A unified energy-optimality criterion predicts human navigation paths and speeds

Curvilinear walking elevates fall risk and modulates slip and compensatory step attributes after unconstrained human slips

While much attention has been paid to understanding slip-related falls in humans, little has been focused on curvilinear paths despite their prevalence, distinct biomechanical demands and increased slipping threat. We determined the mechanics, compensatory stepping reactions and fall risk associated with slips during fixed-speed walking across ranges of path curvature, slipped foot and slip onset phase contexts possible in the community, which builds upon previous work by examining speed-independent effects of curvilinear walking. Twenty-one participants experienced 15 unconstrained slips induced by a wearable friction-reducing device as motion capture and harness load cell data were recorded. Falls were most likely after early stance slips to the inside foot and increased at tighter curvatures. Slip distance and peak velocity decreased as slips began later in stance phase, did not differ between feet, and accelerated on tighter paths. Slipping foot directions relative to heading transitioned from anterior (forward) to posterior (backward) as slips began later in stance, were ipsilateral (toward the slipping foot side) and contralateral (toward the opposite side) for the outside and inside foot, respectively, and became increasingly ipsilateral/contralateral on tighter curvatures. Compensatory steps were placed anteriorly and ipsilaterally after outside and inside foot slips, respectively, and lengthened at later onset phases for outside foot slips only. Our findings illustrate slip magnitude and fall risk relationships that suggest slip direction may influence the balance threat posed by a slip, imply that walking speed may modify slip likelihood, and indicate the most destabilizing curved walking contexts to target in future perturbation-based balance training approaches.

Human foot form and function: variable and versatile, yet sufficiently related to predict function from form

The human foot is a complex structure that plays an important role in our capacity for upright locomotion. Comparisons of our feet with those of our closest extinct and extant relatives have linked shape features (e.g. the longitudinal and transverse arches, heel size and toe length) to specific mechanical functions. However, foot shape varies widely across the human population, so it remains unclear if and how specific shape variants are related to locomotor mechanics. Here we constructed a statistical shape-function model (SFM) from 100 healthy participants to directly explore the relationship between the shape and function of our feet. We also examined if we could predict the joint motion and moments occurring within a person's foot during locomotion based purely on shape features. The SFM revealed that the longitudinal and transverse arches, relative foot proportions and toe shape along with their associated joint mechanics were most variable. However, each of these only accounted for small proportions of the overall variation in shape, deformation and joint mechanics, most likely owing to the high structural complexity of the foot. Nevertheless, a leave-one-out analysis showed that the SFM can accurately predict joint mechanics of a novel foot, based on its shape and deformation.

Walking speeds are lower for short distance and turning locomotion: Experiments and modeling in low-cost prosthesis users

Preferred walking speed is a widely-used performance measure for people with mobility issues, but is usually measured in straight line walking for fixed distances or durations, and without explicitly accounting for turning. However, daily walking involves walking for bouts of different distances and walking with turning, with prior studies showing that short bouts with at most 10 steps could be 40% of all bouts and turning steps could be 8-50% of all steps. Here, we studied walking in a straight line for short distances (4 m to 23 m) and walking in circles (1 m to 3 m turning radii) in people with transtibial amputation or transfemoral amputation using a passive ankle-foot prosthesis (Jaipur Foot). We found that the study participants' preferred walking speeds are lower for shorter straight-line walking distances and lower for circles of smaller radii, which is analogous to earlier results in subjects without amputation. Using inverse optimization, we estimated the cost of changing speeds and turning such that the observed preferred walking speeds in our experiments minimizes the total cost of walking. The inferred costs of changing speeds and turning were larger for subjects with amputation compared to subjects without amputation in a previous study, specifically, being 4x to 8x larger for the turning cost and being highest for subjects with transfemoral amputation. Such high costs inferred by inverse optimization could potentially include non-energetic costs such as due to joint or interfacial stress or stability concerns, as inverse optimization cannot distinguish such terms from true metabolic cost. These experimental findings and models capturing the experimental trends could inform prosthesis design and rehabilitation therapy to better assist changing speeds and turning tasks. Further, measuring the preferred speed for a range of distances and radii could be a more comprehensive subject-specific measure of walking performance than commonly used straight line walking metrics.

