The dynamics of rigid body motion are dependent on the inertial properties of the body - that is, the mass and moment of inertia. For complex systems, it may be necessary to derive these results empirically. Such is the case for manual wheelchairs, which can be modeled as a rigid body frame connected to four wheels. While 3D modeling software is capable of estimating inertial parameters, modeling inaccuracies and ill-defined material properties may introduce significant errors in this estimation technique and necessitate experimental measurements. To that end, this thesis discusses the design of a device called the iMachine that empirically determines the mass, location of the center of mass, and moment of inertia about the vertical (yaw) axis passing through the center of mass of the wheelchair. The iMachine is a spring-loaded rotating platform that freely oscillates about an axis passing through its center due to an initial angular velocity. The mass and location of the center of mass can be determined using a static analysis of a triangular configuration of load cells. An optical encoder records the dynamic angular displacement of the platform, and the natural frequency of free vibration is calculated using several techniques. Finally, the moment of inertia is determined from the natural frequency of the system. In this thesis, test results are presented for the calibration of the load cells and spring rate. In addition, objects with known mass properties were tested and comparisons are made between the analytical and empirical inertia results. In general, the mass measurement of the test object had greater than 99% accuracy. The average relative error for the x and y-coordinates of the center of mass was 0.891% and 1.99%, respectively. For the moment of inertia, a relationship was established between relative error and the ratio of the test object inertia to the inertia of the system. The results suggest that 95% accuracy can be achieved if the test object accounts for at least 25% of the total inertia of the system. Finally, the moment of inertia of a manual wheelchair is determined using the device (I = 1.213 kg-m²), and conclusions are made regarding the reliability and validity of results. The results of this project will feed into energy calculations for the Anatomical Model Propulsion System (AMPS), a wheelchair-propelling robot used to measure the mechanical efficiency of manual wheelchairs.

[pt] Com o aumento da popularidade e acessibilidade de sistemas de realidade virtual (RV) de alta qualidade, tem-se levantado preocupações com relação a tendência dos sistemas de realidade virtual em provocar perda de equilíbrio. O equilíbrio é essencial para o uso seguro da realidade virtual e a perda do mesmo pode causar lesões graves. O objetivo deste trabalho é criar um sistema para avaliar o impacto da realidade virtual no equilíbrio humano. Neste trabalho, propomos e conduzimos um experimento usando o Oculus Rift e o MS Kinect Sensor. Nesse experimento, foi possível observar, quantificar e comparar o efeito de diferentes cenas de RV no equilíbrio dos usuários, bem como o efeito de avisos visuais e sonoros sobre perda de equilíbrio. / [en] With the increasing popularity and accessibility of high-quality Virtual Reality (VR) systems, concerns have been raised about the propensity of VR to induce balance loss. Balance is essential for safe use of VR experience and its loss can result in severe injury. This project is set to create a system able to measure the impact of VR in the human balance system. In this work, we design and conduct an experiment making use of the Oculus Rift VR headset and MS Kinect Sensor. In this experiment, we are able to visualize, quantify, and compare the effect of different VR scenes on the balance of the experiment subjects as well as the effect of visual and auditory warnings of balance loss.

