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Purpose: This study aimed to present a preliminary case analysis of the impact of regular and irregular exercise on autonomic regulation and cardiorespiratory performance in young women by comprehensively investigating the nocturnal heart rate variability (HRV) parameters. Methods: Two young female participants were monitored using noncontact ballistocardiography technology to assess their nocturnal HRV daily for 32 weeks. Participant 1 was a 28-year-old woman who engaged in regular running (approximately three times a week, 5km each time), and participant 2 was a 24-year-old woman who participated in irregular running (typically ≤3 times a week, 5km each time). Additionally, cardiorespiratory fitness was evaluated through maximal oxygen uptake (VO₂max), with running data and VO₂max measurements recorded using a wrist bracelet device. Results: During the experiment, the VO₂max value of participant 1 increased by 11.46%, whereas that of participant 2 increased by 3.42%. A correlation was observed between VO₂max and HRV, particularly in the high-frequency (HF) component. The correlation coefficient between ln HF and VO₂max of participant 1 was 0.64, whereas that of participant 2 was 0.28. Additionally, participant 1 exhibited lower HRV complexity than participant 2, with fuzzy entropy values for ln HF of 0.12 and 0.35, respectively. Conclusions: Long-term assessment revealed a correlation between VO₂max and nocturnal HRV in young female exercisers, particularly for the HF index. However, these findings may not apply to other populations, such as men or older individuals.

We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.

The spring-mass model is a frequently used gait template to describe human and animal locomotion. In this study, we transform the spring-mass model for running into a boundary value problem and use it for the computation of bifurcation points. We show that the analysis of the region of stable solutions can be reduced to the calculation of its boundaries. Using the new bifurcation approach, we investigate the influence of asymmetric leg parameters on the stability of running. Like previously found in walking, leg asymmetry does not necessarily restrict the range of stable running and may even provide benefits for system dynamics.

A previous study found that the patellofemoral joint compressive force (PFJRF) during backward running was less than during forward running at a self-selected speed. Therefore, the purpose of this study was to compare the patellofemoral joint compressive forces during backward and forward running at the same speed. Ten runners (four females, six males) between the ages of 20–25 (X=22.25, SD=2.25) ran in backward and forward directions at a very slow speed of 2.3 mph (1.0 ms^-1). Using a mathematical model of patellofemoral joint that does not assume equal forces of the quadriceps and patellar tendon, the PFJRFs during the very slow backward and forward running were calculated. Results showed that the PFJRF and knee extensor moment during backward and forward running were similar. The PFJRF and knee extensor moment were 3.51 BW and 144.52 Nm, respectively, during the very slow backward running, and 3.41 BW and 141.60 Nm, respectively, during the very slow forward running. In conclusion, slow backward and forward running put similar compressive forces on the patellofemoral joint. Moreover, backward running does not protect the patellofemoral joint from higher compression forces, but very slow speed does.

The aim of this study was to determine changes of peak pressure, maximal force, and contact area in five foot regions with two different insoles during walking and running, thereby obtaining data contributing to optimization of footwear and reduction of lower leg injury.

Twenty-six male soldiers participated in the study. Peak pressure, maximal force, and contact area were measured in five foot regions (lateral and medial heel, midfoot, lateral and medial forefoot, big toe, and toes 2, 3, 4, and 5) with two different insoles (conventional vs. custom molded shock-absorbing insoles) during a walking speed of 5 km/h and running speeds of 8 and 12 km/h using the Pedar-X tensometric system (Novel, St. Paul, MN). Measurements revealed that the shock-absorbing insoles significantly (p < 0.05) attenuated the peak pressures in heel and forefoot region and increased the contact area in the midfoot region which indicates a successful redistribution of forces that arise during the contact phase in walking and running. Shock-absorbing insoles hence may contribute to better plantar pressure distribution during walking and running, and effectively prevent lower leg injuries.

This study identifies the optimal crouched starting positions (elongated, medium, or bunched) from push-off to the first two steps. Seven elite sprinters were recruited as participants in this study (aged: 21$\pm$2 years). A high-speed camera (250Hz) was used to collect motion-based images on a sagittal plane. Kwon3D (software) was used to analyze the center of mass (COM) movement, step length, foot linear velocity, take-off angle, and trunk angle. Participants were tested in a 60m sprint for bunched, medium, and elongated starting positions. A one-way analysis of variance (ANOVA) ($\alpha =0.05$) with repeated measures was performed to determine the difference in kinematics in the three crouched starting positions. The LSD comparison was applied to examine differences among pairs of means. Our results indicated that the medium starting position demonstrated a greater first step length and foot linear velocity when compared to the bunched starting position. In the first step toe-off, a lower COM vertical velocity was observed in the medium starting position when compared with the elongated starting position. This study concluded that the medium starting position was the ideal starting position.