Metabolic cost for isometric force scales nonlinearly and predicts how humans distribute forces across limbs

Muscles consume metabolic energy for force production and movement. A mathematical model of metabolic energy cost will be useful in predicting instantaneous costs during human exercise and in computing effort-minimizing movements via simulations. Previous in vivo data-derived models usually assumed either zero or linearly increasing cost with force, but a nonlinear relation could have significant metabolic or behavioural implications. Here, we show that metabolic cost scales nonlinearly with joint torque with an exponent of about 1.64, using calorimetric measurements of isometric squats. We then demonstrate that this metabolic nonlinearity is reflected in human behaviour: minimizing this nonlinear cost predicts how humans share forces between limbs in additional experiments involving arms and legs. This shows the utility of the nonlinear energy cost in predictive models and its generalizability across limbs. Finally, we show mathematical evidence that the same nonlinear metabolic objective may underlie force sharing at the muscle level.

Higher coactivations of lower limb muscles increase stability during walking on slippery ground in forward dynamics musculoskeletal simulation

The energy efficiency theory of human bipedal locomotion has been widely accepted as a neuro-musculoskeletal control method. However, coactivation of agonist and antagonist muscles in the lower limb has been observed during various limb movements, including walking. The emergence of this coactivation cannot be explained solely by the energy efficiency theory and remains a subject of debate. To shed light on this, we investigated the role of muscle coactivations in walking stability using a forward dynamics musculoskeletal simulation combined with neural-network-based gait controllers. Our study revealed that a gait controller with minimal muscle activations had a high probability of falls under challenging gait conditions such as slippery ground and uneven terrain. Lower limb muscle coactivations emerged in the process of gait controller training on slippery ground. Controllers with physiological coactivation levels demonstrated a significantly reduced probability of falls. Our results suggest that achieving stable walking requires muscle coactivations beyond the minimal level of muscle energy. This study implies that coactivations likely emerge to maintain gait stability under challenging conditions, and both coactivation and energy optimization of lower limb muscles should be considered when exploring the foundational control mechanisms of human walking.

Generalizing stepping concepts to non-straight walking

People rarely walk in straight lines. Instead, we make frequent turns or other maneuvers. Spatiotemporal parameters fundamentally characterize gait. For straight walking, these parameters are well-defined for the task of walking on a straight path. Generalizing these concepts to non-straight walking, however, is not straightforward. People follow non-straight paths imposed by their environment (sidewalk, windy hiking trail, etc.) or choose readily-predictable, stereotypical paths of their own. People actively maintain lateral position to stay on their path and readily adapt their stepping when their path changes. We therefore propose a conceptually coherent convention that defines step lengths and widths relative to predefined walking paths. Our convention simply re-aligns lab-based coordinates to be tangent to a walker's path at the mid-point between the two footsteps that define each step. We hypothesized this would yield results both more correct and more consistent with notions from straight walking. We defined several common non-straight walking tasks: single turns, lateral lane changes, walking on circular paths, and walking on arbitrary curvilinear paths. For each, we simulated idealized step sequences denoting "perfect" performance with known constant step lengths and widths. We compared results to path-independent alternatives. For each, we directly quantified accuracy relative to known true values. Results strongly confirmed our hypothesis. Our convention returned vastly smaller errors and introduced no artificial stepping asymmetries across all tasks. All results for our convention rationally generalized concepts from straight walking. Taking walking paths explicitly into account as important task goals themselves thus resolves conceptual ambiguities of prior approaches.

Pitfall or pratfall? Behavioral differences in infant learning from falling

Researchers routinely infer learning and other unobservable psychological functions based on observable behavior. But what behavioral changes constitute evidence of learning? The standard approach is to infer learning based on a single behavior across individuals, including assumptions about the direction and magnitude of change (e.g., everyone should avoid falling repeatedly on a treacherous obstacle). Here we illustrate the benefits of an alternative "multiexpression, relativist, agnostic, individualized" approach. We assessed infant learning from falling based on multiple behaviors relative to each individual's baseline, agnostic about the direction and magnitude of behavioral change. We tested infants longitudinally (10.5-15 months of age) over the transition from crawling to walking. At each session, infants were repeatedly encouraged to crawl or walk over a fall-inducing foam pit interspersed with no-fall baseline trials on a rigid platform. Our approach revealed two learning profiles. Like adults in previous work, "pit-avoid" infants consistently avoided falling. In contrast, "pit-go" infants fell repeatedly across trials and sessions. However, individualized comparisons to baseline across multiple locomotor, exploratory, and social-emotional behaviors showed that pit-go infants also learned at every session. But they treated falling as an unimpactful "pratfall" rather than an aversive "pitfall." Pit-avoid infants displayed enhanced learning across sessions and partial transfer of learning from crawling to walking, whereas pit-go infants displayed neither. Thus, reliance on a predetermined, "one-size-fits-all" behavioral expression of a psychological function can obscure different behavioral profiles and lead to erroneous inferences. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Generalizing Stepping Concepts To Non-Straight Walking

