An actuated dissipative spring-mass walking model: Predicting human-like ground reaction forces and the effects of model parameters

A simple model of human walking

Aim. We investigate Alexander’s inverted pendulum model, the simplest mathematical model of human walking. Although it successfully explains some kinematic features of human walking, such as the velocity of the body's centre of mass, it does not account for others, like the vertical reaction force and the maximum walking speed. This paper aims to minimally extend Alexander’s model in such a way as to make it a viable and quantitative model of human walking for clinical biomechanics.Material and methods. In order to compare the predictions of Alexander’s model with experimental data on walking, we incorporate in it a robust phenomenological relation between stride frequency and stride length derived in the literature, and we introduce a step-angle dependent muscle force along the pendulum. We then analytically solve the pendulum's motion equation and find the corresponding analytical expression for the average walking speed.Results. The values of the average walking speed for different heights predicted by our model are in excellent agreement with the ones obtained in treadmill experiments. Moreover, it successfully predicts the observed walking-running transition speed, which occurs when the stride length equals the height of an individual. Finally, our extended model satisfactorily reproduces the experimentally observed ground reaction forces in the midstance and terminal stance phases. Consequently, the predicted value of the (height-dependent) maximum walking speed is in reasonable agreement with the one obtained in more sophisticated models of human walking.Conclusions. Augmented with our minimal extensions, Alexander’s model becomes an effective and realistic model of human walking applicable in clinical investigations of the human gate.

Simultaneous Estimation of the Vertical Stiffness in the Knee and Hip for Healthy Human Subjects during Walking

The stiffness of lower limb joints is a critical characteristic of walking. To investigate the potential of establishing a simple and universal model to describe the characteristics related to vertical vibration during human walking, vertical stiffness is introduced at the knee and hip. A multi-mass-spring model of the human body is established in the vertical direction. In the Fourier form, results of experiments on 14 healthy adults show that the vertical displacements of joints are a function of the leg length and walking cadence, while the ground reaction force is a function of the body weight and walking cadence. The obtained universal equations of vertical displacement and ground reaction force are employed as the input parameters to the proposed multi-mass-spring model. Thus, the vertical stiffness in the knee and hip can then be estimated simultaneously by the subject's weight, leg length, and walking cadence. The variation of vertical stiffness shows different time-varying trends in different gait phases across the entire gait cycle. Finally, the proposed model for vertical stiffness estimation is validated by the vertical oscillation of the pelvis. The average error across three gait cycles for all subjects is 20.48%, with a standard deviation of 5.44%. These results display that the vertical stiffness of knee and hip across the entire gait cycle can be directly estimated by individual parameters that are easy to measure. It provides a different view of human walking analysis and may be applied in future pathological gait recognition, bipedal robots, and lower limb exoskeletons.

A novel implantable mechanism-based tendon transfer surgery for adult acquired flatfoot deformity: Evaluating feasibility in biomechanical simulation

Adult acquired flatfoot deformity becomes permanent with stage III posterior tibialis tendon dysfunction and results in foot pain and difficulty walking and balancing. To prevent progression to stage III posterior tibialis tendon dysfunction when conservative treatment fails, a flexor digitorum longus to posterior tibialis tendon transfer is often conducted. However, since the flexor digitorum longus only has one-third the force-capability of the posterior tibialis, an osteotomy is typically also required. We propose the use of a novel implantable mechanism to replace the direct attachment of the tendon transfer with a sliding pulley to amplify the force transferred from the donor flexor digitorum longus to the foot arch. In this work, we created four OpenSim models of an arched foot, a flatfoot, a flatfoot with traditional tendon transfer, and a flatfoot with implant-modified tendon transfer. Paired with these models, we developed a forward dynamic simulation of the stance phase of gait that reproduces the medial/lateral distribution of vertical ground reaction forces. The simulation couples the use of a fixed tibia, moving ground plane methodology with simultaneous activation of nine extrinsic lower limb muscles. The arched foot and flatfoot models produced vertical ground reaction forces with the characteristic double-peak profile of gait, and the medial/lateral distribution of these forces compared well with the literature. The flatfoot model with implant-modified tendon transfer produced a 94.2% restoration of the medial/lateral distribution of vertical ground reaction forces generated by our arched foot model, which also represents a 2.1X improvement upon our tendon transfer model. This result demonstrates the feasibility of a pulley-like implant to improve functional outcomes for surgical treatment of adult acquired flatfoot deformity with ideal biomechanics in simulation. The real-world efficacy and feasibility of such a device will require further exploration of factors such as surgical variability, soft tissue interactions and healing response.