This study examined the influence of running shoe center of gravity relative position shifting forward and backward in sagittal axis on male amateur runners. Twenty-three adult male runners were recruited through social media with paid to participate in this study. The experimental shoe used was the Li Ning Feidian Challenger 3. Forward center of gravity (FCG), defined as the shoe center of gravity located at 10.8cm (15% before midpoint) from shoe toe to heel. Intermediate center of gravity (ICG), defined as the shoe center of gravity, is located at 14.8cm (midpoint) from shoe toe to heel. Backward center of gravity (BCG), defined as the shoe center of gravity, is located at 23.1cm (15% after midpoint) from shoe toe to heel. Questionnaire collection was used to assess the perception of the center of gravity shifting. Ground contact temporal, peak force/pressure of plantar and kinetics indicators data were simultaneously captured by motion capture system and force platform. Three participants (13.04%) correctly perceived the shoe center of gravity shifting forward and backward simultaneously. Shoes ICG peak force underneath Meta 1 increased significantly than BCG by 7.59% ($p<0.05$). Shoes FCG peak force underneath Meta 2 decreased significantly compared to ICG and BCG by 13.62% and 8.96% ($p<0.05$). Shoes BCG peak force underneath Meta 5 decreased significantly compared to ICG and FCG by 18.18% and 23.78% ($p<0.05$). Shoes FCG peak pressure underneath Meta 2 decreased significantly compared to ICG and BCG by 13.02% and 9.19% ($p<0.05$). Shoes FCG peak pressure underneath Meta 2 decreased significantly compared to ICG and BCG by 11.18% and 9.16% ($p<0.05$). However, there are no significant differences in kinetic indicators. The findings suggest that a fraction of participants can correct perceived shoe center of gravity shifting. Shoes’ FCG reduces force and pressure in the middle metatarsal regions. Shoes’ BCG reduces force in the lateral and medial metatarsal region. Healthcare professionals can optimize the design of footwear accordingly to improve rehabilitation outcomes and reduce injury risks in runners.

Technological advances in robotic hardware and software have enabled powered exoskeletons to move from science fiction to the real world. The objective of this article is to emphasize two main points for future research. First, the design of future devices could be improved by exploiting biomechanical principles of animal locomotion. Two goals in exoskeleton research could particularly benefit from additional physiological perspective: (i) reduction in the metabolic energy expenditure of the user while wearing the device, and (ii) minimization of the power requirements for actuating the exoskeleton. Second, a reciprocal potential exists for robotic exoskeletons to advance our understanding of human locomotor physiology. Experimental data from humans walking and running with robotic exoskeletons could provide important insight into the metabolic cost of locomotion that is impossible to gain with other methods. Given the mutual benefits of collaboration, it is imperative that engineers and physiologists work together in future studies on robotic exoskeletons for human locomotion.

This paper discusses the generation of a running pattern for a biped and verifies the validity of the proposed method of running pattern generation via experiments. When a running pattern is created with resolved momentum control, the angular momentum of the robot at the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To resolve this problem, the biped was set to a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual system was determined. Following this, a new periodic running pattern was formulated using the fixed point. The fixed point is easily determined using a numerical approach. In an experiment, the planar biped ran forward using the proposed pattern generation method for running. Its maximum velocity was 2.88 km/h. In the future, faster running of the biped will be realized in a planar plane and the biped will run in an actual environment.

This paper discusses the generation of a running pattern for a humanoid biped and verifies the validity of the proposed method of running pattern generation via experiments. Two running patterns are generated independently in the sagittal plane and in the frontal plane and the two patterns are then combined. When a running pattern is created with resolved momentum control in the sagittal plane, the angular momentum of the robot about the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To solve this problem, the biped was set as a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual under-actuated system was determined. Following this, a periodic running pattern in the sagittal plane was formulated using the fixed point. The fixed point is easily determined in a numerical approach. In this way, a running pattern in the frontal plane was also generated. In an experiment, a humanoid biped known as KHR-2 ran forward using the proposed running pattern generation method. Its maximum velocity was 2.88 km/h.

Human running can be stabilized in a wide range of speeds by automatically adjusting muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics. As the biped center of mass follows the mass of the mass-spring model, the whole biped performs a stable locomotion corresponding to SLIP model. Simulations are done to obtain a repeatable hopping for a three-link underactuated biped model. Results show that periodic hopping gaits can be stabilized, and the presented control strategy provides feasible gait trajectories for stance and swing phases.

This paper documents the mechanical system of the electric cable differential (ECD) leg, and its incorporation into a monopod hopping robot named "Thumper" and a bipedal robot named "Mabel." The ECD leg is designed with physical springs and other passive dynamics to match a mathematically simple, bioinspired mass-spring model, which can exhibit robust and economic walking and running gaits. With this design approach, existing spring-mass theory-based controllers can be used to control the robot. The scientific goals of this work focus on finding an energetically optimal leg stiffness for running, and results from experimentation on Thumper and on a simulation of Thumper are presented.