People rarely walk in straight lines. Instead, we make frequent turns or other maneuvers. Spatiotemporal parameters fundamentally characterize gait. For straight walking, these parameters are well-defined for that task of walking on a straight path. Generalizing these concepts to non-straight walking, however, is not straightforward. People also follow non-straight paths imposed by their environment (store aisle, sidewalk, etc.) or choose readily-predictable, stereotypical paths of their own. People actively maintain lateral position to stay on their path and readily adapt their stepping when their path changes. We therefore propose a conceptually coherent convention that defines step lengths and widths relative to known walking paths. Our convention simply re-aligns lab-based coordinates to be tangent to a walker's path at the mid-point between the two footsteps that define each step. We hypothesized this would yield results both more correct and more consistent with notions from straight walking. We defined several common non-straight walking tasks: single turns, lateral lane changes, walking on circular paths, and walking on arbitrary curvilinear paths. For each, we simulated idealized step sequences denoting "perfect" performance with known constant step lengths and widths. We compared results to path- independent alternatives. For each, we directly quantified accuracy relative to known true values. Results strongly confirmed our hypothesis. Our convention returned vastly smaller errors and introduced no artificial stepping asymmetries across all tasks. All results for our convention rationally generalized concepts from straight walking. Taking walking paths explicitly into account as important task goals themselves thus resolves conceptual ambiguities of prior approaches.

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.

Slipping mechanics during walking along curved paths depend on the biomechanical context at slip onset

Curvilinear walking is common, causing limb- and radius-dependent asymmetries that distinguish it from straight walking and elevated friction demands that increase slip-and-fall risk. However, it is unclear how aspects of curvilinear walking influence the slip perturbations experienced. We cross-sectionally examined how three biomechanical slip contexts (slip onset phase, slipped foot relative to the path, path radius) influence slip direction, distance, and peak velocity. Eighteen young adults experienced unconstrained inside or outside foot slips during early, mid-, or late stance while following 1.0- or 2.0-m radius semicircular paths. We derived slip mechanics from motion-capture data and assessed their dependence on slip context using mixed-effects models. As slip onset phase progressed, slip directions exhibited an anterior-to-posterior transition, shortened mediolaterally, and accelerated anteroposteriorly. The slipped foot modified the direction transition, with inside and outside foot slips moving contralaterally and ipsilaterally, respectively. Inside foot slips were shorter and slower mediolaterally and longer anteroposteriorly than outside foot slips. Increasing path radius caused slips with greater mediolateral direction components. We show a range of context-dependent slips are possible, likely due to instantaneous magnitudes and orientations of shear ground reaction forces. Our results contribute to a comprehensive understanding of walking slips, which fall prevention methods can leverage.

Personalizing exoskeleton assistance while walking in the real world

Personalized exoskeleton assistance provides users with the largest improvements in walking speed1 and energy economy2-4 but requires lengthy tests under unnatural laboratory conditions. Here we show that exoskeleton optimization can be performed rapidly and under real-world conditions. We designed a portable ankle exoskeleton based on insights from tests with a versatile laboratory testbed. We developed a data-driven method for optimizing exoskeleton assistance outdoors using wearable sensors and found that it was equally effective as laboratory methods, but identified optimal parameters four times faster. We performed real-world optimization using data collected during many short bouts of walking at varying speeds. Assistance optimized during one hour of naturalistic walking in a public setting increased self-selected speed by 9 ± 4% and reduced the energy used to travel a given distance by 17 ± 5% compared with normal shoes. This assistance reduced metabolic energy consumption by 23 ± 8% when participants walked on a treadmill at a standard speed of 1.5 m s-1. Human movements encode information that can be used to personalize assistive devices and enhance performance.

