., Todd, F. N., & Ralston, H. J. (1974). Optimization of energy expenditure during level walking. European Journal of Applied Physiology and Occupational Physiology, 33(4), 293-306.
1 2 Voloshina, A. S., Kuo, A. D., Daley, M. A., & Ferris, D. P. (2013). Biomechanics and energetics of walking on uneven terrain. The Journal of Experimental Biology, 216(21), 3963-3970.
1 2 Ijmker, T., Houdijk, H., Lamoth, C. J., Beek, P. J., & van der Woude, L. H. (2013). Energy cost of balance control during walking decreases with external stabilizer stiffness independent of walking speed. Journal of biomechanics,46(13), 2109-2114.
↑ Detrembleur, C., Dierick, F., Stoquart, G., Chantraine, F., & Lejeune, T. (2003). Energy cost, mechanical work, and efficiency of hemiparetic walking. Gait & posture, 18(2), 47-55.
1 2 3 Donelan, J. M., & Kram, R. (2001). Mechanical and metabolic determinants of the preferred step width in human walking. Proceedings of the Royal Society of London. Series B: Biological Sciences, 268(1480), 1985-1992.
1 2 3 .O’Connor, S. M., Xu, H. Z., & Kuo, A. D. (2012). Energetic cost of walking with increased step variability. Gait & posture, 36(1), 102-107.
↑ McNeill Alexander, R. (2002). Energetics and optimization of human walking and running: the 2000 Raymond Pearl memorial lecture. American Journal of Human Biology, 14(5), 641-648.
1 2 Zarrugh, M. Y., & Radcliffe, C. W. (1978). Predicting metabolic cost of level walking. European Journal of Applied Physiology and Occupational Physiology, 38(3), 215-223.
↑ Sekiya, N., Nagasaki, H., Ito, H., & Furuna, T. (1997). Optimal walking in terms of variability in step length. Journal of Orthopaedic & Sports Physical Therapy, 26(5), 266-272.
↑ Grieve, D. W. (1968). Gait patterns and the speed of walking. Biomedical Engineering, 3(3), 119-122.
↑ Cavagna, G. A., & Franzetti, P. (1986). The determinants of the step frequency in walking in humans. The Journal of physiology, 373(1), 235-242.
1 2 3 Bauby, C. E., & Kuo, A. D. (2000). Active control of lateral balance in human walking. Journal of biomechanics, 33(11), 1433-1440.
↑ Owings, T. M., & Grabiner, M. D. (2004). Step width variability, but not step length variability or step time variability, discriminates gait of healthy young and older adults during treadmill locomotion. Journal of biomechanics, 37(6), 935-938.
1 2 Donelan, J. M., Kram, R., & Kuo, A. D. (2002). Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking. Journal of Experimental Biology, 205(23), 3717-3727.
↑ Mochon, S., & McMahon, T. A. (1980). Ballistic walking: An improved model.Mathematical Biosciences, 52(3), 241-260.
1 2 Doke, J., Donelan, J. M., & Kuo, A. D. (2005). Mechanics and energetics of swinging the human leg. The Journal of Experimental Biology, 208(3), 439-445.
↑ Gottschall, J. S., & Kram, R. (2005). Energy cost and muscular activity required for leg swing during walking. Journal of Applied Physiology, 99(1), 23-30.
1 2 Kuo, A. D., Donelan, J. M., & Ruina, A. (2005). Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exercise and sport sciences reviews, 33(2), 88-97.
↑ Kuo, A. D. (1999). Stabilization of lateral motion in passive dynamic walking. The International journal of robotics research, 18(9), 917-930.
↑ Donelan, J. M., Shipman, D. W., Kram, R., & Kuo, A. D. (2004). Mechanical and metabolic requirements for active lateral stabilization in human walking. Journal of biomechanics, 37(6), 827-835.
↑ Bertram, J. E., & Ruina, A. (2001). Multiple walking speed–frequency relations are predicted by constrained optimization. Journal of theoretical Biology, 209(4), 445-453.

External links

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[optimal_speed-1] 1 2 3 Ralston, H. J. (1958). Energy-speed relation and optimal speed during level walking. Internationale Zeitschrift für Angewandte Physiologie Einschliesslich Arbeitsphysiologie, 17(4), 277-283.

[human_COT-2] 1 2 3 Zarrugh, M. Y., Todd, F. N., & Ralston, H. J. (1974). Optimization of energy expenditure during level walking. European Journal of Applied Physiology and Occupational Physiology, 33(4), 293-306.

