Computer optimization of a minimal biped model discovers walking and running

Geometric phase predicts locomotion performance in undulating living systems across scales

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Biomechanical Consequences of Walking With the Suspended Backpacks

OBJECTIVE

This article aimed to investigate the biomechanical mechanisms underlying the energetic advantages of the suspended backpacks during load carriage.

METHODS

In this study, we examined eight adults walking with a 15 kg load at 5 km/h with a designed suspended backpack, in which the load could be switched to locked and suspended with four combinations of stiffness. Mechanical work and metabolic cost were measured during load carriage.

RESULTS

The results showed that the suspended backpacks led to an average reduction of 23.35% in positive work, 24.77% in negative work, and a 12.51% decrease in metabolic cost across all suspended load conditions. Notably, the decreased mechanical work predominantly occurred during single support (averaging 84.19% and 71.16% for positive and negative work, respectively), rather than during double support.

CONCLUSION

Walking with the suspended backpack induced a phase shift between body movement and load movement, altering the human-load interaction. This adjustment caused the body and load to move against each other, resulting in flatter trajectories of the human-load system center of mass (COM) velocities and corresponding profiles in ground reaction forces (GRFs), along with reduced vertical excursions of the trunk. Consequently, this interplay led to flatter trajectories in mechanical work rate and reduced mechanical work, ultimately contributing to the observed reduction in energetic expenditure.

SIGNIFICANCE

Understanding these mechanisms is essential for the development of more effective load-carrying devices and strategies in various applications, particularly for enhancing walking abilities during load carriage.

Estimating the mechanical cost of transport in human walking with a simple kinematic data-driven mechanical model

This work utilizes a simplified, streamlined approach to study the mechanical cost of transport in human walking. Utilizing the kinematic motion data of the center of mass, velocities and accelerations are determined using kinematic analysis; the applied force is then obtained using inverse dynamics. We calculate the mechanical cost of transport per step from both synthetic and measured data, using a very simple mechanical model of walking. The approach studied can serve as an informative gait characteristic to monitor rehabilitation in human walking.

Quantifying changes in individual-specific template-based representations of center-of-mass dynamics during walking with ankle exoskeletons using Hybrid-SINDy

Ankle exoskeletons alter whole-body walking mechanics, energetics, and stability by altering center-of-mass (CoM) motion. Controlling the dynamics governing CoM motion is, therefore, critical for maintaining efficient and stable gait. However, how CoM dynamics change with ankle exoskeletons is unknown, and how to optimally model individual-specific CoM dynamics, especially in individuals with neurological injuries, remains a challenge. Here, we evaluated individual-specific changes in CoM dynamics in unimpaired adults and one individual with post-stroke hemiparesis while walking in shoes-only and with zero-stiffness and high-stiffness passive ankle exoskeletons. To identify optimal sets of physically interpretable mechanisms describing CoM dynamics, termed template signatures, we leveraged hybrid sparse identification of nonlinear dynamics (Hybrid-SINDy), an equation-free data-driven method for inferring sparse hybrid dynamics from a library of candidate functional forms. In unimpaired adults, Hybrid-SINDy automatically identified spring-loaded inverted pendulum-like template signatures, which did not change with exoskeletons (p > 0.16), except for small changes in leg resting length (p < 0.001). Conversely, post-stroke paretic-leg rotary stiffness mechanisms increased by 37-50% with zero-stiffness exoskeletons. While unimpaired CoM dynamics appear robust to passive ankle exoskeletons, how neurological injuries alter exoskeleton impacts on CoM dynamics merits further investigation. Our findings support Hybrid-SINDy's potential to discover mechanisms describing individual-specific CoM dynamics with assistive devices.

Speed-dependent modulations of asymmetric center of body mass trajectory in the gait of above-knee amputee subjects

How to achieve stable locomotion while overcoming various instabilities is an ongoing research topic. One essential factor for achieving a stable gait is controlling the center of body mass (CoM). The CoM yields more instability in the mediolateral direction. Examining speed-dependent modulations of the CoM trajectories in the frontal plane can provide insight into control policies for achieving stable locomotion. Although these modulations have been studied while assuming symmetric CoM trajectories, this assumption is generally incorrect. For example, amputee subjects demonstrate asymmetric CoM trajectories. Here, we investigated speed-dependent modulations of asymmetric CoM trajectories in above-knee amputee subjects using Fourier series expansion. Despite the asymmetric CoM trajectories in amputee subjects, the framework of Fourier series expansion clarified that amputee subjects showed the same speed-dependent modulations as non-amputee subjects whose CoM trajectories were symmetric. Specifically, CoM trajectories became narrower in the mediolateral direction and broader in the superoinferior direction as walking speed increased. The speed-dependent modulations of CoM trajectories had a functional role in improving dynamic stability, and faster walking speeds provided greater dynamic stability on both prosthetic and non-prosthetic sides. Although the asymmetry of foot contact duration and CoM trajectory decreased as walking speed increased, step width and the asymmetry of dynamic stability between prosthetic and non-prosthetic sides remained constant across the walking speed, which corresponded to the predictions by our framework. These findings could offer a better strategy for achieving stable walking for amputee subjects.

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Biomechanical Tradeoffs in Foot Function From Variations in Shoe Design

There is debate and confusion over how to evaluate the biomechanical effects of running shoe design. Here, we use an evolutionary perspective to analyze how key design features of running shoes alter the evolved biomechanics of the foot, creating a range of tradeoffs in force production and transmission that may affect performance and vulnerability to injury.

