Towards a Simulator Tool for Predicting Sprinting and Long Jump Motions with and without Running-Specific Prostheses: An Optimization-Based Approach

The performances of sprinters and long jumpers with below the knee amputation (BKA) have improved continuously since the development of prostheses specifically for athletic movements. In the last years, a number of athletes with BKA have attempted to compete in non-amputee competitions. Due to the specific shape and material properties of the running-specific prosthesis (RSP), concerns exist that it may give athletes an advantage over non-amputee athletes. In this work, we investigate and compare sprinting and long jump movements of athletes with and without unilateral BKA using accurate computer models. In this context, the aim of the work is to describe similarities and differences between the athletes’ movements and to show that the employed model- and optimization-based computations are useful for this purpose. We created subject-specific multi-body models for five different athletes (four non-amputee athletes, one athlete with unilateral BKA) in order to be able to investigate the different movements. Depending on the research question, the models vary in the number of degrees of freedom (DOFs), from 16 DOFs for a two-dimensional model in the sagittal plane to 31 DOFs for a three-dimensional model. For the athlete with BKA, we created a three-segment model of the RSP with one rotational DOF in the sagittal plane. The respective motion is described by a sequence of several phases, which differ by the type of ground contact. Each of these phases is described by its own set of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). We use multi-phase optimal control problems (OCPs) with discontinuities to generate sprint and long jump motions. Three different formulations of OCPs are adopted in this work. (1) We formulate a least squares OCP to reconstruct the dynamics of sprint and long jump motion capture recordings of the individual athletes. (2) For the generation of realistic motions, which can be used for prediction, we formulate a synthesis OCP; this optimizes an objective function consisting of a weighted combination of chosen optimization criteria. (3) Last, in the study of sprint movements, we use an inverse optimal control problem (IOCP): this consists of an inner loop, in which a synthesis OCP is solved, and an outer loop, which adjusts the weights of the individual optimization criteria such that the distance between the inner loop solution and a reference movement becomes minimal. We have successfully applied these three optimization problem formulations to the computation of two sprint steps of three athletes without and one athlete with unilateral transtibial amputation. Here, the movements of the non-amputee athletes differ from that of the amputee athlete in a large number of variables. In particular, the athletes use different actuation strategies for running with and without a RSP. We have observed lower torques in the amputee athlete in the leg affected by the amputation than in the non-amputee control group. In contrast, significantly larger torques occurred in the joints of the upper extremity in the amputee athlete. Furthermore, the comparison has shown that the asymmetry created by the RSP is reflected throughout the body and affects the entire movement. Using the OCPs for motion reconstruction (1) and synthesis (2), we have successfully computed the last three steps of the approach and the jump of a long jump for an athlete without and an athlete with unilateral amputation. In the reconstructed solutions, the amputee athlete achieves a greater jump distance compared to the non-amputee athlete, despite a slower approach velocity, because his take-off is more efficient. In the synthesis solutions, on the other hand, the non-amputee athlete achieves the greater jump distance because he generates a greater vertical force during the take-off and achieves a better ratio of gain of vertical to loss of horizontal velocity. Finally, we have presented our idea of a simulator tool to compare the amputee athlete with himself without amputation and have demonstrated it using the sprint and long jump movements. For this purpose, we have kept the model of the athlete with unilateral transtibial amputation from the previous studies and have created a non-amputee version of the same model by mirroring the biological leg. We have selected one objective function each for sprinting and for long jump and have solved the OCP for motion synthesis (2) for both model versions. Using the differences to the solutions based on the models of two real athletes, we have highlighted the importance of the simulator tool in the evaluation of advantages and disadvantages due to the use of the RSP

Simulation of gait asymmetry and energy transfer efficiency between unilateral and bilateral amputees

