A robust sagittal plane hexapedal running model with serial elastic actuation and simple periodic feedforward control

In this article we present a sagittal plane, sprawled posture hexapedal running model with distributed body inertia, massless legs and serial elastic actuation at the hips as well as along the telescoping legs. We show by simulation that simple, periodic, feedforward controlled actuation is sufficient to obtain steady period 1 running gaits at twice the actuation frequency. We observe a nearly linear relation of average running speed and actuation frequency. The ground reaction profiles of the legs show leg specialization as observed in running insects. Interleg phasing has a strong influence on the foot fall sequence and thus the overall body dynamics. While the single leg ground reaction force profiles show little dependency on interleg actuation phase the total reaction force does. Thus, depending on the interleg actuation phase body motions without flight phase are observed as well as body motions and total ground reaction forces that show similarities to those obtained for the spring loaded inverted pendulum model. Further, we show that including leg damping and a ground friction model the periodic orbits have a large region of attraction with respect to the initial conditions. Additionally, the model quickly rejects step up and step down disturbances as well as force impulses. Finally, we briefly discuss the energetics of the hexapedal running model

The Dynamic characterisation of ESR prosthetic running feet: an investigation of the key parameters affecting their performance.

Prosthetic running feet (referred to as Energy Storing & Returning (ESR) or Running Specific Prostheses (RSP) but better known as ‘blades’) take the form of a carbon fibre leaf spring with a deflecting keel component. Available literature on the subject of their dynamic response is limited but suggests that the amputee with running foot can be considered to act in accordance with Simple Harmonic Motion, but this does not appear to be reflected by the prescription processes currently employed by manufacturers. The research question is asked: ‘Is the current method of prescribing prosthetic ESR running feet appropriate and are there additional factors that should be taken into consideration?’ This thesis aims to first understand the static mechanical characteristics of a single model of prosthetic foot; the Flex Run from Ossur (Reykjavik, Iceland). Previous works carried out (that aim to define the energy return efficiency of the devices but results vary from 63% - 100%) are examined and replicated using a series of fabricated jig fixtures, and the disparity in efficiency results is explained. The running action of an amputee is measured using a wearable measurement system that is developed as well as high-speed video capture. The measured action is then replicated in the laboratory using a rig capable of reproducing the dynamic response of the foot. This rig is subsequently used to manipulate the variables of Simple Harmonic Motion and evaluate the suitability of this assumption to model the running action of an amputee. The research concludes by using the gathered learning to create a tool capable of mathematically replicating the response of a prosthetic foot, and the application of such a tool is discussed. It is found during the course of the research that the available Flex Run feet possess an energy return efficiency of >99% and a variable stiffness along the length of the deflecting keel. As a contribution to knowledge, it was also found that during amputee running the ground contact point (and therefore effective stiffness) of the prosthetic changes significantly from foot strike through to toe-off and the profile of this change is defined. As such the principle of a spring-mass system cannot be applied in such a simplistic manner as previously suggested. Furthermore the relationship between amputee mass, stance length, foot deflection and response timing is defined for the first time. It was also discovered that the passive nature of the prosthetic device (and therefore fixed response) has the potential of limiting the top speed of running of an amputee and as such the current prescription method falls some way short of expectations. Methods of improving the prescription process are discussed and further work is suggested to improve the function of these prosthetic devices and therefore the user experience of the amputee athlete

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019

Bio-inspired swing leg control for spring-mass robots running on ground with unexpected height disturbance

We proposed three swing leg control policies for spring-mass running robots, inspired by experimental data from our recent collaborative work on ground running birds. Previous investigations suggest that animals may prioritize injury avoidance and/or efficiency as their objective function during running rather than maintaining limit-cycle stability. Therefore, in this study we targeted structural capacity (maximum leg force to avoid damage) and efficiency as the main goals for our control policies, since these objective functions are crucial to reduce motor size and structure weight. Each proposed policy controls the leg angle as a function of time during flight phase such that its objective function during the subsequent stance phase is regulated. The three objective functions that are regulated in the control policies are (i) the leg peak force, (ii) the axial impulse, and (iii) the leg actuator work. It should be noted that each control policy regulates one single objective function. Surprisingly, all three swing leg control policies result in nearly identical subsequent stance phase dynamics. This implies that the implementation of any of the proposed control policies would satisfy both goals (damage avoidance and efficiency) at once. Furthermore, all three control policies require a surprisingly simple leg angle adjustment: leg retraction with constant angular acceleration