Phase shift between joint rotation and actuation reflects dominant forces and predicts muscle activation patterns

During behavior, the work done by actuators on the body can be resisted by the body's inertia, elastic forces, gravity, or viscosity. The dominant forces that resist actuation have major consequences on the control of that behavior. In the literature, features and actuation of locomotion, for example, have been successfully predicted by nondimensional numbers (e.g. Froude number and Reynolds number) that generally express the ratio between two of these forces (gravitational, inertial, elastic, and viscous). However, animals of different sizes or motions at different speeds may not share the same dominant forces within a behavior, making ratios of just two of these forces less useful. Thus, for a broad comparison of behavior across many orders of magnitude of limb length and cycle period, a dimensionless number that includes gravitational, inertial, elastic, and viscous forces is needed. This study proposes a nondimensional number that relates these four forces: the phase shift (ϕ) between the displacement of the limb and the actuator force that moves it. Using allometric scaling laws, ϕ for terrestrial walking is expressed as a function of the limb length and the cycle period at which the limb steps. Scale-dependent values of ϕ are used to explain and predict the electromyographic (EMG) patterns employed by different animals as they walk.

Neuromuscular control: from a biomechanist's perspective

Understanding neural control of movement necessitates a collaborative approach between many disciplines, including biomechanics, neuroscience, and motor control. Biomechanics grounds us to the laws of physics that our musculoskeletal system must obey. Neuroscience reveals the inner workings of our nervous system that functions to control our body. Motor control investigates the coordinated motor behaviours we display when interacting with our environment. The combined efforts across the many disciplines aimed at understanding human movement has resulted in a rich and rapidly growing body of literature overflowing with theories, models, and experimental paradigms. As a result, gathering knowledge and drawing connections between the overlapping but seemingly disparate fields can be an overwhelming endeavour. This review paper evolved as a need for us to learn of the diverse perspectives underlying current understanding of neuromuscular control. The purpose of our review paper is to integrate ideas from biomechanics, neuroscience, and motor control to better understand how we voluntarily control our muscles. As biomechanists, we approach this paper starting from a biomechanical modelling framework. We first define the theoretical solutions (i.e., muscle activity patterns) that an individual could feasibly use to complete a motor task. The theoretical solutions will be compared to experimental findings and reveal that individuals display structured muscle activity patterns that do not span the entire theoretical solution space. Prevalent neuromuscular control theories will be discussed in length, highlighting optimality, probabilistic principles, and neuromechanical constraints, that may guide individuals to families of muscle activity solutions within what is theoretically possible. Our intention is for this paper to serve as a primer for the neuromuscular control scientific community by introducing and integrating many of the ideas common across disciplines today, as well as inspire future work to improve the representation of neural control in biomechanical models.

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.

Selection of gait parameters during constrained walking

It is commonly thought that at prescribed speeds humans choose gait parameters that minimize the cost of transportation. However, it is unclear whether and how the relationship between step length and step frequency is affected by the additional physiological factors caused by constraints. We performed a series of experiments to understand the selection of gait parameters under different constraints from a probabilistic perspective. First, we show that the effect of constraining step length on step frequency (i.e., monotonically decrease, Experiment I) is different from the effect of constraining step frequency on step length (i.e., inverted-U, Experiment II). Using the results from Experiment I and II, we summarized the marginal distribution of step length and step frequency and built their joint distribution in a probabilistic model. The probabilistic model predicts the selection of gait parameters by achieving the maximum probability of joint distribution of step length and step frequency. In Experiment III, the probabilistic model could well predict gait parameters at prescribed speeds, and it is similar to minimizing the cost of transportation. Finally, we show that the distribution of step length and step frequency were completely different between constrained and non-constrained walking. We argue that constraints in walking are major factors determining how humans choose gait parameters due to their involvement of mediators, i.e., attention or active control. Using the probabilistic model to account for gait parameters has an advantage compared with fixed-parameter models in that it can still include the effect of hidden mechanical, neurophysiological, or psychological variables by grouping them into distribution curves.

The collisional geometry of economical walking predicts human leg and foot segment proportions

Human walking appears complicated, with many muscles and joints performing rapidly varying roles over the stride. However, the function of walking is simple: to support body weight as it translates economically. Here, a scenario is proposed for the sequence of joint and muscle actions that achieves this function, with the timing of muscle loading and unloading driven by simple changes in geometry over stance. In the scenario, joints of the legs and feet are sequentially locked, resulting in a vaulting stance phase and three or five rapid 'mini-vaults' over a series of 'virtual legs' during the step-to-step transition. Collision mechanics indicate that the mechanical work demand is minimized if the changes in the centre-of-mass trajectory over the step-to-step transition are evenly spaced, predicting an even spacing of the virtual legs. The scenario provides a simple account for the work-minimizing mechanisms of joints and muscles in walking, and collision geometry allows leg and foot proportions to be predicted, accounting for the location of the knee halfway down the leg, and the relatively stiff, plantigrade, asymmetric, short-toed human foot.

How human runners regulate footsteps on uneven terrain

Running stably on uneven natural terrain takes skillful control and was critical for human evolution. Even as runners circumnavigate hazardous obstacles such as steep drops, they must contend with uneven ground that is gentler but still destabilizing. We do not know how footsteps are guided based on the uneven topography of the ground and how those choices influence stability. Therefore, we studied human runners on trail-like undulating uneven terrain and measured their energetics, kinematics, ground forces, and stepping patterns. We find that runners do not selectively step on more level ground areas. Instead, the body's mechanical response, mediated by the control of leg compliance, helps maintain stability without requiring precise regulation of footsteps. Furthermore, their overall kinematics and energy consumption on uneven terrain showed little change from flat ground. These findings may explain how runners remain stable on natural terrain while devoting attention to tasks besides guiding footsteps.

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.

Multimodal bipedal locomotion generation with passive dynamics via deep reinforcement learning

Generating multimodal locomotion in underactuated bipedal robots requires control solutions that can facilitate motion patterns for drastically different dynamical modes, which is an extremely challenging problem in locomotion-learning tasks. Also, in such multimodal locomotion, utilizing body morphology is important because it leads to energy-efficient locomotion. This study provides a framework that reproduces multimodal bipedal locomotion using passive dynamics through deep reinforcement learning (DRL). An underactuated bipedal model was developed based on a passive walker, and a controller was designed using DRL. By carefully planning the weight parameter settings of the DRL reward function during the learning process based on a curriculum learning method, the bipedal model successfully learned to walk, run, and perform gait transitions by adjusting only one command input. These results indicate that DRL can be applied to generate various gaits with the effective use of passive dynamics.