Efficient walking or running requires symmetrical gait. Gait symmetry is one of the key factors in efficient human dynamics, kinematics and kinetics. The desire of individuals with a lower-limb amputation to participate in sports has resulted in the development of energy-storing and-returning (ESR) feet. This paper analyses a case study to show the effect of symmetry and asymmetry as well as energy transfer efficiency during periodic jumping between simulated bilateral and unilateral runners. A custom gait analysis system is developed as part of this project to track the motion of the body of a physically active subject during a set of predefined motions. Stance and aerial times are accurately measured using a high speed camera. Gait frequency, the level of symmetry and the non-uniform displacement between left and right foot and their effects on the position of the Centre of Mass (CM) were used as criteria to calculate both peak energies and transformation efficiency. Gait asymmetry and discrepancy of energy transfer efficiency between the intact foot and the ESR are observed. It is concluded that unilateral runners require excessive effort to compensate for lack of symmetry as well as asymmetry in energy transfer, causing fatigue which could be a reason why bilateral amputee runners using ESR feet have a superior advantage over unilateral amputees

Towards understanding human locomotion

Die zentrale Frage, die in der vorliegenden Arbeit untersucht wurde, ist, wie man die komplizierte Dynamik des menschlichen Laufens besser verstehen kann. In der wissenschaftlichen Literatur werden zur Beschreibung von Laufbewegungen (Gehen und Rennen) oftmals minimalistische "Template"-Modelle verwendet. Diese sehr einfachen Modelle beschreiben nur einen ausgewählten Teil der Dynamik, meistens die Schwerpunktsbahn. In dieser Arbeit wird nun versucht, mittels Template-Modellen das Verständnis des Laufens voranzubringen. Die Analyse der Schwerpunktsbewegung durch Template-Modelle setzt eine präzise Bestimmung der Schwerpunktsbahn im Experiment voraus. Hierfür wird in Kapitel 2.3 eine neue Methode vorgestellt, welche besonders robust gegen die typischen Messfehler bei Laufexperimenten ist. Die am häfigsten verwendeten Template-Modelle sind das Masse-Feder-Modell und das inverse Pendel, welche zur Beschreibung der Körperschwerpunktsbewegung gedacht sind und das Drehmoment um den Schwerpunkt vernachlässigen. Zur Beschreibung der Stabilisierung der Körperhaltung (und damit der Drehimpulsbilanz) wird in Abschnitt 3.3 das Template-Modell "virtuelles Pendel" für das menschliche Gehen eingeführt und mit experimentellen Daten verglichen. Die Diskussion möglicher Realisierungsmechanismen legt dabei nahe, dass die Aufrichtung des menschlichen Gangs im Laufe der Evolution keine große mechanische Hürde war. In der Literatur wird oft versucht, Eigenschaften der Bewegung wie Stabilität durch Eigenschaften der Template-Modelle zu erklären. Dies wird in modifizierter Form auch in der vorliegen Arbeit getan. Hierzu wird zunächst eine experimentell bestimmte Schwerpunktsbewegung auf das Masse-Feder-Modell übertragen. Anschließend wird die Kontrollvorschrift der Schritt-zu-Schritt-Anpassung der Modellparameter identifiziert sowie eine geeignete Näherung angegeben, um die Stabilität des Modells, welches mit dieser Kontrollvorschrift ausgestattet wird, zu analysieren. Der Vergleich mit einer direkten Bestimmung der Stabilität aus einem Floquet-Modell zeigt qualitativ gute Übereinstimmung. Beide Ansätze führen auf das Ergebnis, dass beim langsamen menschlichen Rennen Störungen innerhalb von zwei Schritten weitgehend abgebaut werden. Zusammenfassend wurde gezeigt, wie Template-Modelle zum Verständnis der Laufbewegung beitragen können. Gerade die Identifikation der individuellen Kontrollvorschrift auf der Abstraktionsebene des Masse-Feder-Modells erlaubt zukünftig neue Wege, aktive Prothesen oder Orthesen in menschenähnlicher Weise zu steuern und ebnet den Weg, menschliches Rennen auf Roboter zu übertragen.Human locomotion is part of our everyday life, however the mechanisms are not well enough understood to be transferred into technical devices like orthoses, protheses or humanoid robots. In biomechanics often minimalistic so-called template models are used to describe locomotion. While these abstract models in principle offer a language to describe both human behavior and technical control input, the relation between human locomotion and locomotion of these templates was long unclear. This thesis focusses on how human locomotion can be described and analyzed using template models. Often, human running is described using the SLIP template. Here, it is shown that SLIP (possibly equipped with any controller) cannot show human-like disturbance reactions, and an appropriate extension of SLIP is proposed. Further, a new template to describe postural stabilization is proposed. Summarizing, this theses shows how simple template models can be used to enhance the understanding of human gait