Predicting ground reaction forces of human gait using a simple bipedal spring-mass model

Aircraft design must be lightweight and cost-efficient on the condition of aircraft certification. In addition to standard load cases, human-induced loads can occur in the aircraft interior. These are crucial for optimal design but difficult to estimate. In this study, a simple bipedal spring-mass model with roller feet predicted human-induced loads caused by human gait for use within an end-to-end design process. The prediction needed no further experimental data. Gait movement and ground reaction force (GRF) were simulated by means of two parameter constraints with easily estimable input variables (gait speed, body mass, body height). To calibrate and validate the prediction model, experiments were conducted in which 12 test persons walked in an aircraft mock-up under different conditions. Additional statistical regression models helped to compensate for bipedal model limitations. Direct regression models predicted single GRF parameters as a reference without a bipedal model. The parameter constraint with equal gait speed in experiment and simulation yielded good estimates of force maxima (error 5.3%), while equal initial GRF gave a more reliable prediction. Both parameter constraints predicted contact time very well (error 0.9%). Predictions with the bipedal model including full GRF curves were overall as reliable as the reference.

Measurement, Evaluation, and Control of Active Intelligent Gait Training Systems—Analysis of the Current State of the Art

Gait recognition and rehabilitation has been a research hotspot in recent years due to its importance to medical care and elderly care. Active intelligent rehabilitation and assistance systems for lower limbs integrates mechanical design, sensing technology, intelligent control, and robotics technology, and is one of the effective ways to resolve the above problems. In this review, crucial technologies and typical prototypes of active intelligent rehabilitation and assistance systems for gait training are introduced. The limitations, challenges, and future directions in terms of gait measurement and intention recognition, gait rehabilitation evaluation, and gait training control strategies are discussed. To address the core problems of the sensing, evaluation and control technology of the active intelligent gait training systems, the possible future research directions are proposed. Firstly, different sensing methods need to be proposed for the decoding of human movement intention. Secondly, the human walking ability evaluation models will be developed by integrating the clinical knowledge and lower limb movement data. Lastly, the personalized gait training strategy for collaborative control of human–machine systems needs to be implemented in the clinical applications.

Comparing system identification techniques for identifying human-like walking controllers

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

A model to predict ground reaction force for elastically-suspended backpacks

BACKGROUND

Leg muscle fatigue is the most important factor that affects walking endurance. Considering the legs act as actuators in alternate contact with the ground during walking, the ground reaction force (GRF) of each leg can indirectly reflect the strength of leg muscles. However, it is not clear how the elastically-suspended backpack (ESB) affects GRF of each leg during human level walking.

RESEARCH QUESTION

How is ESB related in GRF of each leg during walking, and how do multiple variables (stiffness and damping of ESB, load mass, walking speed) affect GRF?

METHODS

An extended bipedal walking model (EBW) with a spring-mass-damping system was proposed to predict the GRF of each leg. In order to evaluate the prediction effect of the model, seven healthy subjects were recruited to attend the experiments using our backpack prototype and the GRFs data was compared. Each subject walked under 12 conditions (load states: locked or unlocked, walking speed: 3.6 km/h, 4.0 km/h, 4.5 km/h, 5.0 km/h, 5.5 km/h, 6.0 km/h).

RESULTS

Results showed that the model could quantitatively predict experimental GRFs over the whole gait cycle (R²≥0.9628) and the characteristic forces (two peak forces and one trough force) were close to the experimental data (average predicted accuracy 93.7 %). The model can reflect relationships between variables and GRF. The relationships showed that an apparent tradeoff exists among the three characteristic forces, and the ESB can produce positive or negative effect under different variables.

SIGNIFICANCE

This work could help us understand the experimental GRF phenomena, especially the contradictory experimental phenomenon caused by the different parameters. It could also help designers optimize structural parameters of ESB for excellent effects on human. The ESBs with excellent performance can be wildly used in military and tourism.

The Influence of Different Loads on the Footbridge Dynamic Parameters

Bringing together the experience and knowledge of engineers allowed building modern footbridges as very slender structures. This in turn has led to structural vibration problems, which is a direct consequence of slender structures. In some footbridges, this problem occurs when natural construction frequencies are close to excitation frequencies. This requires a design methodology, which would ensure user safety and convenience of use of the footbridge in operation. Considering the aforementioned dynamic response, the analysis of the finite element model of a footbridge was conducted focusing on critical acceleration and deformation meanings. The model was based on the footbridge prototype located in Vilnius, Lithuania. Two different loading methods were developed to investigate the dynamic effects caused by people crossing a footbridge. The comparison of experimental and finite element model (FEM) results revealed that the footbridge in operation is within the limit values of comfort requirements in terms of its vibrations.