Long-term stability of single neuron activity in the motor system

How an established behavior is retained and consistently produced by a nervous system in constant flux remains a mystery. One possible solution to ensure long-term stability in motor output is to fix the activity patterns of single neurons in the relevant circuits. Alternatively, activity in single cells could drift over time provided that the population dynamics are constrained to produce the same behavior. To arbitrate between these possibilities, we recorded single-unit activity in motor cortex and striatum continuously for several weeks as rats performed stereotyped motor behaviors-both learned and innate. We found long-term stability in single neuron activity patterns across both brain regions. A small amount of drift in neural activity, observed over weeks of recording, could be explained by concomitant changes in task-irrelevant aspects of the behavior. These results suggest that long-term stable behaviors are generated by single neuron activity patterns that are themselves highly stable.

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

Limb, joint and pelvic kinematic control in the quail coping with steps upwards and downwards

Small cursorial birds display remarkable walking skills and can negotiate complex and unstructured terrains with ease. The neuromechanical control strategies necessary to adapt to these challenging terrains are still not well understood. Here, we analyzed the 2D- and 3D pelvic and leg kinematic strategies employed by the common quail to negotiate visible steps (upwards and downwards) of about 10%, and 50% of their leg length. We used biplanar fluoroscopy to accurately describe joint positions in three dimensions and performed semi-automatic landmark localization using deep learning. Quails negotiated the vertical obstacles without major problems and rapidly regained steady-state locomotion. When coping with step upwards, the quail mostly adapted the trailing limb to permit the leading leg to step on the elevated substrate similarly as it did during level locomotion. When negotiated steps downwards, both legs showed significant adaptations. For those small and moderate step heights that did not induce aerial running, the quail kept the kinematic pattern of the distal joints largely unchanged during uneven locomotion, and most changes occurred in proximal joints. The hip regulated leg length, while the distal joints maintained the spring-damped limb patterns. However, to negotiate the largest visible steps, more dramatic kinematic alterations were observed. There all joints contributed to leg lengthening/shortening in the trailing leg, and both the trailing and leading legs stepped more vertically and less abducted. In addition, locomotion speed was decreased. We hypothesize a shift from a dynamic walking program to more goal-directed motions that might be focused on maximizing safety.

Do we all walk the walk? A comparison of walking behaviors across tetrapods

A walking gait has been identified in a range of vertebrate species with different body plans, habitats, and life histories. With increased application of this broad umbrella term, it has become necessary to assess the physical characteristics, analytical approaches, definitions, and diction used to describe walks. To do this, we reviewed studies of slow speed locomotion across a range of vertebrates to refine the parameters used to define walking, evaluate analytical techniques, and propose approaches to maximize consistency across subdisciplines. We summarize nine key parameters used to characterize walking behaviors in mammals, birds, reptiles, amphibians, and fishes. After identifying consistent patterns across groups, we propose a comprehensive definition for a walking gait. A walk is a form of locomotion where the majority of the forward propulsion of the animal comes from forces generated by the appendages interacting with the ground. During a walk, an appendage must be out of phase with the opposing limb in the same girdle and there is always at least one limb acting as ground-support (no suspension phase). Additionally, walking occurs at dimensionless speeds <1 v* and the duty factor of the limbs is always >0.5. Relative to other gaits used by the same species, the stance duration of a walk is long, the cycle frequency is low, and the cycle distance is small. Unfortunately, some of these biomechanical parameters, while effectively describing walks, may also characterize other, non-walking gaits. Inconsistent methodology likely contributes to difficulties in comparing data across many groups of animals; consistent application of data collection and analytical techniques in research methodology can improve these comparisons. Finally, we note that the kinetics of quadrupedal movements are still poorly understood and much work remains to be done to understand the movements of small, exothermic tetrapods.

Complexity of Running and Its Relationship with Joint Kinematics during a Prolonged Run

We investigated the effect of prolonged running on joint kinematics and its association with stride complexity between novice and elite runners. Ten elite marathoners and eleven healthy individuals took part in a 20 min submaximal prolonged running experiment at their preferred running speed (PRS). A three-dimensional motion capture system was utilized to capture and calculate the alpha exponent, stride-to-stride fluctuations (SSFs), and stride-to-stride variability (SSV) of spatiotemporal parameters and joint kinematics. In the results, the elite athletes ran at a considerably higher PRS than the novice runners, yet no significant differences were found in respiratory exchange ratio with increasing time intervals. For the spatiotemporal parameters, we observed a significant increase in the step width and length variability in novice runners with increasing time-interval (p < 0.05). However, we did not observe any differences in the alpha exponent of spatiotemporal parameters. Significant differences in SSF of joint kinematics were observed, particularly in the sagittal plane for ankle, knee, and hip at heel strike (p < 0.05). While in mid-stance, time-interval differences were observed in novices who ran with a lower knee flexion angle (p < 0.05). During toe-off, significantly higher SSV was observed, particularly in the hip and ankle for novices (p < 0.05). The correlation analysis of joint SSV revealed a distinct negative relationship with the alpha exponent of step-length and step-width for elite runners, while, for novices, a positive relation was observed only for the alpha exponent of step-width. In conclusion, our study shows that increased step-width variability seen in novices could be a compensatory mechanism to maintain performance and mitigate the loss of stability. On the other hand, elite runners showed a training-induced effective modulation of lower-limb kinematics to improve their running 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.

