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.

Optimization of energy and time predicts dynamic speeds for human walking.

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual's movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (N=10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.

A biomechanics dataset of healthy human walking at various speeds, step lengths and step widths.

The biomechanics of human walking are well documented for standard conditions such as for self-selected step length and preferred speed. However, humans can and do walk with a variety of other step lengths and speeds during daily living. The variation of biomechanics across gait conditions may be important for describing and determining the mechanics of locomotion. To address this, we present an open biomechanics dataset of steady walking at a broad range of conditions, including 33 experimentally-controlled combinations of speed (0.7-2.0 m·s-1), step length (0.5-1.1 m), and step width (0-0.4 m). The dataset contains ground reaction forces and motions from healthy young adults (N = 10), collected using split-belt instrumented treadmill and motion capture systems respectively. Most trials also include pre-computed inverse dynamics, including 3D joint positions, angles, torques and powers, as well as intersegmental forces. Apart from raw data, we also provide five strides of good quality data without artifacts for each trial, and sample software for visualization and analysis.

TimTrack: A drift-free algorithm for estimating geometric muscle features from ultrasound images.

Ultrasound imaging is valuable for non-invasively estimating fascicle lengths and other features of pennate muscle, especially when performed computationally. Effective analysis techniques to date typically use optic flow to track displacements from image sequences, but are sensitive to integration drift for longer sequences. We here present an alternative algorithm that objectively estimates geometric features of pennate muscle from ultrasound images, without drift sensitivity. The algorithm identifies aponeuroses and estimates fascicle angles to derive fascicle lengths. Length estimates of human vastus lateralis and gastrocnemius fascicles in healthy subjects (N = 9 and N = 17 respectively) compared well (overall root-mean-square difference, RMSD = 0.52 cm) to manual estimates by independent observers (n = 3), with overall coefficient of multiple correlation (CMC) of 0.98. Our tests yielded accuracy (CMC, RMSD) and processing speed similar to or exceeding that of state-of-the-art algorithms. The algorithm requires minimal manual intervention and can optionally extrapolate fascicle lengths that extend beyond the image frame. It thus facilitates automated analysis of ultrasound images without drift.

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.

The energetic basis for smooth human arm movements.

The central nervous system plans human reaching movements with stereotypically smooth kinematic trajectories and fairly consistent durations. Smoothness seems to be explained by accuracy as a primary movement objective, whereas duration seems to economize energy expenditure. But the current understanding of energy expenditure does not explain smoothness, so that two aspects of the same movement are governed by seemingly incompatible objectives. Here, we show that smoothness is actually economical, because humans expend more metabolic energy for jerkier motions. The proposed mechanism is an underappreciated cost proportional to the rate of muscle force production, for calcium transport to activate muscle. We experimentally tested that energy cost in humans (N = 10) performing bimanual reaches cyclically. The empirical cost was then demonstrated to predict smooth, discrete reaches, previously attributed to accuracy alone. A mechanistic, physiologically measurable, energy cost may therefore explain both smoothness and duration in terms of economy, and help resolve motor redundancy in reaching movements.

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.

Soft tissue deformations explain most of the mechanical work variations of human walking.

Humans perform mechanical work during walking, some by leg joints actuated by muscles, and some by passive, dissipative soft tissues. Dissipative losses must be restored by active muscle work, potentially in amounts sufficient to cost substantial metabolic energy. The most dissipative, and therefore costly, walking conditions might be predictable from the pendulum-like dynamics of the legs. If this behavior is systematic, it may also predict the work distribution between active joints and passive soft tissues. We therefore tested whether the overall negative work of walking, and the fraction owing to soft tissue dissipation, are both predictable by a simple dynamic walking model across a wide range of conditions. The model predicts whole-body negative work from the leading leg's impact with the ground (termed the collision), to increase with the squared product of walking speed and step length. We experimentally tested this in humans (N=9) walking in 26 different combinations of speed (0.7-2.0 m s-1) and step length (0.5-1.1 m), with recorded motions and ground reaction forces. Whole-body negative collision work increased as predicted (R2=0.73), with a consistent fraction of approximately 63% (R2=0.88) owing to soft tissues. Soft tissue dissipation consistently accounted for approximately 56% of the variation in total whole-body negative work, across a wide range of speed and step length combinations. During typical walking, active work to restore dissipative losses could account for 31% of the net metabolic cost. Soft tissue dissipation, not included in most biomechanical studies, explains most of the variation in negative work of walking, and could account for a substantial fraction of the metabolic cost.

