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Tool actions are characterized by a transformation between movements and their resulting consequences in the environment. This transformation has to be taken into account when tool actions are planned and executed. We investigated how angular shift transformations between circling movements and their visual feedback affect the coordination of this feedback with visual events in the environment. We used a task that required participants to coordinate the visual feedback of a circular hand movement (presented on the right side of a screen) with a circling stimulus (presented on the left side of a screen). Four stimulus-visual feedback relations were instructed: same or different rotations of stimulus and visual feedback, either in same or different y-directions. Visual speed was varied in three levels (0.8, 1, and 1.2 Hz). The movement-visual feedback relation was manipulated using eight angular shifts: (-180, -135, -90, -45, 0, 45, 90, and 135°). Participants were not able to perform the different rotation/different y-direction pattern, but instead fell into the different rotation/same y-direction pattern. The different rotation/same y-direction pattern and the same rotation/same y-direction pattern were performed equally well, performance was worse in the same rotation/different y-direction pattern. Best performance was observed with angular shifts 0 and -45° and performance declined with larger angular shifts. Further, performance was better with negative angular shifts than with positive angular shifts. Participants did not fully take the angular shift transformation into account: when the angular shifts were negative the visual feedback was more in advance, and when angular shifts were positive the visual feedback was less in advance of the stimulus than in 0° angular shift. In conclusion, the presence and the magnitude of angular shift transformations affect performance. Internal models do not fully take the shift transformation into account.

There is a need for objective methods for wrist angular velocity measurements for accurate risk assessments because there is a high frequency of musculoskeletal disorder in workers. The goal of this project was to validate the accuracy of inertial measurement unit sensors to measure the angular velocity. More specifically, the purpose of this master thesis project was to apply an alternative algorithm to compute the markers velocity, other than the one from the optical system that Jenny Wingqvist, and Josephine Lantz used. The project used an experimental data of 10 participants from the previous project done by Jenny Wingqvist and Josephine Lantz. To validate the accuracy, the data of angular velocity of the sensors was compared with the data of angular velocity of markers. The lowest mean value of the root mean square differences value was 23.5 degrees/s during flexion and deviation standard movements at 40 BPM (Beats Per Minute) and the maximum value was 110.5 degrees/s at 140 BPM. The mean value of the correlation coefficients between markers and sensors angular velocities in standard movements of flexion and deviation were 0.85, 0.88, and 0.89 at 40 BPM, 90 BPM, and 140 BPM, respectively. The smallest and the largest mean value of the absolute difference in 50th percentile was found in 40 BPM (19.4±11.3), and 140 BPM (51.2±28.5) respectively. The decorrelation coefficient between the subjects 50th percentile of the angular velocity was 0.91 for the standard movements. The upper limit of agreement for the standard movements was 78.36 degrees/s, while the lower limit of agreement was -13.76 degrees/s.  The results show that the error was too large, so there is a need of further research to measure the wrist angular velocity using IMU sensors.

<p>The purpose of this thesis is to explore the angular response to dose of the MatriXX Evolution, manufactured by IBA Dosimetry, a 2-dimensional ion chamber array used for patient specific quality assurance of advanced radiotherapy techniques such as IMRT and VMAT. Investigations were made to characterize the angular response of the MatriXX and describe any differences from the Philips Pinnacle³ Treatment Planning System (TPS) used at the Juravinski Cancer Centre.</p> <p>A comparison was made between the gantry angle dependent correction factors supplied by the manufacturer and those derived by measurement. Gantry angle dependent correction factors were derived, with the MatriXX under 5cm polystyrene build-up and without any build-up, for the 5 x 5 cm², 10 x 10 cm² and 20 x 20 cm² field sizes.</p> <p>For gantry angles ranging from 320^o to 40^o the maximum difference between the derived gantry angle dependent correction factors and those provided by the manufacturer is 1.5%, at a gantry angle of 320^o, a 5 x 5 cm² field and without build-up. The differences for the 10 x 10 cm² and 20 x 20 cm² fields within this gantry angle range are less than 1%. Between gantry angles of 50^o and 130^o the largest difference is 4.9% at 100^o, for the 5 x 5 cm²field without build-up. The other field sizes show similar differences; 4.7% at gantry angle of 120^o for 10 x 10 cm² with build-up and 4.0% at a gantry angle of 80^o without build-up. Between gantry angles of 140^o to 220^o the greatest discrepancy is for the 5 x 5 cm² field with build-up, a difference of 3.0%. The 10 x 10 cm² has a maximum difference of 2.4% at gantry angles of 180^o and 200^o, both when the MatriXX has build-up. The maximum discrepancy for gantry angle dependent correction factors for the 20 x 20 cm² fields is at a gantry angle of 140^o, when the MatriXX has build-up. Between the gantry angles of 230^o to 310^o the largest discrepancy occurs between the derived gantry angle dependent correction factors and those supplied by the manufacturer. For the 5 x 5 cm², 10 x 10 cm² and 20 x 20 cm² fields respectively the largest differences are 5.9%, 4.5% and 4.9%. All three occur when there is no build-up.</p> / Master of Science (MSc)

