Understanding the dynamics of bipedal walking is essential for advancements in biomechanics and robotics. This study examines the impact of swing-leg dynamics on overall gait mechanics using an augmented inverted pendulum model that incorporates a swing leg and an upper-body segment (HAT). We hypothesized that the HAT segment compensates for swing-leg dynamics, thereby minimizing their effect on ground reaction forces (GRFs). Contrary to expectations, our findings reveal that the trunk contributes minimally to this compensation, leading to significant GRF modulation during active swing-leg propulsion. However, introducing an initial velocity to the swing leg during terminal stance markedly reduces these modulations, aligning simulated GRFs with experimental data for human walking. This result highlights the need to dynamically decouple the swing leg from upper-body dynamics to achieve efficient, human-like locomotion. The presented model provides a framework for optimizing bipedal gait designs in humanoid robotics and advancing our understanding of human biomechanics.

Animals have to navigate complex environments and perform intricate swimming maneuvers in the real world. To conquer these challenges, animals evolved a variety of motion control strategies. While it is known that many factors contribute to motion control, we specifically focus on the role of stretch sensory feedback. We investigate how stretch feedback potentially serves as a way to coordinate locomotion, and how different stretch feedback topologies, such as networks spanning varying ranges along the spinal cord, impact the locomotion. We conduct our studies on a simulated robot model of the lamprey consisting of an articulated spine with eleven segments connected by actuated joints. The stretch feedback is modeled with neural networks trained with deep reinforcement learning. We find that the topology of the feedback influences the energy efficiency and smoothness of the swimming, along with various other metrics characterizing the locomotion, such as frequency, amplitude and stride length. By analyzing the learned feedback networks, we highlight the importances of very local, caudally-directed, as well as stretch derivative information. Our results deliver valuable insights into the potential mechanisms and benefits of stretch feedback control and inspire novel decentralized control strategies for complex robots.

During walking, the brain and nervous system coordinate muscle activity to efficiently regulate body movement. Simultaneously, passive structures in the legs interact with the ground, generating reaction forces that contribute to leg and body motion. A well-known example of this active-passive coordination is the human ankle, which plays a crucial role in propelling both the leg and the entire body forward with each step. Human walking efficiency relies on the elastic recoil of the Achilles tendon, facilitated by a “catapult mechanism” that stores energy during stance and releases it during push-off. The catapult release mechanism could include the passive flexion of the knee, as the main part of knee flexion was reported to happen passively after leading leg touch-down. This study is the first to investigate the effects of passive versus active knee flexion initiation, using the bipedal EcoWalker-2 robot with passive ankles. By leveraging the precision of robotic measurements, this study aimed to elucidate the importance of timing of gait events and its impact on momentum and kinetic energy changes of the robot. The EcoWalker-2 walked successfully with both initiation methods, maintaining toe clearance. Passive knee flexion initiation delayed the onset of ankle plantar flexion by 3% of the gait cycle compared to active knee flexion initiation, leading to 87% larger increase in the trailing leg horizontal momentum, and 188% larger magnitude increase in the center of mass momentum vector during the step-to-step transition. The findings highlight the role of knee flexion in the release of the catapult and timing of gait events. These insights contribute to improving the control and mechanics of human-centered robotic and assistive devices. Specifically, enabling passive knee flexion initiation could be beneficial in humanoid robots with passive ankles, and in ankle-knee prostheses and orthoses with passive ankles for saving on control effort, and reducing hardware complexity otherwise required for active knee flexion before the step-to-step transition. Additionally, this approach enhances horizontal momentum gain in the trailing leg during the step-to-step transition, with the potential to improve locomotion efficiency.