A Biomechanical Analysis of Back Squats: Motion Capture, Electromyography, and Musculoskeletal Modeling

Previous literature evaluating maximal back squats have failed to identify key components of the study decisions and procedures that would allow for duplication. Firstly, the existence of a sticking region in maximally weighted resistance exercises is frequently discussed and has been described as a force-reduced transition phase between an acceleration phase and a strength phase of a lift. However, the etiology has yet to be agreed upon. Second, Electromyography (EMG) is frequently used to assess muscle activations. However, no best practice for EMG normalization has been proposed. Two methods are commonly implemented for normalizing EMG: a maximum voluntary isometric contraction (MVIC) and a dynamic maximum during the task being performed (DMVC). Finally, musculoskeletal modeling software has been increasingly utilized to evaluate muscle forces during weighted back squats. The quality of analyses of muscle forces, excitation, etc. are dependent upon inverse kinematics (IK). However, the methods used when examining IKs have also been short on details making duplication impossible. This dissertation is in a multiple-article (n=3) format. The first two studies are published in refereed journals. These studies 1) determined the effects of load on lower extremity biomechanics during back squats, 2) examined the influence of normalization method on rectus femoris, vastus medialis, and biceps femoris activations during back squats, and 3) compared different inverse kinematic strategies for calculating hip, knee, ankle, and foot kinematics utilized in modeling of the back squat. For all studies, participants performed the NSCA’s one-repetition maximum (1RM) testing protocol. Three-dimensional motion capture (trunk, pelvis, and lower extremity), force dynamometry (force plates), and EMG were recorded during all squats. The results of these studies found 1) vertical acceleration was a better discriminative measure than velocity for identifying the sticking region and there is a clear transition from knee to hip dominance for successful maximal squats, 2) the DMVC was more reliable and less variable than MVIC for normalizing EMG, and 3) creating a weld constraint between the foot and the floor results in the most closely matched foot kinematics to the DK results of the methods assessed. These results indicate that 1) submaximum squats performed at increased velocities can provide similar moments at the ankle and knee, but not hip, as maximal loads, 2) significant emphasis on hip strength is necessary for heavy back squats, 3) normalization to DMVC is the superior method for weighted exercises, and 4) while the Weld model IKs most closely matched the foot DK results, the untenable ankle kinematics the Weld model produced demonstrated it might be the superior choice for modeling foot IKs, but not ankle IKs in maximally weighted back squats

Development and application of an optimization model for elite level shot putting

Shot putting is one of the most ancient forms of athletic competition. Considerable research has been performed on the event. Despite this fact, research examining performance in the women’s shot put and using the spin technique is very limited. Also, only one attempt has been made to optimize the movement of elite shot putting and no attempts have been made to use the optimization model as a standard for technical training intervention. A series of three experiments were used to explore the development of an optimization model for shot putting and its application as a basis for technical intervention for elite athletes. Experiment 1 served as an exploratory study that explored the feasibility of developing an optimization model for shot putting. The results indicated that there are 8 variables that are highly linked with performance in the shot put and supported the notion that an optimization model for the shot put could be developed. Experiment 2 expanded on and validated the findings of the first study. Results of this study yielded a five variable optimization model for the shot put. Finally, Experiment 3 sought to apply the optimization model developed in Experiment 2 to elite athletes. The results indicated that a technical intervention based on an optimization model produces meaningful changes in performance that can be attributed to changes in optimization model parameters

Advancing Musculoskeletal Robot Design for Dynamic and Energy-Efficient Bipedal Locomotion