Sex differences in limb and joint stiffnes in recreational runners

Purpose. Female runners are known to be at greater risk from chronic running injuries than age-matched males, although the exact mechanisms are often poorly understood. The aim of the current investigation was to determine if female recreational runners exhibit distinct limb and joint stiffness characteristics in relation to their male counterparts. Methods. Fourteen male and fourteen female runners ran over a force platform at 4.0 m · s–1. Lower limb kinematics were collected using an eight-camera optoelectric motion capture system operating at 250 Hz. Measures of limb and joint stiffness were calculated as a function of limb length and joint moments divided by the extent of limb and joint excursion. All stiffness and joint moment parameters were normalized to body mass. Sex differences in normalized limb and knee and ankle joint stiffness were examined statistically using independent samples t tests. Results. The results indicate that normalized limb (male = 0.18 ± 0.07, female = 0.37 ± 0.10 kN · kg · m–1) and knee stiffness (male = 5.59 ± 2.02, female = 7.34 ± 1.78 Nm · kg · rad–1) were significantly greater in female runners. Conclusions. On the basis that normalized knee and limb stiffness were shown to be significantly greater in female runners, the findings from the current investigation may provide further insight into the aetiology of the distinct injury patterns observed between sexes

Robustness: a new SLIP model based criterion for gait transitions in bipedal locomotion

Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In the current study, we introduce the robustness criterion which defines the conditions for stable locomotion when steps are taken with imprecise angle of attack. Intuitively, the necessity of a higher precision indicates the difficulty to continue moving with a given gait. We show that the spring-loaded inverted pendulum model, under the robustness criterion, is consistent with previously reported findings on attentional demand during human locomotion. This criterion allows transitions between running and walking, many of which conserve forward speed. Simulations of transitions predict Froude numbers below the ones observed in humans, nevertheless the model satisfactorily reproduces several biomechanical indicators such as hip excursion, gait duty factor and vertical ground reaction force profiles. Furthermore, we identify reversible robust walk-run transitions, which allow the system to execute a robust version of the hopping gait. These findings foster the spring-loaded inverted pendulum model as the unifying framework for the understanding of bipedal locomotion.Comment: unpublished, in preparatio

The influence of push-off timing in a robotic ankle-foot prosthesis on the energetics and mechanics of walking

Background: Robotic ankle-foot prostheses that provide net positive push-off work can reduce the metabolic rate of walking for individuals with amputation, but benefits might be sensitive to push-off timing. Simple walking models suggest that preemptive push-off reduces center-of-mass work, possibly reducing metabolic rate. Studies with bilateral exoskeletons have found that push-off beginning before leading leg contact minimizes metabolic rate, but timing was not varied independently from push-off work, and the effects of push-off timing on biomechanics were not measured. Most lower-limb amputations are unilateral, which could also affect optimal timing. The goal of this study was to vary the timing of positive prosthesis push-off work in isolation and measure the effects on energetics, mechanics and muscle activity. Methods: We tested 10 able-bodied participants walking on a treadmill at 1.25 m.s(-1). Participants wore a tethered ankle-foot prosthesis emulator on one leg using a rigid boot adapter. We programmed the prosthesis to apply torque bursts that began between 46% and 56% of stride in different conditions. We iteratively adjusted torque magnitude to maintain constant net positive push-off work. Results: When push-off began at or after leading leg contact, metabolic rate was about 10% lower than in a condition with Spring-like prosthesis behavior. When push-off began before leading leg contact, metabolic rate was not different from the Spring-like condition. Early push-off led to increased prosthesis-side vastus medialis and biceps femoris activity during push-off and increased variability in step length and prosthesis loading during push-off. Prosthesis push-off timing had no influence on intact-side leg center-of-mass collision work. Conclusions: Prosthesis push-off timing, isolated from push-off work, strongly affected metabolic rate, with optimal timing at or after intact-side heel contact. Increased thigh muscle activation and increased human variability appear to have caused the lack of reduction in metabolic rate when push-off was provided too early. Optimal timing with respect to opposite heel contact was not different from normal walking, but the trends in metabolic rate and center-of-mass mechanics were not consistent with simple model predictions. Optimal push-off timing should also be characterized for individuals with amputation, since meaningful benefits might be realized with improved timing

Don't break a leg: Running birds from quail to ostrich prioritise leg safety and economy in uneven terrain

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