Ankle push-off is important for efficient, human-like walking, and many prosthetic devices mimic push-off using motors or elastic elements. The knee is extended throughout the stance phase and begins to buckle just before push-off, with timing being crucial. However, the exact mechanisms behind this buckling are still unclear. We use a predictive neuromuscular simulation to investigate whether active muscles are required for knee buckling and to what extent ground reaction forces (GRFs) drive it. In a systematic parameter search, we tested how long the knee muscles vastus (VAS), gastrocnemius (GAS), and hamstrings could be deactivated while maintaining a stable gait with impulsive push-off. VAS deactivation up to 35% of the gait cycle resulted in a dynamic gait with increased ankle peak power. GAS deactivation up to 20% of the gait cycle was detrimental to gait efficiency and showed reduced ankle peak power. At the start of knee buckling, the GRF vector is positioned near the knee joint’s neutral axis, assisting in knee flexion. However, this mechanism is likely not enough to drive knee flexion independently. Our findings contribute to the biomechanical understanding of ankle push-off, with applications in prosthetic and bipedal robotic design, and fundamental research on human gait mechanics.

Predictive neuromuscular simulations are a powerful tool for studying the biomechanics of human walking, and deriving design criteria for technical devices like prostheses or biorobots. Good agreement between simulation and human data is essential for transferability to the real world. The human foot is often modeled with a single rigid element, but knowledge of how the foot model affects gait prediction is limited. Standardized procedures for selecting appropriate foot models are lacking. We performed 2D predictive neuromuscular simulations with six different foot models of increasing complexity to answer two questions: What is the effect of a mobile arch, a toe joint, and the coupling of toe and arch motion through the plantar fascia on gait prediction? and How much of the foot's anatomy do we need to model to predict sagittal plane walking kinematics and kinetics in good agreement with human data? We found that the foot model had a significant impact on ankle kinematics during terminal stance, push-off, and toe and arch kinematics. When focusing only on hip and knee kinematics, rigid foot models are sufficient. We hope our findings will help guide the community in modeling the human foot according to specific research goals and improve neuromuscular simulation accuracy.

The impulsive ankle push-off is crucial for natural leg dynamics and efficiency in human walking. To study the biomechanics of the ankle push-off, we use 2D predictive neuromuscular simulations. Assessing the sensitivity of model outputs to input variations is necessary to evaluate the reliability of model predictions. Sensitivity analysis (SA) can quantify how uncertainty in model outputs is related to different sources of uncertainty in model inputs. This work presents a new open-source software framework for global SA of predictive neuromuscular simulations using SCONE-Hyfydy and the SAFE toolbox. With the framework, we investigate how sensitive the ankle push-off and related gait characteristics are to variations in muscle-tendon unit (MTU) stiffness and tendon slack length (TSL) of Soleus (SOL), Gastrocnemius (GAS), and hip flexor muscles (HFL), the muscles active during push-off. To characterize the quality of the ankle push-off, we evaluate the models' maximum positive ankle power, maximum normalized cross-correlation of simulated ankle kinematics with human data to assess the signal similarity, cost of transport (CoT), and walking speed. Four different SA methods are compared: EET, FAST, PAWN, and VBSA. We found GAS MTU stiffness and TSL to have a significant impact on the models' CoT, walking speed, and ankle kinematics. Variations of SOL and HFL properties had limited to no effect on the assessed outputs. The four SA methods showed similar trends, but the computational costs and detailed results varied. With this work, we provide the biomechanics community with a software framework for SA of predictive neuromuscular simulations. Our results will improve the functional understanding of the ankle push-off, aiding in developing robotic devices and prostheses.

Some reductionist models match human walking dynamics surprisingly well. For reasons of simplicity, the swing leg and its dynamics have been neglected in the past. A dynamic effect would, however, be expected of the high acceleration and deceleration required to recirculate approximately 15% of the entire body mass during the very short swing phase. This paper documents the investigation of the effect of a simplified swing leg on the dynamics of a reductionist walking model. The findings suggest the dynamic decoupling of the swing leg and the remaining body.