Achieving bipedal robot locomotion performance that approaches human performance is a challenging research topic in the field of humanoid robotics, requiring interdisciplinary expertise from various disciplines, including neuroscience and biomechanics. Despite the remarkable results demonstrated by current humanoid robots---they can walk, stand, turn, climb stairs, carry a load, push a cart---the versatility, stability, and energy efficiency of humans have not yet been achieved. However, with robots entering our lives, whether in the workplace, in clinics, or in normal household environments, such improvements are increasingly important. The current state of research in bipedal robot locomotion reveals that several groups have continuously demonstrated enhanced locomotion performance of the developed robots. But each of these groups has taken a unilateral approach and placed the focus on only one aspect, in order to achieve enhanced movement abilities;---for instance, the motion control and postural stability or the mechanical design. The neural and mechanical systems in human and animal locomotion, however, are strongly coupled and should therefore not be treated separately. Human-inspired musculoskeletal design of bipedal robots offers great potential for enhanced dynamic and energy-efficient locomotion but also imposes major challenges for motion planning and control. In this thesis, we first present a detailed review of the problems related to achieving enhanced dynamic and energy-efficient bipedal locomotion, from various important perspectives, and examine the essential properties of the human locomotory apparatus. Subsequently, existing insights and approaches from biomechanics, to understand the neuromechanical motion apparatus, and from robotics, to develop more human-like robots that can move in our environment, are discussed in detail. These thorough investigations of the interrelated essential design decisions are used to develop a novel design for a musculoskeletal bipedal robot, BioBiped1, such that, in the long term, it is capable of realizing dynamic hopping, running, and walking motions. The BioBiped1 robot features a highly compliant tendon-driven actuation system that mimics key functionalities of the human lower limb system. In experiments, BioBiped1's locomotor function for the envisioned gaits is validated globally. It is shown that the robot is able to rebound passively, store and release energy, and actively push off from the ground. The proof of concept of BioBiped1's locomotor function, however, marks only the starting point for our investigations, since this novel design concept opens up a number of questions regarding the required design complexity for the envisioned motions and the appropriate motion generation and control concept. For this purpose, a simulator specifically designed for the requirements of musculoskeletally actuated robotic systems, including sufficiently realistic ground reaction forces, is developed. It relies on object-oriented design and is based on a numerical solver, without model switching, to enable the analysis of impact peak forces and the simulation of flight phases. The developed library also contains the models of the actuated and passive mono- and biarticular elastic tendons and a penalty-based compliant contact model with nonlinear damping, to incorporate the collision, friction, and stiction forces occurring during ground contact. Using these components, the full multibody system (MBS) dynamics model is developed. To ensure a sufficiently similar behavior of the simulated and the real musculoskeletal robot, various measurements and parameter identifications for sub-models are performed. Finally, it is shown that the simulation model behaves similarly to the real robot platform. The intelligent combination of actuated and passive mono- and biarticular tendons, imitating important human muscle groups, offers tremendous potential for improved locomotion performance but also requires a sophisticated concept for motion control of the robot. Therefore, a further contribution of this thesis is the development of a centralized, nonlinear model-based method for motion generation and control that utilizes the derived detailed dynamics models of the implemented actuators. The concept is used to realize both computer-generated hopping and human jogging motions. Additionally, the problem of appropriate motor-gear unit selection prior to the robot's construction is tackled, using this method. The thesis concludes with a number of simulation studies in which several leg actuation designs are examined for their optimality with regard to systematically selected performance criteria. Furthermore, earlier paradoxical biomechanical findings about biarticular muscles in running are presented and, for the first time, investigated by detailed simulation of the motion dynamics. Exploring the Lombard paradox, a novel reduced and energy-efficient locomotion model without knee extensor has been simulated successfully. The models and methods developed within this thesis, as well as the insights gained, are already being employed to develop future prototypes. In particular, the optimal dimensioning and setting of the actuators, including all mono- and biarticular muscle-tendon units, are based on the derived design guidelines and are extensively validated by means of the simulation models and the motion control method. These developments are expected to significantly enhance progress in the field of bipedal robot design and, in the long term, to drive improvements in rehabilitation for humans through an understanding of the neuromechanics underlying human walking and the application of this knowledge to the design of prosthetics