Theory of Fast Walking With Human-Driven Load-Carrying Robot Exoskeletons

Reaching and maintaining high walking speeds is challenging for a human when carrying extra weight, such as walking with a heavy backpack. Robotic limbs can support a heavy backpack when standing still, but accelerating a backpack within a couple of steps to race-walking speeds requires limb force and energy beyond natural human ability. Here, we conceive a human-driven robot exoskeleton that could accelerate a heavy backpack faster and maintain top speeds higher than what the human alone can when not carrying a backpack. The key components of the exoskeleton are the mechanically adaptive but energetically passive spring limbs. We show that by optimally adapting the stiffness of the limbs, the robot can achieve near-horizontal center of mass motion to emulate the load-bearing mechanics of the bicycle. We find that such an exoskeleton could enable the human to accelerate one extra body weight up to top race-walking speeds in ten steps. Our finding predicts that human-driven mechanically adaptive robot exoskeletons could extend human weight-bearing and fast-walking ability without using external energy.

Modulating Energy Among Foot-Ankle Complex With an Unpowered Exoskeleton Improves Human Walking Economy

Over the course of both evolution and development, the human musculoskeletal system has been well shaped for the cushion function of the foot during foot-strike and the impulsive function of the ankle joint during push-off. Nevertheless, an efficient energy interaction between foot structure and ankle joint is still lacking in the human body itself, which may limit the further potential of economical walking. Here we showed the metabolic expenditure of walking can be lessened by an unpowered exoskeleton robot that modulates energy among the foot-ankle complex towards a more effective direction. The unpowered exoskeleton recycles negative mechanical energy of the foot that is normally dissipated in heel-strike, retains the stored energy before mid-stance, and then transfers the energy to the ankle joint to assist the push-off. The modulation process of the exoskeleton consumes no input energy, yet reduces the metabolic cost of walking by 8.19 ± 0.96 % (mean ± s.e.m) for healthy subjects. The electromyography measurements demonstrate the activities of target ankle plantarflexors decreased significantly without added effort for the antagonistic muscle, suggesting the exoskeleton enhanced the subjects' energy efficiency of the foot-ankle complex in a natural manner. Furthermore, the exoskeleton also provides cushion assistance for walking, which leads to significantly decreased activity of the quadriceps muscle during heel-strike. Rather than strengthening the functions of existing biological structures, developing the complementary energy loop that does not exist in the human body itself also shows its potential for gait assistance.

Mechanical intelligence for learning embodied sensor-object relationships

Intelligence involves processing sensory experiences into representations useful for prediction. Understanding sensory experiences and building these contextual representations without prior knowledge of sensor models and environment is a challenging unsupervised learning problem. Current machine learning methods process new sensory data using prior knowledge defined by either domain knowledge or datasets. When datasets are not available, data acquisition is needed, though automating exploration in support of learning is still an unsolved problem. Here we develop a method that enables agents to efficiently collect data for learning a predictive sensor model-without requiring domain knowledge, human input, or previously existing data-using ergodicity to specify the data acquisition process. This approach is based entirely on data-driven sensor characteristics rather than predefined knowledge of the sensor model and its physical characteristics. We learn higher quality models with lower energy expenditure during exploration for data acquisition compared to competing approaches, including both random sampling and information maximization. In addition to applications in autonomy, our approach provides a potential model of how animals use their motor control to develop high quality models of their sensors (sight, sound, touch) before having knowledge of their sensor capabilities or their surrounding environment.

Bidirectional Locomotion of Soft Inchworm Crawler Using Dynamic Gaits

Inchworm-styled locomotion is one of the simplest gaits for mobile robots, which enables easy actuation, effective movement, and strong adaptation in nature. However, an agile inchworm-like robot that realizes versatile locomotion usually requires effective friction force manipulation with a complicated actuation structure and control algorithm. In this study, we embody a friction force controller based on the deformation of the robot body, to realize bidirectional locomotion. Two kinds of differential friction forces are integrated into a beam-like soft robot body, and along with the cyclical actuation of the robot body, two locomotion gaits with opposite locomotion directions can be generated and controlled by the deformation process of the robot body, that is, the dynamic gaits. Based on these dynamic gaits, two kinds of locomotion control schemes, the amplitude-based control and the frequency-based control, are proposed, analyzed, and validated with both theoretical simulations and prototype experiments. The soft inchworm crawler achieves the versatile locomotion result via a simple system configuration and minimalist actuation input. This work is an example of using soft structure vibrations for challenging robotic tasks.

The spring-mass model and other reductionist models of bipedal locomotion on inclines

The spring-mass model is a model of locomotion aimed at giving the essential mathematical laws of the trajectory of the center of mass of an animal during bouncing gaits, such as hopping (one-dimensional) and running (two-dimensional). This reductionist mechanical system has been extensively investigated for locomotion over horizontal surfaces, whereas it has been largely neglected on other ecologically relevant surfaces, including inclines. For example, how the degree of inclination impacts the dynamics of the center of mass of the spring-mass model has not been investigated thoroughly. In this work, we derive a mathematical model which extends the spring-mass model to inclined surfaces. Among our results, we derive an approximate solution of the system, assuming a small angular sweep of the limb and a small spring compression during stance, and show that this approximation is very accurate, especially for small inclinations of the ground. Furthermore, we derive theoretical bounds on the difference between the Lagrangian and Lagrange equations of the true and approximate system, and discuss locomotor stability questions of the approximate solutions. We test our models through a sensitivity analysis using parameters relevant to the locomotion of bipedal animals (quail, pheasant, guinea fowl, turkey, ostrich, and humans) and compare our approximate solution to the numerically derived solution of the exact system. We compare the two-dimensional spring-mass model on inclines with the one-dimensional spring-mass model to which it reduces under the limit of no horizontal velocity; we compare the two-dimensional spring-mass model on inclines with the inverted-pendulum model on inclines towards which it converges in the case of high stiffness-to-mass ratio. We include comparisons with historically prevalent no-gravity approximations of these models, as well. The insights we have gleaned through all these comparisons and the ability of our approximation to replicate some of the kinematic changes observed in animals moving on different inclines (e.g. reduction in vertical oscillation of the center of mass and decreased stride length) underlines the valuable and reasonable contributions that very simple, reductionist models, like the spring-mass model, can provide.