Bipedal walking, the habitual gait for man, is rather unique in nature and poses particular challenges for balance and propulsion. The characteristic double-humped ground reaction force profile has been widely observed but not put into functional context. We propose a mathematical model that captures the dynamics of the human foot in walking including the characteristic motion of the center of pressure. Using this model, we analyze the functional interplay of all essential biomechanical contributors to foot dynamics in walking. Our results demonstrate the intricate interplay of a self-stabilizing mechanism which allows extending a leg's stance phase while simultaneously powering rapid swing by condensing the essentials of foot dynamics into a reductionist, biomechanical model. A theory is presented which identifies the foot to be the key functional element and which explains the global dynamics of human walking. The provided insights will impact gait therapy and rehabilitation, the development of assistive devices, such as leg prostheses and exoskeletons, and provide guidelines for the design and control of versatile humanoid robots.

Bipedal walking is the most prevalent form of human locomotion — versatile, robust, and efficient. However, it is a form of motion few other animals share, and plantigrade bipedalism is fairly unique to our species. Plantigrade feet play an important role in shaping the fundamental gait dynamics, and understanding their role unlocks a huge potential for biomechanical insights for locomotion research, gait rehabilitation, and humanoid robotics. Still, a comprehensive functional model of the foot, which ties the fundamental dynamics of walking to the interaction of foot and ground, does not yet exist due to the inherent mechanical complexity. In this paper, we present a set of assumptions in detail to simplify the development of a mathematical description of the foot’s motion during stance phase in human walking. These assumptions are validated using experimental data. We can show that the complex motion of the foot can be ultimately reduced to a simple rotation, which allows the formulation of a single degree of freedom equation of motion that ties proximal dynamics and constraints into a planar foot model of dynamic interactions.

For the impulsive ankle push-off (APO) observed in human walking two muscle-tendon-units (MTUs) spanning the ankle joint play an important role: Gastrocnemius (GAS) and Soleus (SOL). GAS and SOL load the Achilles tendon to store elastic energy during stance followed by a rapid energy release during APO. We use a neuromuscular simulation (NMS) and a bipedal robot to investigate the role of GAS and SOL on the APO. We optimize the simulation for a robust gait and then sequentially replace the MTUs of (1) GAS, (2) SOL and (3) GAS and SOL by linear springs. To validate the simulation, we implement NMS-3 on a bipedal robot. Simulation and robot walk steady for all trials showing an impulsive APO. Our results imply that the elastic MTU properties shape the impulsive APO. For prosthesis or robot design that is, no complex ankle actuation is needed to obtain an impulsive APO, if more mechanical intelligence is incorporated in the design.

Legged locomotion in humans is governed by natural dynamics of the human body and neural control. One mechanism that is assumed to contribute to the high efficiency of human walking is the impulsive ankle push-off, which potentially powers the swing leg catapult. However, the mechanics of the human lower leg with its complex muscle-tendon units spanning over single and multiple joints is not yet understood. Legged robots allow testing the interaction between complex leg mechanics, control, and environment in real-world walking gait. We developed a 0.49m tall, 2.2kg anthropomorphic bipedal robot with Soleus and Gastrocnemius muscle-tendon units represented by linear springs, acting as mono- and biarticular elastic structures around the robot's ankle and knee joints. We tested the influence of three Soleus and Gastrocnemius spring-tendon configurations on the ankle power curves, the coordination of the ankle and knee joint movements, the total cost of transport, and walking speed. We controlled the robot with a feed-forward central pattern generator, leading to walking speeds between 0.35m/s and 0.57m/s at 1.0Hz locomotion frequency, at 0.35m leg length. We found differences between all three configurations; the Soleus spring-tendon modulates the robot's speed and energy efficiency likely by ankle power amplification, while the Gastrocnemius spring-tendon changes the movement coordination between ankle and knee joints during push-off.