An optimality principle for locomotor central pattern generators.

Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands (even in the absence of feedback, termed "fictive locomotion"), and reflex circuits driven by sensory feedback. Each circuit alone serves a clear purpose, and the two together are understood to cooperate during normal locomotion. The difficulty is in explaining their relative balance objectively within a control model, as there are infinite combinations that could produce the same nominal motor pattern. Here we propose that optimization in the presence of uncertainty can explain how the circuits should best be combined for locomotion. The key is to re-interpret the CPG in the context of state estimator-based control: an internal model of the limbs that predicts their state, using sensory feedback to optimally balance competing effects of environmental and sensory uncertainties. We demonstrate use of optimally predicted state to drive a simple model of bipedal, dynamic walking, which thus yields minimal energetic cost of transport and best stability. The internal model may be implemented with neural circuitry compatible with classic CPG models, except with neural parameters determined by optimal estimation principles. Fictive locomotion also emerges, but as a side effect of estimator dynamics rather than an explicit internal rhythm. Uncertainty could be key to shaping CPG behavior and governing optimal use of feedback.

The high energetic cost of rapid force development in muscle.

Muscles consume metabolic energy for active movement, particularly when performing mechanical work or producing force. Less appreciated is the cost for activating muscle quickly, which adds considerably to the overall cost of cyclic force production. However, the cost magnitude relative to the cost of mechanical work, which features in many movements, is unknown. We therefore tested whether fast activation is costly compared with performing work or producing isometric force. We hypothesized that metabolic cost would increase with a proposed measure termed force rate (rate of increase in muscle force) in cyclic tasks, separate from mechanical work or average force level. We tested humans (N=9) producing cyclic knee extension torque against an isometric dynamometer (torque 22 N m, cyclic waveform frequencies 0.5-2.5 Hz), while also quantifying quadriceps muscle force and work against series elasticity (with ultrasonography), along with metabolic rate through respirometry. Net metabolic rate increased by more than four-fold (10.5 to 46.8 W) with waveform frequency. At high frequencies, the hypothesized force-rate cost accounted for nearly half (40%) of energy expenditure. This exceeded the cost for average force (17%) and was comparable to the cost for shortening work (43%). The force-rate cost is explained by additional active calcium transport necessary for producing forces at increasing waveform frequencies, owing to rate-limiting dynamics of force production. The force-rate cost could contribute substantially to the overall cost of movements that require cyclic muscle activation, such as locomotion.

Human walking in the real world: Interactions between terrain type, gait parameters, and energy expenditure.

Humans often traverse real-world environments with a variety of surface irregularities and inconsistencies, which can disrupt steady gait and require additional effort. Such effects have, however, scarcely been demonstrated quantitatively, because few laboratory biomechanical measures apply outdoors. Walking can nevertheless be quantified by other means. In particular, the foot's trajectory in space can be reconstructed from foot-mounted inertial measurement units (IMUs), to yield measures of stride and associated variabilities. But it remains unknown whether such measures are related to metabolic energy expenditure. We therefore quantified the effect of five different outdoor terrains on foot motion (from IMUs) and net metabolic rate (from oxygen consumption) in healthy adults (N = 10; walking at 1.25 m/s). Energy expenditure increased significantly (P < 0.05) in the order Sidewalk, Dirt, Gravel, Grass, and Woodchips, with Woodchips about 27% costlier than Sidewalk. Terrain type also affected measures, particularly stride variability and virtual foot clearance (swing foot's lowest height above consecutive footfalls). In combination, such measures can also roughly predict metabolic cost (adjusted R2 = 0.52, partial least squares regression), and even discriminate between terrain types (10% reclassification error). Body-worn sensors can characterize how uneven terrain affects gait, gait variability, and metabolic cost in the real world.