Biomechanics research shows that the ability of the human locomotor system depends on the functionality of a highly compliant motor system that enables a variety of different motions (such as walking and running) and control paradigms (such as flexible combination of feedforward and feedback controls strategies) and reliance on stabilizing properties of compliant gaits. As a new approach of transferring this knowledge into a humanoid robot, the design and implementation of the first of a planned series of biologically inspired, compliant, and musculoskeletal robots is presented in this paper. Its three-segmented legs are actuated by compliant mono- and biarticular structures, which mimic the main nine human leg muscle groups, by applying series elastic actuation consisting of cables and springs in combination with electrical actuators. By means of this platform, we aim to transfer versatile human locomotion abilities, namely running and later on walking, into one humanoid robot design. First experimental results for passive rebound, as well as push-off with active knee and ankle joints, and synchronous and alternate hopping are described and discussed. BioBiped1 will serve for further evaluation of the validity of biomechanical concepts for humanoid locomotion.

Running robots often have their center-of-mass (CoM) of the torso located on the hip, to allow for simple control schemes. However, an offset between the CoM and the hip might increase a robot's ability to recover from disturbances. In this simulation study, we investigated the effect of the CoM-location on the largest disturbance that can be corrected within one or two steps. We found that, for one-step recovery strategies, the optimal CoM-location is above the hip for a step-down disturbance and below the hip for a push disturbance. For two-step recovery strategies, we found that the performance increases for increasing offset of the CoM. An offset of the CoM-location can increase the disturbance rejection up to a factor of 10 compared to the CoM at the hip.

Dynamic balance has to be maintained during motions of biped systems when their feet are in contact with the ground. As a necessary condition, this indicates that the calculated zero moment point (ZMP) position should be within the specified foot support region throughout the entire motion. A critical term in the ZMP formulation is the rate of angular momentum (RAM) for each link, which should be evaluated accurately and efficiently in motion planning and simulations. In this study, we propose a recursive Lagrangian method based on Denavit–Hartenberg convention to calculate the RAM for each link and the corresponding sensitivity. This method allows the evaluation of each link’s dynamic contribution to the ZMP position. The effectiveness of the proposed approach is demonstrated by simulating bipedal motions of walking and running along with their comparison against existing approaches (direct method and global force method). The accurate RAM calculation in ZMP based on the proposed approach resulted in the improved motion trajectories and reliable ground reaction forces for high-speed bipedal motion predictions.

Re-planning of gait trajectory is a crucial ability to compensate for external disturbances. To date, a large number of methods for re-planning footsteps and timing have been proposed. However, robots with the ability to change gait from walking to running or from walking to hopping were never proposed. In this paper, we propose a method for re-planning not only for footsteps and timing but also for the types of gait which consists of walking, running and hopping. The re-planning method of gait type consists of parallel computing and a ranking system with a novel cost function. To validate the method, we conducted push recovery experiments which were pushing in the forward direction when walking on the spot and pushing in the lateral direction when walking in the forward direction. Results of experiments showed that the proposed algorithm effectively compensated for external disturbances by making a gait transition.

Supporting the design process for running biped robots, analytical models are presented for two aspects of running: the duty factor (DF) of the gait, and the stiffness value of the leg. For a given running speed, an optimal DF exists that minimizes the energy expenditure. Based on a model of the energetics, we present a formula for the optimal DF. This formula is validated by both human data and simulation results. In addition, a model is presented for the stiffness value of the leg as a function of the physical properties, speed, and DF. The Gait Resonance Point is proposed as a design target for compliant running. At this point, the gait matches the spring resonance and the stiffness value becomes independent of the DF.

This paper investigates the relations between leg configuration and performance during running and walking operations. Specifically, we use standard kinematic techniques to visualize impact forces and kinetic energy loss during inelastic collisions with the environment in order to gain fundamental insights into robotic leg design. We show that for a two-link planar leg with revolute joints, a slightly crouched stance with a backward-facing knee (in contrast to humans) is optimal for both impact rejection and energy economy.

Soft ground is a ubiquitous hazard for legged locomotion and has yet to be conquered in a robust, dynamic, and economical manner. In search of a controller to meet these demands, we found that a simple force controller is energy optimal for spring-loaded running on unknown ground dissipation. The simplicity of this optimal controller suggests a fundamental insight into legged locomotion.

ATRIAS 1.0 is a spring-legged, monopod robot designed and built as a prototype towards a human-scale 3D biped. The monopod has to meet certain requirements concerning locomotion dynamics and energy efficiency to meet the goal of a biped that can autonomously walk and run efficiently and robustly outdoors, untethered over realistic (non-ideal) terrain. The design of ATRIAS 1.0 includes adequate control authority for robust locomotion as well as incorporating the idea of passive dynamics for high energy economy. Towards this effort, the passive dynamics of ATRIAS 1.0 are designed to match the key features of the Spring Loaded Inverted Pendulum model: a massless leg, mass centered at the hip joint, and a series spring between the ground and the mass at the hip joint. In this paper the authors discuss the key features of this unique robot design.