The split-belt rimless wheel

Split-belt treadmill walking, in which the two belts move at different speeds, reveals a mechanism through which energy can be extracted from the environment. When a person walks with positive step length asymmetry on a split-belt treadmill, the treadmill can perform net positive work on the person. Here we use a split-belt rimless wheel model to explore how people could take advantage of the treadmill. We show that a split-belt rimless wheel can passively walk steadily by capturing energy from the treadmill to overcome collision losses, whereas it loses energy on each step with no way to recover the losses when walking on tied belts. Our simulated split-belt rimless wheel can walk steadily for a variety of leg angle and belt speed combinations, tolerating both speed disturbances and ground height variability. The wheel can even capture enough energy to walk uphill. We also built a physical split-belt rimless wheel robot and demonstrated that it can walk continuously without additional energy input. In comparing the wheel solutions to human split-belt gait, we found that humans do not maximize positive work performed by the treadmill. Other aspects of walking, such as costs associated with swing, balance, and free vertical moments, likely limit people’s ability to benefit from the treadmill. This study uses a simple walking model to characterize the mechanics and energetics of split-belt walking, demonstrating that energy capture through intermittent contact with two belts is possible and providing a simple model framework for understanding human adaptation during split-belt walking.

Frontal plane balance during pre-planned and late-cued 90 degree turns while walking

This study evaluated frontal-plane dynamic balance control during 90° left turns while walking. Ten healthy young adults performed straight-line gait, pre-planned turns, and turns cued visually (late-cued turns). We quantified rotational balance control via the range of frontal-plane angular momentum (Hf) about the center of mass (COM), and the relative positioning of the COM and the feet using the horizontal distance from the COM to the lateral edge of the base of support (lateral distance) and the mediolateral margin of stability (MOSml). We hypothesized that the Hf range would increase and the lateral distance and MOSml minima would decrease during each turn type vs. straight-line gait and during late-cued vs. pre-planned turns. We found that the range of Hf was significantly greater during each turn type vs. straight-line gait and during late-cued vs. pre-planned turns. Also, the lateral distance minima were significantly smaller during turns vs. straight-line gait, and during pre-planned vs. late-cued turns. Our hypotheses about MOSml were partially supported because the MOSml minima patterns were specific to right or left steps and were not significantly different between straight-line gait and pre-planned turns overall, but the right step's MOSml minima were more negative during late-cued vs. pre-planned turns and between either turn and straight-line gait. Finally, we observed slower gait speeds, fewer footfalls, shorter turn phase duration, and different turn strategies used during late-cued vs. pre-planned turns. Overall, these findings reveal multifaceted control of frontal-plane balance during turns encountered during everyday mobility.

Effects of the direction and speed strategies on pedestrian dynamics

In this work, we propose a velocity-based model for pedestrian movements containing two sub-models to study how the direction and speed selection strategies affect pedestrian dynamics. Affected by others in the view, pedestrians deviate their moving direction from the desired one to resolve space and velocity conflicts, the sensitivity to which is adjusted by two proportional parameters. After determining the moving direction, they choose a reasonable speed to avoid immediate collisions. The tolerance of personal-space violations is considered given that people accept physical contacts in some contexts and may squeeze despite the lack of space instead of matching the speed of the one in front. Simulation results demonstrate that the direction and speed selection strategies affect pedestrian dynamics in several aspects, including the time and metabolic energy cost, density-velocity relations, and crowd stability. Intriguingly, the discrepant empirical fundamental diagrams of pedestrians can be reproduced and explained in a natural way.

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 energy cost of split-belt walking for a variety of belt speed combinations

Walking on a split-belt treadmill is often compared to walking on tied belts at the average speed, but the relationship between the metabolic energy costs of split- and tied-belt walking remains largely unexplored. Recent simulation work has suggested that people could take advantage of a belt speed difference and lower their energy costs, but this effect has not yet been observed experimentally. To relate metabolic energy costs across a range of belt speed combinations, we had 10 participants each complete 14 tied-belt and 39 split-belt walking trials, with early split-belt trials incorporating additional time for training. The average speeds ranged from 0.6 to 1.8 m/s with belt speed differences up to 1.4 m/s. We used ANOVA to determine differences in energy cost due to average speed and belt speed difference. We fit a linear model to estimate the tied-belt speed with the same energy cost as a given pair of split belt speeds. The cost of split-belt walking was on average just 0.13 ± 0.32 W/kg more expensive than the cost of tied-belt walking at the average speed. Contrary to predictions from simple dynamical models, increased belt speed difference resulted in increased energy cost, and the energetically equivalent tied-belt speed could be estimated as v_eq=v_avg+0.065⋅Δv. Clinicians designing rehabilitation protocols can balance the therapeutic benefits of higher belt speed difference with increased energetic demands. Open questions remain about why people cannot fully take advantage of mechanical work performed by a split-belt treadmill.