Anticipatory Control of Momentum for Bipedal Walking on Uneven Terrain.

Humans and other walking bipeds often encounter and compensate for uneven terrain. They might, for example, regulate the body's momentum when stepping on stones to cross a stream. We examined what to do and how far to look, as a simple optimal control problem, where forward momentum is controlled to compensate for a step change in terrain height, and steady gait regained with no loss of time relative to nominal walking. We modeled planar, human-like walking with pendulum-like legs, and found the most economical control to be quite stereotypical. It starts by gaining momentum several footfalls ahead of an upward step, in anticipation of the momentum lost atop that step, and then ends with another speed-up to regain momentum thereafter. A similar pattern can be scaled to a variety of conditions, including both upward or downward steps, yet allow for considerably reduced overall energy and peak power demands, compared to compensation without anticipation. We define a "persistence time" metric from the transient decay response after a disturbance, to describe how momentum is retained between steps, and how far ahead a disturbance should be planned for. Anticipatory control of momentum can help to economically negotiate uneven terrain.

Optimal regulation of bipedal walking speed despite an unexpected bump in the road.

Bipedal locomotion may occur over imperfect surfaces with bumps or other features that disrupt steady gait. An unexpected bump in the road is generally expected to slow down most types of locomotion. On wheels, speed may be regained quite readily with "cruise control" performed in continuous time. But legged locomotion is less straightforward, because the stance leg may be under-actuated, and the continuous-time dynamics are periodically disrupted by discrete ground contact events. Those events may also afford good control opportunities, albeit subject to the delay between discrete opportunities. The regulation of walking speed should ideally use these opportunities to compensate for lost time, and with good economy if possible. However, the appropriate control strategy is unknown. Here we present how to restore speed and make up for time lost going over a bump in the road, through discrete, once-per-step control. We use a simple dynamic walking model to determine the optimal sequence of control actions-pushing off from the leg at the end of each stance phase-for fast response or best economy. A two-step, deadbeat sequence is the fastest possible response, and reasonably economical. Slower responses over more steps are more economical overall, but a bigger difference is that they demand considerably less peak power. A simple, reactive control strategy can thus compensate for an unexpected bump, with explicit trade-offs in time and work. Control of legged locomotion is not as straightforward as with wheels, but discrete control actions also allow for effective and economical reactions to imperfect terrain.

The high cost of swing leg circumduction during human walking.

Humans tend to walk economically, with preferred step width and length corresponding to an energetic optimum. In the case of step width, it is costlier to walk with either wider or narrower steps than normally preferred. Wider steps require more mechanical work to redirect the body's motion laterally with each step, but the cost for narrower steps remains unexplained. Here we show that narrow steps are costly because they require the swing leg to be circumducted around the stance leg. Healthy adults (N=8) were tested walking with varying levels of circumduction, induced through lightweight, physical obstructions ("Fins") attached medially to the lower legs, during treadmill walking at fixed speed (1.25ms-1) and step width. The net rate of metabolic energy expenditure increased approximately with the square of circumduction amplitude, by about 50% for an amplitude (measured at mid-swing) of about 18cm. Subjects also generated greater stance leg torque and more arm motion to counter the circumduction, among other compensatory motions that may contribute to energy expenditure. The costs of producing and countering lateral leg motion partially explains the poorer economy of some gait pathologies where circumduction may occur, for example stiff-knee gait. And for healthy individuals, it explains how the energetically optimal average step width, along with the additional variability inherent with multiple steps, should be narrow enough to avoid excessive redirection of the body, yet wide enough to avoid costly circumduction. Humans appear to prefer a step width that compromises between the competing energetic costs for either wider or narrower steps.

The stabilizing properties of foot yaw in human walking.