Quantification of knee extensor muscle forces: a multimodality approach

Given the growing interest of using musculoskeletal (MSK) models in a large number of clinical applications for quantifying the internal loading of the human MSK system, verification and validation of the model’s predictions, especially at the knee joint, have remained as one of the biggest challenges in the use of the models as clinical tools. This thesis proposes a methodology for more accurate quantification of knee extensor forces by exploring different experimental and modelling techniques that can be used to enhance the process of verification and validation of the knee joint model within the MSK models for transforming the models to a viable clinical tool. In this methodology, an experimental protocol was developed for simultaneous measurement of the knee joint motion, torques, external forces and muscular activation during an isolated knee extension exercise. This experimental protocol was tested on a cohort of 11 male subjects and the measurements were used to quantify knee extensor forces using two different MSK models representing a simplified model of the knee extensor mechanism and a previously-developed three-dimensional MSK model of the lower limb. The quantified knee extensor forces from the MSK models were then compared to evaluate the performance of the models for quantifying knee extensor forces. The MSK models were also used to investigate the sensitivity of the calculated knee extensor forces to key modelling parameters of the knee including the method of quantifying the knee centre of rotation and the effect of joint translation during motion. In addition, the feasibility of an emerging ultrasound-based imaging technique (shear wave elastography) for direct quantification of the physiologically-relevant musculotendon forces was investigated. The results in this thesis showed that a simplified model of the knee can be reliably used during a controlled planar activity as a computationally-fast and effective tool for hierarchical verification of the knee joint model in optimisation-based large-scale MSK models to provide more confidence in the outputs of the models. Furthermore, the calculation of knee extensor muscle forces has been found to be sensitive to knee joint translation (moving centre of rotation of the knee), highlighting the importance of this modelling parameter for quantifying physiologically-realistic knee muscle forces in the MSK models. It was also demonstrated how the movement of the knee axis of rotation during motion can be used as an intuitive tool for understanding the functional anatomy of the knee joint. Moreover, the findings in this thesis indicated that the shear wave elastography technique can be potentially used as a novel method for direct quantification of the physiologically-relevant musculotendon forces for independent validation of the predictions of musculotendon forces from the MSK models.Open Acces

Estimation des forces musculaires du membre supérieur humain par optimisation dynamique en utilisant une méthode directe de tir multiple

