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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.

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.

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 ( R 2 = 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.

This work comprises the use of a biomechanical model of the human lower limb proposed by Geyer and Herr in 2010, possessing the reproduction of the human skeletal, muscular and neural systems to simulate human gait. This approach was used to study characteristic parameters at joint level, such as range of motion and torques, during physiological and anterior cruciate ligament (ACL) pathological gait. The model kinematics when simulating healthy gait were in very good agreement with kinematics reported in literature. Regarding to the kinetics, the ankle joint torque plot was corroborated with literature, whilst the hip and knee torques presented differences both in magnitude and in shape. The implementation of pathology consisted of penalizing the torque produced by the muscles, namely the quadriceps and hamstrings, affected by an ACL injury after surgical reconstruction and rehabilitation. Healthy and pathological cases were compared. The variable closer to literature was the knee angle, whilst the other kinetic and kinematic data differed. This strategy aims at aiding the development of more efficient rehabilitation strategies to be prescribed after an ACL injury. These and other issues will be object of study in the context of this investigation.

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.

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.

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.

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics.

The human musculo-skeletal system comprises high complexity which makes it difficult to identify underlying basic principles of bipedal locomotion. To tackle this challenge, a common approach is to strip away complexity and formulate a reductive model. With utter simplicity a bipedal spring-mass model gives good predictions of the human gait dynamics, however, it has not been fully investigated whether center of mass motion over time of walking and running is comparable between the model and the human body over a wide range of speed. To test the model's ability in this respect, we compare sagittal center of mass trajectories of model and human data for speeds ranging from 0.5 m/s to 4 m/s. For simulations, system parameters and initial conditions are extracted from experimental observations of 28 subjects. The leg parameters stiffness and length are extracted from functional fitting to the subjects' leg force-length curves. With small variations of the touch-down angle of the leg and the vertical position of the center of mass at apex, we find successful spring-mass simulations for moderate walking and medium running speeds. Predictions of the sagittal center of mass trajectories and ground reaction forces are good, but their amplitudes are overestimated, while contact time is underestimated. At faster walking speeds and slower running speeds we do not find successful model locomotion with the extent of allowed parameter variation. We conclude that the existing limitations may be improved by adding complexity to the model.

The control system of a highly dynamic robot requires the ability to respond quickly to changes in the robot’s state. This type of system is needed in varying fields such as dynamic locomotion, multicopter control, and human-robot interaction. Robots in these fields require software and hardware capable of hard real-time, high frequency control. In addition, the application outlined in this paper requires modular components, remote guidance, and mobile control. The described system integrates a computer on the robot for running a control algorithm, a bus for communicating with microcontrollers connected to sensors and actuators, and a remote user interface for interacting with the robot. Current commercial solutions can be expensive, and open source solutions are often time consuming. The key innovation described in this paper is the building of a control system from existing — mostly open source — components that can provide realtime, high frequency control of the robot. This paper covers the development of such a control system based on ROS, OROCOS, and EtherCAT, its implementation on a dynamic bipedal robot, and system performance test results.

SummaryRapid unloading and a peak in power output of the ankle joint has been widely observed during push-off in human walking. Model based studies hypothesize this push-off to cause redirection of the body center of mass just before touch-down of the leading leg. Other research suggests, that work done by the ankle extensors provides kinetic energy for the initiation of swing. Also, muscle work is discussed to power a catapult-like action in late stance of human walking. However, there is a lack of knowledge about the biomechanical process leading to this widely observed high power output of the ankle extensors. In our study, we use kinematic and dynamic data of human walking collected at speeds between 0.5 and 2.5m/s for a comprehensive analysis of push-off mechanics. We identify two distinct phases, which divide the push-off: First, starting with positive ankle power output, an alleviation phase, where the trailing leg is alleviated from supporting the body mass, and second, a launching phase, where stored energy in the ankle joint is released. Our results show a release of just a small part of the energy stored in the ankle joint during the alleviation phase. A larger impulse for the trailing leg than for the remaining body is observed during the launching phase. Here, the buckling knee joint inhibits transfer of power from the ankle to the remaining body. It appears that swing initiation profits from an impulsive ankle push-off resulting from a catapult without escapement.

In biomechanics, explanatory template models are used to identify the basic mechanisms of human locomotion. However, model predictions often lack verification in a realistic environment. We present a method that uses template model mechanics as a blueprint for a bipedal robot and a corresponding computer simulation. The hypotheses derived from template model studies concerning the function of heel-off in walking are analysed and discrepancies between the template model and its real-world anchor are pointed out. Neither extending the ground clearance of the swinging leg nor an impact reduction at touch-down as an effect of heel lifting was supported by the experiments. To confirm the relevance of the experimental findings, a comparison of robot data to human walking data is discussed and we speculate on an alternative explanation of heel-off in human walking, i.e. that the push-off powers the following leg swing.

Biomechanical studies of human walking reveal that compliance plays an important role at least in natural and smooth motions as well as for self-stabilization. Inspired by this, we present here the development of a new lower leg segment of the dynamic biped robot “RunBot”. This new lower leg segment features a compliant ankle connected to a flat foot. It is mainly employed to realize robust self-stabilization in a passive manner. In general, such self-stabilization is achieved through mechanical feedback due to elasticity. Using real-time walking experiments, this study shows that the new lower leg segment improves dynamic walking behavior of the robot in two main respects compared to an old lower leg segment consisting of rigid ankle and curved foot: 1) it provides better self-stabilization after stumbling and 2) it increases passive dynamics during some stages of the gait cycle of the robot; i.e., when the whole robot moves unactuated. As a consequence, a combination of compliance (i.e., the new lower leg segment) and active components (i.e., actuated hip and knee joints) driven by a neural mechanism (i.e., reflexive neural control) enables RunBot to perform robust self-stabilization and at the same time natural, smooth, and energy-efficient walking behavior without high control effort.

The function of the locomotor system in human gait is still an open question. Today robot bipeds are not able to reproduce the versatility of human locomotion. In this article a robotic knee joint and an experimental setup are proposed. The leg function is tested and the acquired data is compared to human leg behaviour in running observed in experiments.

Robots of any kind, highly integrated mechatronic systems, are smart combinations of mechanics, electronics and information technology. The development of bipedal robots in particular, which perform human-like locomotion, challenges scientists on even higher levels. Facing this challenge, this article presents a biomimetic bottom-up approach to use knowledge of biomechanical experiments on human walking and running, computer simulation and neuronal control concepts to sequentially design highly adaptable and compliant walking machines.