A common problem within positron emission tomography examinations of the brain is the motion of the patient. If the patients ́ head moves during an examination all the data acquired after the movement will not be suited for clinical use. This means that a lot of data recovered from PET is not used at all. Motion tracking during PET acquisitions of the brain is not a well explored issue within medical imaging in relation to the magnitude of the problem. Due to the radiation risks of the examination and the logistics at the hospital, a second acquisition is not preferred. Therefore a method to avoid a second acquisition would be welcome. PET data saved in list mode makes it possible to analyze the data during an examination. By calculating the center of mass of the object examined in list mode only using the raw data from PET and use it as a tracking point, it would be possible to track a motion during an acquisition. The center of mass could therefore possibly be used as a reference to connect two different time intervals on each side of the moment were the motion occurred. The raw PET data used for this project was acquired in the Nuclear Medicine Department in Karolinska University Hospital in Huddinge and covered four turns of one minute acquisitions in different positions and with two different objects that were saved in list mode. The acquisitions were analyzed with the Siemens software e7-tools and sliced into time intervals. To calculate the center of mass within these time intervals, two methods were developed. One method only used the Siemens software e7-tools and histogrammed the time of flight bin position. The other method used each event position in its sinogram to calculate a center of mass sinusoidal equation. This equation lead to coordinates describing the center of mass in a specific slice. / Ett vanligt problem inom positronemissiontomografiundersökningar av hjärnan är rörelser från patienten. Om patienten rör sitt huvud under undersökningen kommer all förvärvad data inte vara kliniskt lämpad. Detta innebär att en stor del av datan från en PET-undersökning inte används över huvud taget. Rörelsespårning under PET undersökningar av hjärnan är ett relativt outforskat ämne inom medicinsk bildgivning i relation till amplituden av problemet. På grund av strålningsrisken av un- dersökningen och logistiken på sjukhusen, är en andra bildtagning inte att föredra. Därför skulle en metod för att undvika en andra bildtagning vara uppskattad. PET-rådata sparad i list mode möjliggör analys av data inom tidsspektrat av en undersökning. Genom att beräkna det undersökta objektets barocentrum genom att enbart använda rådata sparad i list mode och använda detta som en referenspunkt, så finns en möjlighet att följa en rörelse under en undersökning. Objektets barocentrum skulle kunna fungera som en referenspunkt för att binda ihop två olika tidsegment på varsin sida om tillfället då en rörelse har skett. Rådatan som användes i detta projekt var förvärvad vid nukleärmedicinska avdelningen på Karolinska Universetetssjukhuset i Huddinge och täckte fyra stycken undersökningar på en minut vardera i olika positioner och två olika objekt som sparades i list mode. Datainsamlingarna över- sattes med Siemens-mjukvaran e7-tools och delades sedan upp i tidsegment. För att räkna ut ett barocentrum i dessa tidssegment så utvecklades två metoder. En metod använde sig enbart av Siemens-mjukvaran e7-tools och använde dess funktion ”histogramming” för att dela upp alla events time of flight position. Den andra metoden använde varje events position i dess sinogram för att beräkna en barocentrisk sinusformad funktion. Denna funktion ledde till koordinater som beskrev masscentrum i en specifik skiva.

The purpose of this study was to examine the differences in technique between sprinters and baseball players while running at maximal speeds. 20 male NCAA Division I athletes participated; ten members of the track and field team specializing in the 100 m or 200 m sprint or the 100 m hurdles and ten members of the baseball team. Each subject performed a maximal effort 80 m sprint while their sprint times were recorded every 10 m starting at the 20 m mark. Each subject was filmed at they ran through a set10 m marking that included where they reached their top speed allowing the camera to capture at least one complete stride. By using the Peak Motus System, each subject's minimum knee flexion, minimum hip angle, knee extension at toe off, contact time, stride length, center of mass at touchdown and shank angle were measured. ANOVA with repeated measures found that sprinters and baseball players display significant differences in their sprinting technique in all variables except shank angle with the sprinters displaying a shorter 10 m split time. It was concluded that proper sprint training during baseball practice could prove to be beneficial to baseball players, however, further research would need to be conducted to support this claim.