[uneven_terrain-3] 1 2 Voloshina, A. S., Kuo, A. D., Daley, M. A., & Ferris, D. P. (2013). Biomechanics and energetics of walking on uneven terrain. The Journal of Experimental Biology, 216(21), 3963-3970.

[external_stabilizer-4] 1 2 Ijmker, T., Houdijk, H., Lamoth, C. J., Beek, P. J., & van der Woude, L. H. (2013). Energy cost of balance control during walking decreases with external stabilizer stiffness independent of walking speed. Journal of biomechanics,46(13), 2109-2114.

[hemiparetic_gait-5] Detrembleur, C., Dierick, F., Stoquart, G., Chantraine, F., & Lejeune, T. (2003). Energy cost, mechanical work, and efficiency of hemiparetic walking. Gait & posture, 18(2), 47-55.

[optimal_step_width-6] 1 2 3 Donelan, J. M., & Kram, R. (2001). Mechanical and metabolic determinants of the preferred step width in human walking. Proceedings of the Royal Society of London. Series B: Biological Sciences, 268(1480), 1985-1992.

[step_variability-7] 1 2 3 .O’Connor, S. M., Xu, H. Z., & Kuo, A. D. (2012). Energetic cost of walking with increased step variability. Gait & posture, 36(1), 102-107.

[min_metabolic-8] McNeill Alexander, R. (2002). Energetics and optimization of human walking and running: the 2000 Raymond Pearl memorial lecture. American Journal of Human Biology, 14(5), 641-648.

[optimal_step_length_&_cadence-9] 1 2 Zarrugh, M. Y., & Radcliffe, C. W. (1978). Predicting metabolic cost of level walking. European Journal of Applied Physiology and Occupational Physiology, 38(3), 215-223.

[optimal_step_length_variability-10] Sekiya, N., Nagasaki, H., Ito, H., & Furuna, T. (1997). Optimal walking in terms of variability in step length. Journal of Orthopaedic & Sports Physical Therapy, 26(5), 266-272.

[step_length_and_speed_relation_equation-11] Grieve, D. W. (1968). Gait patterns and the speed of walking. Biomedical Engineering, 3(3), 119-122.

[determinants_of_step_frequency-12] Cavagna, G. A., & Franzetti, P. (1986). The determinants of the step frequency in walking in humans. The Journal of physiology, 373(1), 235-242.

[preferred_step_width-13] 1 2 3 Bauby, C. E., & Kuo, A. D. (2000). Active control of lateral balance in human walking. Journal of biomechanics, 33(11), 1433-1440.

[step_variability_indicates_age-14] Owings, T. M., & Grabiner, M. D. (2004). Step width variability, but not step length variability or step time variability, discriminates gait of healthy young and older adults during treadmill locomotion. Journal of biomechanics, 37(6), 935-938.

[dynamic_walking_2002-15] 1 2 Donelan, J. M., Kram, R., & Kuo, A. D. (2002). Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking. Journal of Experimental Biology, 205(23), 3717-3727.

[ballistic_walking-16] Mochon, S., & McMahon, T. A. (1980). Ballistic walking: An improved model.Mathematical Biosciences, 52(3), 241-260.

[dynamic_walking_leg_swing-17] 1 2 Doke, J., Donelan, J. M., & Kuo, A. D. (2005). Mechanics and energetics of swinging the human leg. The Journal of Experimental Biology, 208(3), 439-445.

[leg_swing_muscle_activity-18] Gottschall, J. S., & Kram, R. (2005). Energy cost and muscular activity required for leg swing during walking. Journal of Applied Physiology, 99(1), 23-30.

[dynamic_walking_2005-19] 1 2 Kuo, A. D., Donelan, J. M., & Ruina, A. (2005). Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exercise and sport sciences reviews, 33(2), 88-97.

[passive_dynamics_walker-20] Kuo, A. D. (1999). Stabilization of lateral motion in passive dynamic walking. The International journal of robotics research, 18(9), 917-930.

[external_stabilizer_II-21] Donelan, J. M., Shipman, D. W., Kram, R., & Kuo, A. D. (2004). Mechanical and metabolic requirements for active lateral stabilization in human walking. Journal of biomechanics, 37(6), 827-835.

[constrained_optimization-22] Bertram, J. E., & Ruina, A. (2001). Multiple walking speed–frequency relations are predicted by constrained optimization. Journal of theoretical Biology, 209(4), 445-453.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]