Running in the wild: Energetics explain ecological running speeds

Human runners have long been thought to have the ability to consume a near-constant amount of energy per distance traveled, regardless of speed, allowing speed to be adapted to particular task demands with minimal energetic consequence.^1-3 However, recent and more precise laboratory measures indicate that humans may in fact have an energy-optimal running speed.^4-6 Here, we characterize runners' speeds in a free-living environment and determine if preferred speed is consistent with task- or energy-dependent objectives. We analyzed a large-scale dataset of free-living runners, which was collected via a commercial fitness tracking device, and found that individual runners preferred a particular speed that did not change across commonly run distances. We compared the data from lab experiments that measured participants' energy-optimal running speeds with the free-living preferred speeds of age- and gender-matched runners in our dataset and found the speeds to be indistinguishable. Human runners prefer a particular running speed that is independent of task distance and is consistent with the objective of minimizing energy expenditure. Our findings offer an insight into the biological objectives that shape human running preferences in the real world-an important consideration when examining human ecology or creating training strategies to improve performance and prevent injury.

Distinct forms of resonant optimality within insect indirect flight motors

Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties-an illustration of the extraordinary robustness of these natural motors.

Antagonistic co-contraction can minimize muscular effort in systems with uncertainty

Muscular co-contraction of antagonistic muscle pairs is often observed in human movement, but it is considered inefficient and it can currently not be predicted in simulations where muscular effort or metabolic energy are minimized. Here, we investigated the relationship between minimizing effort and muscular co-contraction in systems with random uncertainty to see if muscular co-contraction can minimize effort in such system. We also investigated the effect of time delay in the muscle, by varying the time delay in the neural control as well as the activation time constant. We solved optimal control problems for a one-degree-of-freedom pendulum actuated by two identical antagonistic muscles, using forward shooting, to find controller parameters that minimized muscular effort while the pendulum remained upright in the presence of noise added to the moment at the base of the pendulum. We compared a controller with and without feedforward control. Task precision was defined by bounding the root mean square deviation from the upright position, while different perturbation levels defined task difficulty. We found that effort was minimized when the feedforward control was nonzero, even when feedforward control was not necessary to perform the task, which indicates that co-contraction can minimize effort in systems with uncertainty. We also found that the optimal level of co-contraction increased with time delay, both when the activation time constant was increased and when neural time delay was added. Furthermore, we found that for controllers with a neural time delay, a different trajectory was optimal for a controller with feedforward control than for one without, which indicates that simulation trajectories are dependent on the controller architecture. Future movement predictions should therefore account for uncertainty in dynamics and control, and carefully choose the controller architecture. The ability of models to predict co-contraction from effort or energy minimization has important clinical and sports applications. If co-contraction is undesirable, one should aim to remove the cause of co-contraction rather than the co-contraction itself.

Control of Mammalian Locomotion by Somatosensory Feedback

When animals walk overground, mechanical stimuli activate various receptors located in muscles, joints, and skin. Afferents from these mechanoreceptors project to neuronal networks controlling locomotion in the spinal cord and brain. The dynamic interactions between the control systems at different levels of the neuraxis ensure that locomotion adjusts to its environment and meets task demands. In this article, we describe and discuss the essential contribution of somatosensory feedback to locomotion. We start with a discussion of how biomechanical properties of the body affect somatosensory feedback. We follow with the different types of mechanoreceptors and somatosensory afferents and their activity during locomotion. We then describe central projections to locomotor networks and the modulation of somatosensory feedback during locomotion and its mechanisms. We then discuss experimental approaches and animal models used to investigate the control of locomotion by somatosensory feedback before providing an overview of the different functional roles of somatosensory feedback for locomotion. Lastly, we briefly describe the role of somatosensory feedback in the recovery of locomotion after neurological injury. We highlight the fact that somatosensory feedback is an essential component of a highly integrated system for locomotor control. © 2021 American Physiological Society. Compr Physiol 11:1-71, 2021.

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.

Variability in the Center of Mass State During Initiation of Accurate Forward Step Aimed at Targets of Different Sizes

Motor control for forward step initiation begins with anticipatory postural adjustments (APAs). During APAs, the central nervous system controls the center of pressure (CoP) to generate an appropriate center of mass (CoM) position and velocity for various task requirements. In this study, we investigated the effect of required stepping accuracy on the CoM and CoP parameters during APA for a step initiation task. Sixteen healthy young participants stepped forward onto the targets on the ground as soon as and as fast as possible in response to visual stimuli. Two target sizes (small: 2 cm square and large: 10 cm square) and two target distances (short: 20% and long: 40% of the body height) were tested. CoP displacement during the APA and the CoM position, velocity, and extrapolated CoM at the timing of the takeoff of the lead leg were compared among the conditions. In the small condition, comparing with the large condition, the CoM position was set closer to the stance limb side during the APA, which was confirmed by the location of the extrapolated center of mass at the instance of the takeoff of the lead leg [small: 0.09 ± 0.01 m, large: 0.06 ± 0.01 m, mean and standard deviation, F _{(1, 15)} = 96.46, p < 0.001, η² = 0.87]. The variability in the mediolateral extrapolated center of mass location was smaller in the small target condition than large target condition when the target distance was long [small: 0.010 ± 0.002 m, large: 0.013 ± 0.004 m, t(15) = 3.8, p = 0.002, d = 0.96]. These findings showed that in the step initiation task, the CoM state and its variability were task-relevantly determined during the APA in accordance with the required stepping accuracy.