The deep learning technique Human Pose Estimation (or Human Keypoint Detection) is a promising field in tracking a person and identifying its posture. As posture and balance are two closely related concepts, the use of human pose estimation could be applied to fall prevention. By deriving the location of a persons Center of Mass and thereafter its Center of Pressure, one can evaluate the balance of a person without the use of force plates or sensors and solely using cameras. In this study, a human pose estimation model together with a predefined human weight distribution model were used to extract the location of a persons Center of Pressure in real time. The proposed method utilized two different methods of acquiring depth information from the frames - stereoscopy through two RGB-cameras and with the use of one RGB-depth camera. The estimated location of the Center of Pressure were compared to the location of the same parameter extracted while using the force plate Wii Balance Board. As the proposed method were to operate in real-time and without the use of computational processor enhancement, the choice of human pose estimation model were aimed to maximize software input/output speed. Thus, three models were used - one smaller and faster model called Lightweight Pose Network, one larger and accurate model called High-Resolution Network and one model placing itself somewhere in between the two other models, namely Pose Residual Network. The proposed method showed promising results for a real-time method of acquiring balance parameters. Although the largest source of error were the acquisition of depth information from the cameras. The results also showed that using a smaller and faster human pose estimation model proved to be sufficient in relation to the larger more accurate models in real-time usage and without the use of computational processor enhancement. / Djupinlärningstekniken Kroppshållningsestimation är ett lovande medel gällande att följa en person och identifiera dess kroppshållning. Eftersom kroppshållning och balans är två närliggande koncept, kan användning av kroppshållningsestimation appliceras till fallprevention. Genom att härleda läget för en persons tyngdpunkt och därefter läget för dess tryckcentrum, kan utvärdering en persons balans genomföras utan att använda kraftplattor eller sensorer och att enbart använda kameror. I denna studie har en kroppshållningsestimationmodell tillsammans med en fördefinierad kroppsviktfördelning använts för att extrahera läget för en persons tryckcentrum i realtid. Den föreslagna metoden använder två olika metoder för att utvinna djupseende av bilderna från kameror - stereoskopi genom användning av två RGB-kameror eller genom användning av en RGB-djupseende kamera. Det estimerade läget av tryckcentrat jämfördes med läget av samma parameter utvunnet genom användning av tryckplattan Wii Balance Board. Eftersom den föreslagna metoden var ämnad att fungera i realtid och utan hjälp av en GPU, blev valet av kroppshållningsestimationsmodellen inriktat på att maximera mjukvaruhastighet. Därför användes tre olika modeller - en mindre och snabbare modell vid namn Lightweight Pose Network, en större och mer träffsäker modell vid namn High-Resolution Network och en model som placerar sig någonstans mitt emellan de två andra modellerna gällande snabbhet och träffsäkerhet vid namn Pose Resolution Network. Den föreslagna metoden visade lovande resultat för utvinning av balansparametrar i realtid, fastän den största felfaktorn visade sig vara djupseendetekniken. Resultaten visade att användning av en mindre och snabbare kroppshållningsestimationsmodellen påvisar att hålla måttet i jämförelse med större och mer träffsäkra modeller vid användning i realtid och utan användning av externa dataprocessorer.

This bachelor thesis at the Royal Institute of Technology in Stockholm, Sweden, aims to clarify how the minimum bandwidth of a stabilised mobile inverted pendulum is affected by the position of its center of mass and the frequency of measuring the state variables. The scope is to apply basic theories in automation control and electronic systems when designing the system. The mechatronical system in the experimental trials is constructed with the main components consisting of bipolar stepper motors, stepper motor drivers (DRV8825), potentiometer and Arduino UNO. The mobile pendulum in question consists of a cart on a rail with a potentiomoter and a rod mounted to it. In the experimental trials in this paper, three different radial positions of the center of mass are analysed with regards to the bandwidth of relevant measurements. A variety of PID parameters, for both the angle and position regulation, are the essential basis on which these stability trials are performed. The results are limited to the resolution of the potentiometer outputs, the length of the rail and the stiffness of the rod. The result is presented by comparisons between data of the greatest angles which are stabilised and the corresponding maximal latency of the angle corrections. These data concludes to that the minimum required bandwidth to sustain stability decreases for an increasing length between the center of mass and the point of rotation. / Denna kandidatexamensuppsats genomfördes på Kungliga Tekniska Högskolan, i Stockholm, Sverige, och har som mål att klargöra hur den minsta bandbredden för en stabiliserad inverterad pendel påverkas av positionen av dess tyngdpunkt samt nätfrekvensen av tillståndsvariablerna. Projektet omfattar grundläggande teorier om reglerteknik och elektriska system.  Det mekatroniska systemet som används i experimenten är uppbyggt av följande nyckelkomponenter: bipolära stegmotorer, stegmotordrivare (DRV8825), potentionmeter och Arduino UNO. Den mobila pendeln består av en stång och en potentiometer som är monterad på en vagn löpandes på en räls. I de utförda experimenten i denna rapport analyseras tre radiella positioner på masscentrum med hänsyn till bandbredden och relevanta mätningar. En reglering med olika PID parametrar, för både vinkel- och positionsreglering, är den kritiska process som lade grunden för analyserna av stabiliteten. Resultaten är begränsade av upplösningen hos potentiometerns utsignal, längden av rälsen och stångens styvhet.  Resultaten presenteras genom jämförelser mellan data för de största vinklarna som stabiliseras och de motsvarande maximala fördröjningarna. Sammanfattningsvis minskar den minst nödvändiga bandbredden för att upprätthålla stabilitet för ökande längder mellan pendelns tyngdpunkt och rotationspunkten.