There are various simplifying models that describe balance strategies of human walking. In one model it is assumed that ground reaction forces are directed to a point (virtual pivot point) above the center of mass during the whole stride. This was observed in several experimental investigations, but only for the single support phase. It has not yet been concretely considered whether humans use the same stabilization strategy during the double support phase. For analyzing this, nine volunteers walked at self-selected speed while kinetic and kinematic data were measured. We found that in contrast to the single support phase, where the virtual pivot point was significantly above the center of mass, in the double support phase of human walking the ground reaction forces point around the center of mass with a small spread (R2=92.5%). The different heights of the virtual pivot point in the different support phases could be caused by the vertical movement of the center of mass, which has a lower amplitude in the double support phase. This is also reflected in the ground reaction forces, whereby the ratio of the horizontal and vertical ground reaction forces can explain the height of the virtual pivot point. In the double support phase the ratio is shifted in favor of the horizontal component compared to the single support phase, because of a shorter contact time and a delayed braking impulse. Thus, the whole body seems to rotate around the center of mass, which presumably minimizes required energy.

The purpose of this systematic review is to report the characteristics and methods utilized in human lower limb or knee joint only biomechanical models to provide state-of-the-art knowledge on the topic. This review was conducted according to the preferred reporting items for systematic reviews and meta-analyses guidelines. PubMed, Scopus and Web of Science were searched up to 24th April 2018 to look for musculoskeletal models of the human lower limb or knee joint only without any associated pathology. A 15-item checklist was used to assess the methodological quality of the included studies. Twenty-one studies were included, with seventeen of them modelling the lower limb and four only the knee joint. The methodological quality of the studies varied considerably, with the reporting of model characteristics showing very low quality. Among studies including experimental setup, subjects were instructed to perform vertical jumping, running at different speeds, drop landing and isokinetic knee extension (5%), static conditions (9%), knee’s flexion/extension (14%) and walking at constant (29%) and different (33%) speeds. A great variety of modelling strategies was found for the reproduction of the human musculoskeletal system in terms of number of segments, muscles and muscle models. The reviewed musculoskeletal models were able to reproduce human movement dynamics similar to results present in literature and to experimentally measured records. However, standardized methods for reporting the characteristics and methods of these models are missing and should be addressed in future studies.

Knee disorders are a fundamental problem in modern society. For this reason, the design of medical devices, such as an orthosis to provide rehabilitation, is of great importance. However, no significant effort has been made to design and model a compliant, weight-bearing knee exoskeleton that is suitable for the day-to-day activities but also sports. This paper presents a device capable of reducing the load experienced by the impaired knee. Its series elastic actuator was modeled to aid in the selection of the elastic stiffness (150 kN/m) and test the controller which displayed adequate tracking performance with a maximum provided torque of about 6 Nm. On the other hand, the actuator should be optimized in the future to meet the high torque operation demanded by the simulated biped model.

This work comprises the use of a biomechanical model of the human lower limb proposed by Geyer and Herr in 2010 to study joint characteristic parameters throughout physiological and anterior cruciate ligament (ACL) pathological gait. The model kinematics when simulating healthy gait were in good agreement with literature. Regarding to the kinetics, the ankle joint torque was corroborated with literature, while the hip and knee torques presented differences in magnitude and in shape. The implementation of pathology consisted of penalizing the torque produced by the muscles (quadriceps and hamstrings) affected by an ACL injury. Healthy and pathological cases were compared. Knee kinematic results for pathological gait were well reproduced, whilst the other kinematic and kinetic data diverged. This strategy aims at aiding the development of more efficient rehabilitation strategies to be prescribed after ACL injury. These and other issues will be object of study in the context of this investigation.