Energy optimization during walking involves implicit processing

Gait adaptations, in response to novel environments, devices or changes to the body, can be driven by the continuous optimization of energy expenditure. However, whether energy optimization involves implicit processing (occurring automatically and with minimal cognitive attention), explicit processing (occurring consciously with an attention-demanding strategy) or both in combination remains unclear. Here, we used a dual-task paradigm to probe the contributions of implicit and explicit processes in energy optimization during walking. To create our primary energy optimization task, we used lower-limb exoskeletons to shift people's energetically optimal step frequency to frequencies lower than normally preferred. Our secondary task, designed to draw explicit attention from the optimization task, was an auditory tone discrimination task. We found that adding this secondary task did not prevent energy optimization during walking; participants in our dual-task experiment adapted their step frequency toward the optima by an amount and at a rate similar to participants in our previous single-task experiment. We also found that performance on the tone discrimination task did not worsen when participants were adapting toward energy optima; accuracy scores and reaction times remained unchanged when the exoskeleton altered the energy optimal gaits. Survey responses suggest that dual-task participants were largely unaware of the changes they made to their gait during adaptation, whereas single-task participants were more aware of their gait changes yet did not leverage this explicit awareness to improve gait adaptation. Collectively, our results suggest that energy optimization involves implicit processing, allowing attentional resources to be directed toward other cognitive and motor objectives during walking.

Deep reinforcement learning for modeling human locomotion control in neuromechanical simulation

Modeling human motor control and predicting how humans will move in novel environments is a grand scientific challenge. Researchers in the fields of biomechanics and motor control have proposed and evaluated motor control models via neuromechanical simulations, which produce physically correct motions of a musculoskeletal model. Typically, researchers have developed control models that encode physiologically plausible motor control hypotheses and compared the resulting simulation behaviors to measurable human motion data. While such plausible control models were able to simulate and explain many basic locomotion behaviors (e.g. walking, running, and climbing stairs), modeling higher layer controls (e.g. processing environment cues, planning long-term motion strategies, and coordinating basic motor skills to navigate in dynamic and complex environments) remains a challenge. Recent advances in deep reinforcement learning lay a foundation for modeling these complex control processes and controlling a diverse repertoire of human movement; however, reinforcement learning has been rarely applied in neuromechanical simulation to model human control. In this paper, we review the current state of neuromechanical simulations, along with the fundamentals of reinforcement learning, as it applies to human locomotion. We also present a scientific competition and accompanying software platform, which we have organized to accelerate the use of reinforcement learning in neuromechanical simulations. This “Learn to Move” competition was an official competition at the NeurIPS conference from 2017 to 2019 and attracted over 1300 teams from around the world. Top teams adapted state-of-the-art deep reinforcement learning techniques and produced motions, such as quick turning and walk-to-stand transitions, that have not been demonstrated before in neuromechanical simulations without utilizing reference motion data. We close with a discussion of future opportunities at the intersection of human movement simulation and reinforcement learning and our plans to extend the Learn to Move competition to further facilitate interdisciplinary collaboration in modeling human motor control for biomechanics and rehabilitation research

The loss of the 'pelvic step' in human evolution

Human bipedalism entails relatively short strides compared with facultatively bipedal primates. Unique non-sagittal-plane motions associated with bipedalism may account for part of this discrepancy. Pelvic rotation anteriorly translates the hip, contributing to bipedal stride length (i.e. the 'pelvic step'). Facultative bipedalism in non-human primates entails much larger pelvic rotation than in humans, suggesting that a larger pelvic step may contribute to their relatively longer strides. We collected data on the pelvic step in bipedal chimpanzees and over a wide speed range of human walking. At matched dimensionless speeds, humans have 26.7% shorter dimensionless strides, and a pelvic step 5.4 times smaller than bipedal chimpanzees. Differences in pelvic rotation explain 31.8% of the difference in dimensionless stride length between the two species. We suggest that relative stride lengths and the pelvic step have been significantly reduced throughout the course of hominin evolution.

Human biomechanics perspective on robotics for gait assistance: challenges and potential solutions

Technological advancements in robotic devices have the potential to transform human mobility through gait assistance. However, the integration of physical hardware and software control algorithms with users to assist with impaired gait poses several challenges, such as allowing the user to adopt a variety of gaits and the process for evaluating the efficacy and performance of these assistive devices. Here, I discuss some of the challenges in the development of assistive devices and the use of biomechanical concepts and tools for control and test validation. Several potential solutions are proposed through the case study of one project that aimed to provide gait assistance for individuals with a spinal cord injury. Further challenges and future directions are discussed, with emphasis that diverse perspectives and approaches in gait assistance will accelerate engineering solutions towards regaining mobility.

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

Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality criterion that predicts disparate non-straight-line walking phenomena, with straight-line walking as a special case. We first characterized the metabolic cost of turning, deriving the cost landscape as a function of turning radius and rate. We then generalized this cost landscape to arbitrarily complex trajectories, allowing the velocity direction to deviate from body orientation (holonomic walking). We used this generalized optimality criterion to mathematically predict movement patterns in multiple contexts of varying complexity: walking on prescribed paths, turning in place, navigating an angled corridor, navigating freely with end-point constraints, walking through doors, and navigating around obstacles. In these tasks, humans moved at speeds and paths predicted by our optimality criterion, slowing down to turn and never using sharp turns. We show that the shortest path between two points is, counterintuitively, often not energy-optimal, and, indeed, humans do not use the shortest path in such cases. Thus, we have obtained a unified theoretical account that predicts human walking paths and speeds in diverse contexts. Our model focuses on walking in healthy adults; future work could generalize this model to other human populations, other animals, and other locomotor tasks.

A planar piecewise continuous lumped muscle parameter model for prediction of walking gait

GOAL

This work aims to develop a planar piecewise continuous lumped muscle parameter (PPCLMP) model that can utilize inputs that can be obtained in a clinical or home setting using simple tools (e.g. video cameras and inertial sensors) to predict human walking gait.