La chute est un problème de santé publique qui touche principalement les personnes âgées. Nos travaux portent sur la caractérisation des stratégies biomécaniques et cognitives impliquées dans le maintien et le rattrapage de l'équilibre et qui permettent à une personne âgée d'éviter de chuter. En particulier, nous nous sommes intéressé à une population âgée, encore autonome et en bonne santé, dans le but d'identifier les personnes à risque et de permettre une intervention le plus tôt possible. Nous avons pu mettre en évidence que, dans cette population, les tests cliniques classiques ne permettent pas de bien discriminer les « chuteurs » des « non-chuteurs » et que le problème de la chute ne réside pas que dans une déficience musculaire mais aussi cognitive et/ou sensorielle qui affecte les réponses biomécaniques de rattrapage. Les tests les plus discriminants sont identifiés et un outil d'évaluation du risque de chute, permettant d'identifier rapidement les déficiences, est proposé. Enfin, nous fournissons des informations sur les mécanismes impliqués dans les pas protectifs, une stratégie d'équilibration prévalente mais peu évaluée dans les tests cliniques / Falling is a common and concerning health problem for the elderly population. This research work focuses on the characterization of the biomechanical and cognitive strategies involved in the balance maintain and balance recovery that help elderly to avoid a fall. Particularly, we interested in a community-dwelling elderly population, in order to identify the persons who are at risk of fall and suggest a forward preventive intervention. We show, for this population, that usual clinical tests do not well discriminate between “fallers” and “non-fallers” and that the fall problem is more concerned by cognitive and/or sensorial troubles than by muscular troubles that affect biomechanical responses. The most discriminant tests are identified and a risk of fall assessment tool is suggested to give informations about the deficient mechanisms. Finally, we provide informations about the mechanisms involved in protective steps, a prevalent balance strategy which not used in balance clinical assessments

[pt] Esta tese apresenta o estudo dinâmico de três sistemas pendulares e de um sistema de corpo livre no espaço com 3 graus de liberdade. O primeiro sistema pendular consiste de um pêndulo acoplado ao centro de uma roda, que rola sem escorregar na direção horizontal, enquanto o segundo, se baseia num pêndulo simples, porém com comprimento variável, que ao mudar seu tamanho consegue ganhar/perder energia para aumentar/diminuir a amplitude de seu movimento e finalmente o terceiro está baseado num pêndulo duplo que, a despeito de restrições impostas ao movimento consegue inserir/retirar energia do sistema de forma similar ao segundo. O modelo de corpo livre no espaço está baseado na suspensão cardânica de um giroscópio e se utiliza de um modelo didático real de um giroscópio para observação das características dinâmicas. A partir destes exemplos estudou-se formas de controle não-linear para movimentar os sistemas de maneira a utilizar-se da mudança de posição interna do centro de massa para injetar e retirar energia dos sistemas. Foram gerados modelos matemáticos simulados no Simulink valendo-se do Matlab para análise, e geradas animações também com o Matlab para melhor observação dos efeitos. Em paralelo, para dois destes sistemas foram construídos em bancada experimentos para comprovação dos resultados numéricos, e os resultados são comparados em cada caso, analisando as diferenças. Ao final, todas as observações sobre os estudos foram analisadas, e comentários feitos baseados nos resultados, além de sugerir trabalhos futuros. / [en] This thesis presents the study of the dynamics of three pendulum systems and a 3DoF free body in space. The first pendular system is based on a simple pendulum coupled to the center of a wheel that translates horizontally without slip; while the second system is based on a simple pendulum, with variable length, which is able to acquire/lose energy to grow/diminish the amplitude of its movement; and finally the third one is based on a double pendulum that, in spite of movement restrictions, can as well inject/drop energy like the second system. The free body in space is based on a real gyroscope for didactical use, which is helpful for the observation of the dynamic characteristics of the motion. Using these examples a non-linear control was designed to drive the system by using the property that changing the internal position of the center of mass it is possible to inject or to subtract energy from the systems. Mathematical models were simulated with Simulik software, Matlab was used for the analysis, and animations were created also with Matlab for a better sight of the effects. In parallel, there were developed 2 test rig systems for verification of the numerical results. In the conclusions all the considerations about the study were analyzed, and comments made on the results, as well also future developments are suggested.