La modélisation musculo-squelettique permet d’estimer les forces internes du corps humain, à savoir, les forces musculaires et articulaires. Ces estimations sont nécessaires pour comprendre l’anatomie fonctionnelle, les mécanismes de blessures ou encore de concevoir des aides techniques à la motricité. Le défi est d’utiliser l’ensemble des données biomécaniques existantes pour prédire des forces internes qui tiennent compte des stratégies neuro-musculo-squelettiques propres à chacun. L’objectif de cette thèse était d’estimer les forces musculaires du membre supérieur humain par optimisation dynamique, en proposant une méthode innovante de suivi simultané des données électromyographiques (EMG) et cinématiques. À cet égard, nos quatre objectifs spécifiques étaient de : (1) résoudre ce problème d’optimisation dynamique en utilisant une méthode directe de tir multiple ; (2) déterminer sa pertinence et sa performance par rapport aux autres algorithmes existants ; (3) valider son applicabilité à des données expérimentales ; et (4) caractériser des techniques d’identification (numériques et expérimentales) des propriétés musculaires, notamment à l’aide d’un ergomètre isocinétique. Nos différentes études ont permis d’établir que, en un temps de calcul raisonnable (~ 1 heure), notre nouvelle méthode de suivi simultané en optimisation dynamique est à-même de reproduire la cinématique attendue avec une précision de l’ordre de 5°. En outre, l'erreur quadratique moyenne sur les forces musculaires a été réduite d’au moins cinq fois avec notre nouvelle méthode, comparativement aux optimisations statique, hybride et dynamique reposant sur des fonctions-objectif de moindres-activations/excitations (erreur sur les forces musculaires de 18,45 ± 12,60 N avec notre nouvelle méthode contre 85,10 ± 116,40 N avec une optimisation hybride faisant le suivi des moments articulaires). Notre algorithme a également montré son efficacité lors de l’identification des propriétés musculaires d’un modèle musculo-squelettique générique : ce faisant, des excitations musculaires avec deux fois moins d’erreurs vis-à-vis de l’EMG expérimental ont été obtenues, comparativement à l’optimisation statique. Finalement, en termes de calibration du modèle musculo-squelettique, nous avons pu établir que la mesure expérimentale du moment articulaire à l’épaule au moyen de l’ergomètre isocinétique est inadéquate, en particulier lors de mouvements de rotation interne/externe de l’épaule. En effet, les composantes en flexion et abduction du moment à l’épaule mesurées par l’ergomètre isocinétique sont significativement sous-estimées (jusqu'à 94,9% par rapport au moment résultant calculé à partir des efforts tridimensionnels à la main et au coude, mesurés par des capteurs de force six axes). Par conséquent, cette thèse a mis en évidence l’importance du suivi simultané de l’EMG et de la cinématique en optimisation dynamique, afin de rendre fiables les estimations de forces musculaires du membre supérieur – notamment, dans les cas de forte co-contraction musculaire. Elle également a permis d’établir des recommandations qui serviront lors de la calibration du modèle à partir de l’ergomètre isocinétique. Notre méthode innovante pourra être appliquée à des populations pathologiques, afin de comprendre la pathomécanique et mieux intervenir auprès des professionnels de la santé et de leurs patients.Musculoskeletal modeling is used to estimate the internal forces of the human body, namely, muscle and joint forces. These estimates are necessary to understand functional anatomy and pathogenesis or to design technical devices supporting the movement. The challenge is to use all existing biomechanical data to predict internal forces that account for the neuro-musculoskeletal strategies of each individual. The purpose of this thesis was to estimate the human upper-limb muscles forces using forward dynamic optimisation. To do so, we proposed an innovative method tracking both electromyographic (EMG) and kinematic data directly into the optimisation objective-function. In this regard, our four specific objectives were: (1) solving the forward-dynamic optimisation problem using a direct multiple shooting method; (2) determining its relevance and performance compared to other existing algorithms in the literature; (3) validating its applicability to experimental data; and (4) characterizing techniques to identify the model muscle properties using the isokinetic dynamometer. In our different studies, we have demonstrated that, in a reasonable computation time (~ 1 hour), our new dynamic-optimisation method is able to predict the joint kinematics with an accuracy of about 5°. In addition, the muscle forces root-mean-square error was reduced by at least five times with our new method compared to static, hybrid, and dynamic optimisations based on least-activations/excitations objective-functions (muscle forces error of 18.45 ± 12.60 N with our new method vs. 85.10 ± 116.40 N with a traditional hybrid optimisation tracking the joint torques). Our new algorithm also proved to be efficient in identifying the muscle properties of a generic musculoskeletal model: in doing so, the error between the optimised muscle excitations and the experimental EMG was two time lower than the one obtained with static optimisation. Finally, regarding the calibration of the musculoskeletal model, we established that the experimental joint torque measurement at the shoulder using the isokinetic dynamometer was not suitable, especially during internal/external rotation movements of the shoulder. In fact, the flexion and abduction components of the shoulder torque measured by the isokinetic dynamometer are significantly underestimated (up to 94.9% compared to the resulting torque calculated from the three-dimensional forces at the hand and at the elbow, measured by six-axis force sensors). Therefore, this thesis has emphasized the importance of tracking both EMG and kinematics in dynamic optimisation, in order to make reliable estimations of the upper-limb muscle forces – specifically when high co-contraction occurs. Besides, recommendations were issued about calibrating the musculoskeletal model from the experimental torques measured with the isokinetic dynamometer. It will be possible to apply our innovative forward-dynamic optimisation method to pathological populations to increase understanding of the pathomechanics of human movement and better assist health professionals and their patients