METHODS

The model characterizes the sagittal-plane movement of the lower limbs during the single stance phase as an inverted pendulum, the double stance phase as a kinematic chain, and the swing phase as a double pendulum. The joint angles and angular velocities at the end of one phase are used as the initial conditions of the next phase. The model predicts the gait cycle based on the initial joint angles and angular velocities via forward dynamics. The errors between the initial and end conditions are minimized by changing the input initial joint angles and angular velocities of the gait cycle.

RESULTS

Sensitivity analysis showed that the errors between the initial and end conditions of a gait cycle were sensitive to the initial joint angles. The step length was sensitive to subject stature. The model only works for a certain range of initial conditions.

CONCLUSIONS

The model can predict gait cycles based on forward dynamics and selects initial conditions that minimize the errors between the initial and end conditions of the gait cycle. The model utilizes 2-D representations of lower limbs and simplified representations of joint torques to reduce the required inputs for gait prediction and builds the foundation of gait assessment tools.

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 Impact of Locomotor Speed on the Human Metatarsophalangeal Joint Kinematics

This paper aims to further our previous study to investigate the effect of speed on the human metatarsophalangeal (MP) joint kinematics during running on level ground. The 3D motion of the foot segments was captured by a twelve-camera motion analysis system, and the ground reaction forces and moments were recorded by using a six-force plate array. The relative movement between the tarsometatarsi (hindfoot) and phalanges (forefoot) segments were recorded to obtain the 3D orientation and position of the functional axis (FA) of the MP joint. The results show that the FA locates about an average of 19% foot length (FL) anterior to the anatomical axis (AA) across all running speeds, and is also 4.8% FL inferior to the AA during normal and fast run. Similar to walking, the functional axis is more oblique than the anatomical axis with a more anterior–inferior orientation across all the running speeds. This suggests that representing MP joint with the AA may mislead the calculation of joint moment/power and muscle moment arms in both running and walking gait. Compared with previous study, we found that walking and running speeds have statistically significant effects on the position of the FA. The functional axis moves frontward to a more anterior position when the speed increases during walking and running. It transfers upward in the superior direction with increasing speed of walking, but moves more toward the inferior position when the velocity increased further to running. Also, the orientation of FA in sagittal plane became more oblique toward the vertical direction as the speed increased. This may help in moderating the muscular effort, increase the muscle EMA and improve the locomotor performance. These results would contribute to understanding the in vivo biomechanical function of the MP joint and also the foot propulsion during human locomotion.

A grid gradient approximation method of energy-efficient gait planning for biped robots

In this article, an energy-efficient gait planning algorithm that utilizes both 3D body motion and an allowable zero moment point region (AZR) is presented for biped robots based on a five-mass inverted pendulum model. The product of the load torque and angular velocity of all joint motors is used as an energy index function (EIF) to evaluate the energy consumption during walking. The algorithm takes the coefficients of the finite-order Fourier series to represent the motion space of the robot body centroid, and the motion space is gridded by discretizing these coefficients. Based on the geometric structure of the leg joints, an inverse kinematics method for calculating grid intersection points is designed. Of the points that satisfy the AZR constraints, the point with the lowest EIF value in each network line is selected as the seed. In the neighborhood of the seed, the point with the minimum EIF value in the motion space is successively approximated by the gradient descent method, and the corresponding joint angle sequence is stored in the database. Given a distance to be traveled, our algorithm plans a complete walking trajectory, including two starting steps, multiple cyclic steps, and two stopping steps, while minimizing the energy consumption. According to the preset AZR, the joint angle sequences of the robot are read from the database, and these sequences are adjusted for each step according to the zero-moment-point feedback during walking. To determine the effectiveness of the proposed algorithm, both dynamic simulation and walking experiment in the real environment were carried out. The experimental results show that compared with algorithms based on the fixed body height or vertical body motion, our gait algorithm has a significant energy-saving effect.

Perspective on musculoskeletal modelling and predictive simulations of human movement to assess the neuromechanics of gait

Locomotion results from complex interactions between the central nervous system and the musculoskeletal system with its many degrees of freedom and muscles. Gaining insight into how the properties of each subsystem shape human gait is challenging as experimental methods to manipulate and assess isolated subsystems are limited. Simulations that predict movement patterns based on a mathematical model of the neuro-musculoskeletal system without relying on experimental data can reveal principles of locomotion by elucidating cause-effect relationships. New computational approaches have enabled the use of such predictive simulations with complex neuro-musculoskeletal models. Here, we review recent advances in predictive simulations of human movement and how those simulations have been used to deepen our knowledge about the neuromechanics of gait. In addition, we give a perspective on challenges towards using predictive simulations to gain new fundamental insight into motor control of gait, and to help design personalized treatments in patients with neurological disorders and assistive devices that improve gait performance. Such applications will require more detailed neuro-musculoskeletal models and simulation approaches that take uncertainty into account, tools to efficiently personalize those models, and validation studies to demonstrate the ability of simulations to predict gait in novel circumstances.

The Murphy number: how pitch moment of inertia dictates quadrupedal walking and running energetics

Many quadrupedal mammals transition from a four-beat walk to a two-beat run (e.g. trot), but some transition to a four-beat run (e.g. amble). Recent analysis shows that a two-beat run minimizes work only for animals with a small pitch moment of inertia (MOI), though empirical MOI were not reported. It was also unclear whether MOI affects gait energetics at slow speeds. Here, I show that a particular normalization of the pitch moment of inertia (the Murphy number) has opposite effects on walking and running energetics. During walking, simultaneous forelimb and hindlimb contacts dampen pitching energy, favouring a four-beat gait that can distribute expensive transfer of support. However, the required pitching of a four-beat walk becomes more expensive as Murphy number increases. Using trajectory optimization of a simple model, I show that both the walking and slow running strategies used by dogs, horses, giraffes and elephants can be explained by work optimization under their specific Murphy numbers. Rotational dynamics have been largely ignored in quadrupedal locomotion, but appear to be a central factor in gait selection.