Humans perform a variety of feedback adjustments to maintain balance during walking. These include lateral footfall placement, and center of pressure adjustment under the stance foot, to stabilize lateral balance. A less appreciated possibility would be to steer for balance like a bicycle, whose front wheel may be turned toward the direction of a lean to capture the center of mass. Humans could potentially combine steering with other strategies to distribute balance adjustments across multiple degrees of freedom. We tested whether human balance can theoretically benefit from steering, and experimentally tested for evidence of steering for balance. We first developed a simple dynamic walking model, which shows that bipedal walking may indeed be stabilized through steering-externally rotating the foot about vertical toward the direction of lateral lean for each footfall-governed by linear feedback control. Moreover, least effort (mean-square control torque) is required if steering is combined with lateral foot placement. If humans use such control, footfall variability should show a statistical coupling between external rotation with lateral placement. We therefore examined the spontaneous fluctuations of hundreds of strides of normal overground walking in healthy adults (N=26). We found significant coupling (P=9·10-8), of 0.54rad of external rotation per meter of lateral foot deviation. Successive footfalls showed a weaker, negative correlation with each other, similar to how a bicycle׳s steering adjustment made for balance must be followed by gradual corrections to resume the original travel direction. Steering may be one of multiple strategies to stabilize balance during walking.

Determinants of preferred ground clearance during swing phase of human walking.

During each step of human walking, the swing foot passes close to the ground with a small but (usually) non-zero clearance. The foot can occasionally scuff against the ground, with some risk of stumbling or tripping. The risk might be mitigated simply by lifting the foot higher, but presumably at increased effort, of unknown amount. Perhaps the normally preferred ground clearance is a trade-off between competing costs, one for lifting the foot higher and one for scuffing it. We tested this by measuring the metabolic energy cost of lifting and scuffing the foot, treating these apparently dissimilar behaviors as part of a single continuum, where scuffing is a form of negative foot lift. We measured young, healthy adults (N=9) lifting or scuffing the foot by various amounts mid-swing during treadmill walking, and observed substantial costs, each well capable of doubling the net metabolic rate for normal walking (gross cost minus that for standing). In relative terms, the cost for scuffing increased over twice as steeply as that for lifting. That relative difference means that the expected value of cost, which takes into account movement variability, occurs at a non-zero mean clearance, approximately matching the preferred clearance we observed. Energy cost alone is only a lower bound on the overall disadvantages of inadvertent ground contact, but it is sufficient to show how human behavior may be determined not only by the separate costs of different trade-offs but also by movement variability, which can influence the average cost actually experienced in practice.

Mechanical and energetic consequences of reduced ankle plantar-flexion in human walking.

The human ankle produces a large burst of 'push-off' mechanical power late in the stance phase of walking, reduction of which leads to considerably poorer energy economy. It is, however, uncertain whether the energetic penalty results from poorer efficiency when the other leg joints substitute for the ankle's push-off work, or from a higher overall demand for work due to some fundamental feature of push-off. Here, we show that greater metabolic energy expenditure is indeed explained by a greater demand for work. This is predicted by a simple model of walking on pendulum-like legs, because proper push-off reduces collision losses from the leading leg. We tested this by experimentally restricting ankle push-off bilaterally in healthy adults (N=8) walking on a treadmill at 1.4 m s(-1), using ankle-foot orthoses with steel cables limiting motion. These produced up to ∼50% reduction in ankle push-off power and work, resulting in up to ∼50% greater net metabolic power expenditure to walk at the same speed. For each 1 J reduction in ankle work, we observed 0.6 J more dissipative collision work by the other leg, 1.3 J more positive work from the leg joints overall, and 3.94 J more metabolic energy expended. Loss of ankle push-off required more positive work elsewhere to maintain walking speed; this additional work was performed by the knee, apparently at reasonably high efficiency. Ankle push-off may contribute to walking economy by reducing dissipative collision losses and thus overall work demand.

Influence of contextual task constraints on preferred stride parameters and their variabilities during human walking.