This work involves the design and implementation of a real-time Machine Vision-based Human Computer Interface (HCI) that analyzes and interprets a music conductor's gestures to detect the musical "beat". This HCI system interfaces directly with the "Virtual Orchestra", an electronic MIDI sequenced "orchestra". Prior to the development of this HCI system, the real time control of the tempo of the "Virtual Orchestra" could only be controlled by tapping a tempo on a MIDI controller device--a process that is foreign to most music conductors. The real-time beat information detected by this HCI system allows a conductor to conduct the "Virtual Orchestra" as if it were a live orchestra. This system was developed using the Broadway real-time color image capture board manufactured by Data Translation, Incorporated. The implementation involved the use of Microsoft Visual C++, Microsoft Foundation Classes (MFC) for the Graphical User Interface (GUI), Video For Windows (VFW), MIDI note generation, and Intel assembly level code optimization. Algorithms were developed for rapid RGB color thresholding, multiple contour extraction, fast contour based area and center of mass calculations, and gesture interpretation. Real time, live-video interpretation has been achieved and an end-to-end system has been demonstrated in conjuction with a MIDI sequencer.

Ce mémoire de thèse concerne l'interpolation sur les variétés de Grassmann et ses applications à la réduction de modèles en mécanique et plus généralement aux systèmes d'équations aux dérivées partielles d'évolution. Après une description de la méthode POD, nous introduisons les fondements théoriques en géométrie des variétés de Grassmann, qui seront utilisés dans le reste de la thèse. Ce chapitre donne à ce mémoire à la fois une rigueur mathématique au niveau des algorithmes mis au point, leur domaine de validité ainsi qu'une estimation de l'erreur en distance grassmannienne, mais également un caractère auto-contenu "self-contained" du manuscrit. Ensuite, on présente la méthode d'interpolation sur les variétés de Grassmann introduite par David Amsallem et Charbel Farhat. Cette méthode sera le point de départ des méthodes d'interpolation que nous développerons dans les chapitres suivants. La méthode de Amsallem-Farhat consiste à choisir un point d'interpolation de référence, envoyer l'ensemble des points d'interpolation sur l'espace tangent en ce point de référence via l'application logarithme géodésique, effectuer une interpolation classique sur cet espace tangent, puis revenir à la variété de Grassmann via l'application exponentielle géodésique. On met en évidence par des essais numériques l'influence du point de référence sur la qualité des résultats. Dans notre premier travail, nous présentons une version grassmannienne d'un algorithme connu dans la littérature sous le nom de Pondération par Distance Inverse (IDW). Dans cette méthode, l'interpolé en un point donné est considéré comme le barycentre des points d'interpolation où les coefficients de pondération utilisés sont inversement "proportionnels" à la distance entre le point considéré et les points d'interpolation. Dans notre méthode, notée IDW-G, la distance géodésique sur la variété de Grassmann remplace la distance euclidienne dans le cadre standard des espaces euclidiens. L'avantage de notre algorithme, dont on a montré la convergence sous certaines conditions assez générales, est qu'il ne requiert pas de point de référence contrairement à la méthode de Amsallem-Farhat. Pour remédier au caractère itératif (point fixe) de notre première méthode, nous proposons une version directe via la notion de barycentre généralisé. Notons enfin que notre algorithme IDW-G dépend nécessairement du choix des coefficients de pondération utilisés. Dans notre second travail, nous proposons une méthode qui permet un choix optimal des coefficients de pondération, tenant compte de l'auto-corrélation spatiale de l'ensemble des points d'interpolation. Ainsi, chaque coefficient de pondération dépend de tous les points d'interpolation et non pas seulement de la distance entre le point considéré et un point