Walk and Run Test in Patients with Degenerative Compression of the Cervical Spinal Cord

Impaired gait is one of the cardinal symptoms of degenerative cervical myelopathy (DCM) and frequently its initial presentation. Quantitative gait analysis is therefore a promising objective tool in the disclosure of early cervical cord impairment in patients with degenerative cervical compression. The aim of this cross-sectional observational cohort study was to verify whether an objective and easily-used walk and run test is capable of detecting early gait impairment in a practical proportion of non-myelopathic degenerative cervical cord compression (NMDCC) patients and of revealing any correlation with severity of disability in DCM. The study group consisted of 45 DCM patients (median age 58 years), 126 NMDCC subjects (59 years), and 100 healthy controls (HC) (55.5 years), all of whom performed a standardized 10-m walk and run test. Walking/running time/velocity, number of steps and cadence of walking/running were recorded; analysis disclosed abnormalities in 66.7% of NMDCC subjects. The DCM group exhibited significantly more pronounced abnormalities in all walk/run parameters when compared with the NMDCC group. These were apparent in 84.4% of the DCM group and correlated closely with disability as quantified by the modified Japanese Orthopaedic Association scale. A standardized 10-m walk/run test has the capacity to disclose locomotion abnormalities in NMDCC subjects who lack other clear myelopathic signs and may provide a means of classifying DCM patients according to their degree of disability.

Quadrupedal Robots’ Gaits Identification via Contact Forces Optimization

The purpose of the present paper is the identification of optimal trajectories of quadruped robots through genetic algorithms. The method is based on the identification of the optimal time history of forces and torques exchanged between the ground and the body, without any constraints on leg kinematics. The solutions show how it is possible to obtain similar trajectories to those of a horse’s walk but obtaining better performance in terms of energy cost. Finally, a map of the optimal gaits found according to the different speeds is presented, identifying the transition threshold between the walk and the trot as a function of the total energy spent.

Walking humans trade off different task goals to regulate lateral stepping

People walk in complex environments where they must adapt their steps to maintain balance and satisfy changing task goals. How people do this is not well understood. We recently developed computational models of lateral stepping, based on Goal Equivalent Manifolds that serve as motor regulation templates, to identify how people regulate walking movements from step-to-step. In normal walking, healthy adults strongly maintain step width, but also lateral position on their path. Here, we used this framework to pose empirically-testable hypotheses about how humans might adapt their lateral stepping dynamics when asked to prioritize different stepping goals. Participants walked on a treadmill in a virtual-reality environment under 4 conditions: normal walking and, while given direct feedback at each step, walking while trying to maintain constant step width, constant absolute lateral position, or constant heading (direction). Time series of lateral stepping variables were extracted, and variability and statistical persistence (reflecting step-to-step regulation) quantified. Participants exhibited less variability of the prescribed stepping variable compared to normal walking during each feedback condition. Stepping regulation results supported our models' predictions: to maintain constant step width or position, people either maintained or increased regulation of the prescribed variable, but also decreased regulation of its complement. Thus, people regulated lateral foot placements in predictable and systematic ways determined by specific task goals. Humans regulate stepping movements to not only "just walk" (step without falling), but also to achieve specific goal-directed tasks within a specific environment. The framework and motor regulation templates presented here capture these important interactions.

Predicting Temporal Gait Kinematics: Anthropometric Characteristics and Global Running Pattern Matter

Equations predicting stride frequency (SF) and duty factor (DF) solely based on running speed have been proposed. However, for a given speed, kinematics vary depending on the global running pattern (GRP), i.e., the overall individual movement while running, which depends on the vertical oscillation of the head, antero-posterior motion of the elbows, vertical pelvis position at ground contact, antero-posterior foot position at ground contact, and strike pattern. Hence, we first verified the validity of the aforementioned equations while accounting for GRP. Kinematics during three 50-m runs on a track (n = 20) were used with curve fitting and linear mixed effects models. The percentage of explained variance was increased by ≥133% for DF when taking into account GRP. GRP was negatively related to DF (p = 0.004) but not to SF (p = 0.08), invalidating DF equation. Second, we assessed which parameters among anthropometric characteristics, sex, training volume, and GRP could relate to SF and DF in addition to speed, using kinematic data during five 30-s runs on a treadmill (n = 54). SF and DF linearly increased and quadratically decreased with speed (p < 0.001), respectively. However, on an individual level, SF was best described using a second-order polynomial equation. SF and DF showed a non-negligible percentage of variance explained by random effects (≥28%). Age and height were positively and negatively related to SF (p ≤ 0.05), respectively, while GRP was negatively related to DF (p < 0.001), making them key parameters to estimate SF and DF, respectively, in addition to speed.

Why highly compliant poles are not energetically beneficial during running: Evidence from an optimization-based biped model

Springy poles are a unique load-carrying tool and inspire novel designs of other load-carrying systems. Previous experiments have shown that highly compliant poles with a natural frequency lower than step frequency are more economical than rigid poles during load carriage in walking and this was successfully explained in later modeling studies. However, an energetic benefit was not observed during running with highly compliant poles. We speculate that gait type (running versus walking) may be a factor accounting for the different observations. An optimization-based biped model is adopted to predict the energy cost of load carriage with poles during running, with the parameters from previous experimental studies. The predicted load motion and load-body interaction force agree well with experimental measurements. Compared to running with rigid poles, the highly compliant pole results in reduced peak ground reaction force, longer stance phase duration, and higher energy cost. The changes in running energetics are further found to depend on the natural frequency of the load-pole system relative to the step frequency, but with an opposite trend compared to the changes in walking energetics during pole carriage. Highly compliant poles cost more energy than rigid poles during running, while stiffer poles with a higher natural frequency may offer energetic benefits. This study indicates that the fundamental difference in gait type has a profound influence on the energetic performance of load-carrying devices and this should be taken into consideration in future device designs.