Walking is not always a free and unencumbered task. Everyday activities such as walking in pairs, in groups, or on structured walkways can limit the acceptable gait patterns, leading to motor behavior that differs from that observed in more self-selected gait. Such different contexts may lead to gait performance different than observed in typical laboratory experiments, for example, during treadmill walking. We sought to systematically measure the impact of such task constraints by comparing gait parameters and their variability during walking in different conditions over-ground, and on a treadmill. We reconstructed foot motion from foot-mounted inertial sensors, and characterized forward, lateral and angular foot placement while subjects walked over-ground in a straight hallway and on a treadmill. Over-ground walking was performed in three variations: with no constraints (self-selected, SS); while deliberately varying walking speed (self-varied, SV); and while following a toy pace car programmed to vary speed (externally-varied, EV). We expected that these conditions would exhibit a statistically similar relationship between stride length and speed, and between stride length and stride period. We also expected treadmill walking (TM) would differ in two ways: first, that variability in stride length and stride period would conform to a constant-speed constraint opposite in slope from the normal relationship; and second, that stride length would decrease, leading to combinations of stride length and speed not observed in over-ground conditions. Results showed that all over-ground conditions used similar stride length-speed relationships, and that variability in treadmill walking conformed to a constant-speed constraint line, as expected. Decreased stride length was observed in both TM and EV conditions, suggesting adaptations due to heightened awareness or to prepare for unexpected changes or problems. We also evaluated stride variability in constrained and unconstrained tasks. We observed that in treadmill walking, lateral variability decreased while forward variability increased, and the normally-observed correlation between wider foot placement and external foot rotation was eliminated. Preferred stride parameters and their variability appear significantly influenced by the context and constraints of the walking task.

Subjective valuation of cushioning in a human drop landing task as quantified by trade-offs in mechanical work.

Humans can perform motor tasks in a variety of ways, yet often favor a particular strategy. Some factors governing the preferred strategy may be objective and quantifiable, (e.g. metabolic energy or mechanical work) while others may be more subjective and less measurable, (e.g. discomfort, pain, or mental effort). Subjectivity can make it challenging to explain or predict preferred movement strategies. We propose that subjective factors might nevertheless be characterized indirectly by their trade-offs against more objective measures such as work. Here we investigated whether subjective costs that influence human movement during drop landings could be indirectly assessed by quantifying mechanical work performed. When landing on rigid ground, humans typically absorb much of the collision actively by bending their knees, perhaps to avoid the discomfort of stiff-legged landings. We measured how work performed by healthy adults (N=8) changed as a function of surface cushioning for drop landings (fixed at about 0.4m) onto varying amounts of foam. Landing on more foam dissipated more energy passively in the surface, thus reducing the net dissipation required of subjects, due to relatively fixed landing energy. However, subjects actually performed even less work in the dissipative collision, as well as in the subsequent active, positive work to return to upright stance (approximately linear decrease of about 1.52 J per 1 cm of foam thickness). As foam thickness increased, there was also a corresponding reduction in center-of-mass vertical displacement after initial impact by up to 43%. Humans appear to subjectively value cushioning, revealed by the extra work they perform landing without it. Cushioning is thus worth more than the energy it dissipates, in an amount that indicates the subjective discomfort of stiff landings.

The cost of leg forces in bipedal locomotion: a simple optimization study.

Simple optimization models show that bipedal locomotion may largely be governed by the mechanical work performed by the legs, minimization of which can automatically discover walking and running gaits. Work minimization can reproduce broad aspects of human ground reaction forces, such as a double-peaked profile for walking and a single peak for running, but the predicted peaks are unrealistically high and impulsive compared to the much smoother forces produced by humans. The smoothness might be explained better by a cost for the force rather than work produced by the legs, but it is unclear what features of force might be most relevant. We therefore tested a generalized force cost that can penalize force amplitude or its n-th time derivative, raised to the p-th power (or p-norm), across a variety of combinations for n and p. A simple model shows that this generalized force cost only produces smoother, human-like forces if it penalizes the rate rather than amplitude of force production, and only in combination with a work cost. Such a combined objective reproduces the characteristic profiles of human walking (R² = 0.96) and running (R² = 0.92), more so than minimization of either work or force amplitude alone (R² = -0.79 and R² = 0.22, respectively, for walking). Humans might find it preferable to avoid rapid force production, which may be mechanically and physiologically costly.