d'interpolation. Il s'agit d'une version grassmannienne de la méthode de Krigeage, très utilisée en géostatique. La méthode de Krigeage grassmannienne utilise également le point de référence. Dans notre dernier travail, nous proposons une version grassmannienne de l'algorithme de Neville qui permet de calculer le polynôme d'interpolation de Lagrange de manière récursive via l'interpolation linéaire entre deux points. La généralisation de cet algorithme sur une variété grassmannienne est basée sur l'extension de l'interpolation entre deux points (géodésique/droite) que l'on sait faire de manière explicite. Cet algorithme ne requiert pas le choix d'un point de référence, il est facile d'implémentation et très rapide. De plus, les résultats numériques obtenus sont remarquables et nettement meilleurs que tous les algorithmes décrits dans ce mémoire. / This dissertation deals with interpolation on Grassmann manifolds and its applications to reduced order methods in mechanics and more generally for systems of evolution partial differential systems. After a description of the POD method, we introduce the theoretical tools of grassmannian geometry which will be used in the rest of the thesis. This chapter gives this dissertation a mathematical rigor in the performed algorithms, their validity domain, the error estimate with respect to the grassmannian distance on one hand and also a self-contained character to the manuscript. The interpolation on Grassmann manifolds method introduced by David Amsallem and Charbel Farhat is afterward presented. This method is the starting point of the interpolation methods that we will develop in this thesis. The method of Amsallem-Farhat consists in chosing a reference interpolation point, mapping forward all interpolation points on the tangent space of this reference point via the geodesic logarithm, performing a classical interpolation on this tangent space and mapping backward the interpolated point to the Grassmann manifold by the geodesic exponential function. We carry out the influence of the reference point on the quality of the results through numerical simulations. In our first work, we present a grassmannian version of the well-known Inverse Distance Weighting (IDW) algorithm. In this method, the interpolation on a point can be considered as the barycenter of the interpolation points where the used weights are inversely proportional to the distance between the considered point and the given interpolation points. In our method, denoted by IDW-G, the geodesic distance on the Grassmann manifold replaces the euclidean distance in the standard framework of euclidean spaces. The advantage of our algorithm that we show the convergence undersome general assumptions, does not require a reference point unlike the method of Amsallem-Farhat. Moreover, to carry out this, we finally proposed a direct method, thanks to the notion of generalized barycenter instead of an earlier iterative method. However, our IDW-G algorithm depends on the choice of the used weighting coefficients. The second work deals with an optimal choice of the weighting coefficients, which take into account of the spatial autocorrelation of all interpolation points. Thus, each weighting coefficient depends of all interpolation points an not only on the distance between the considered point and the interpolation point. It is a grassmannian version of the Kriging method, widely used in Geographic Information System (GIS). Our grassmannian Kriging method require also the choice of a reference point. In our last work, we develop a grassmannian version of Neville's method which allow the computation of the Lagrange interpolation polynomial in a recursive way via the linear interpolation of two points. The generalization of this algorithm to grassmannian manifolds is based on the extension of interpolation of two points (geodesic/straightline) that we can do explicitly. This algorithm does not require the choice of a reference point, it is easy to implement and very quick. Furthermore, the obtained numerical results are notable and better than all the algorithms described in this dissertation.