Wearable devices to assist abnormal gaits require controllers that interact with the user in an intuitive and unobtrusive manner. To design such a controller, we investigated a bio-inspired walking controller for orthoses and prostheses. We present (i) a Simulink neuromuscular control library derived from a computational model of reflexive neuromuscular control of human gait with a central pattern generator (CPG) extension, (ii) an ankle reflex controller for the Achilles exoskeleton derived from the library, and (iii) the mechanics and energetics of healthy subjects walking with an actuated ankle orthosis using the proposed controller. As this controller was designed to mimic human reflex patterns during locomotion, we hypothesize that walking with this controller would lead to lower energetic costs, compared to walking with the added mass of the device only, and allow for walking at different speeds without explicit control. Preliminary results suggest that the neuromuscular controller does not disturb walking dynamics in both slow and normal walking cases and can also reduce the net metabolic cost compared to transparent mode of the device. Reductions in tibialis anterior and soleus activity were observed, suggesting the controller could be suitable, in future work, for augmenting or replacing normal walking functions. We also investigated the impedance patterns generated by the neuromuscular controller. The validity of the equivalent variable impedance controller, particularly in stance phase, can facilitate serving subject-specific features by linking impedance measurement and neuromuscular controller.

ATRIAS is a human-scale 3D-capable bipedal robot designed to mechanically embody the spring-mass model for dynamic walking and running. To help bring the extensive work on this theoretical model further into practice, we present the design and validation of a spring-mass robot that can operate in real-world settings (i.e. off-tether and without planarizing restraints). We outline the mechanisms and design choices necessary to meet these specifications, particularly ATRIAS’ four-bar series-elastic leg design. We experimentally demonstrate the following robot capabilities, which are characteristics of the target model. 1) We present the robot’s physical capability for both grounded and aerial gaits, including planar walking and sustained hopping, while being more efficient than similarly gait-versatile bipeds. 2) The robot can be controlled by enforcing quantities derived from the simpler spring-mass model, such as leg angles and leg forces. 3) ATRIAS replicates the center-of-mass dynamics of human hopping and (novelly) walking, a key spring-mass model feature. Lastly, we present dynamically stable stepping in 3D without external support, demonstrating that this theoretical model has practical potential for real-world locomotion.

approved: Jonathan W. Hurst This thesis details the derivation and application of template-based controls on a bipedal robot, as well as a description of the software framework that enabled experimentation. The software framework uses a combination of open-source tools including ROS, ORO­ COS, EtherCAT, and Xenomai to create a real-time environment for the controllers. The first controller makes the robot (ATRIAS) walk as if it was the Spring Loaded In­ verted Pendulum (SLIP) model. This demonstrates that ATRIAS, which was designed to be as close to the SLIP model as possible, can behave similarly to the reduced-order model. While the first controller is implemented with a torso that is mechanically fixed in place, the second controller handles an unlocked torso, which adds another degree of freedom. This controller is implemented based on a Torso SLIP (TSLIP) reduced-order model. The controller imposes a Virtual Pivot Point (VPP) by redirecting ground reac­ tion forces to a geometrically fixed point with respect to the torso above the center of mass. Using VPP control, ATRIAS is able to take up to 22 steps on its own without using other techniques to keep its torso upright or inject energy, and it is shown that the generated ground reaction forces are similar to those produced by the reduced-order model. These controllers demonstrate that SLIP-like reduced-order control methods can be implemented on ATRIAS, and are a promising avenue for further research. ©Copyright by Andrew T. Peekema March 16, 2015 All Rights Reserved Template-Based Control of the Bipedal Robot ATRIAS

A common approach in designing legged robots is to build fully actuated machines and control the machine dynamics entirely in software, carefully avoiding impacts and expending a lot of energy. However, these machines are outperformed by their human and animal counterparts. Animals achieve their impressive agility, efficiency, and robustness through a close integration of passive dynamics, implemented through mechanical components, and neural control. Robots can benefit from this same integrated approach, but a strong theoretical framework is required to design the passive dynamics of a machine and exploit them for control. For this framework, we use a bipedal spring-mass model, which has been shown to approximate the dynamics of human locomotion. This paper reports the first implementation of spring-mass walking on a bipedal robot. We present the use of template dynamics as a control objective exploiting the engineered passive spring-mass dynamics of the ATRIAS robot. The results highlight the benefits of combining passive dynamics with dynamics-based control and open up a library of spring-mass model-based control strategies for dynamic gait control of robots.