This dissertation addresses novel techniques in determining gyroless micro-satellite attitude and attitude rate. The main objective of this thesis is to explore the possibility of using commercially available low cost micro-light star sensor as a stand-alone sensor for micro-satellite attitude as well as attitude rate determination. The objective is achieved by developing accurate and computationally efficient algorithms for the realization of onboard operation of a low fidelity star sensor. All the algorithms developed here are tested with the measurement noise presented in the catalog of the sensor array STAR-1000. A novel accurate second order sliding mode observer (SOSMO) is designed for discrete time uncertain linear multi-output system. Our design procedure is effective for both matched and unmatched bounded uncertain ties and/or disturbances. The bound on uncertainties and/or disturbances is assumed to be unknown. This problem is addressed in this work using the second order multiple sliding modes approach. Second order sliding manifold and corresponding sliding condition for discrete time system is defined similar on the lines of continuous counterpart. Our design is not restricted to a particular class of uncertain (matched) discrete time system. Moreover, it can handle multiple outputs unlike single out-put systems. The observer design is achieved by driving the state observation error and its first order finite difference to the vicinity of the equilibrium point (0,0) in a finite steps and maintaining them in the neighborhood thereafter. The estimation synthesis is based on Quasi Sliding Mode (QSM) design. The problem of designing sliding mode observer for a linear system subjected to unknown inputs requires observer matching condition. This condition is needed to ensure that the state estimation error is a asymptotically stable and is independent of the unknown input during the sliding motion. In the absence of a matching condition, asymptotic stability of the reduced order error dynamics on the sliding surface is not guaranteed. However, unknown bounded inputs guarantee bounded error on state estimation. The QSM design guarantees an ultimate error bound by incorporating Boundary Layer (BL) in its design procedure. The observer achieves one order of magnitude improvement in estimation accuracy than the conventional sliding mode observer (SMO) design for an unknown input. The observer estimation errors, satisfying the given stability conditions, converge to an ultimate finite bound (with in the specified BL) of O(T2), where T Is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The robustness of the proposed observer with respect to measurement noise is also analyzed. The design algorithm is very simple to apply and is implemented for two examples with different classes of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results show the robustness with respect to the measurement noise for SOSMO. Second order sliding mode observer gain can be calculated off-line and the same gain can work for large band of disturbance as long as the disturbance acting on the continuous time system is bounded and smooth. The SOSMO is simpler to implement on board compared to the other traditional nonlinear filters like Pseudo-Linear-Kalman-filter(PLKF); Extended Kalman Filter(EKF). Moreover, SMO possesses an automatic adaptation property same as optimal state estimator(like Kalman filter) with respect to the intensity of the measurement noise. The SMO rejects the noisy measurements automatically, in response to the increased noise intensity. The dynamic performance of the observer on the sliding surface can be altered and no knowledge of noise statistics is required. It is shown that the SOSMO performs more accurately than the PLKF in application to micro-satellite angular rate estimation since PLKF is not an optimal filter. A new method for estimation of satellite angular rates through derivative approach is proposed. The method is based on optic flow of star image patterns formed on a star sensor. The satellite angular rates are derived directly from the 2D-coordinates of star images. Our algorithm is computationally efficient and requires less memory allocation compared to the existing vector derivative approaches, where there is also no need for star identification. The angular rates are computed using least square solution method, based on the measurement equation obtained by optic flow of star images. These estimates are then fed into discrete time second order sliding mode observer (SOSMO). The performance of angular rate estimation by SOSMO is compared with the discrete time First order SMO and PLKF. The SOSMO gives the best estimates as compared to the other two schemes in estimating micro-satellite angular rates in all three axes. The improvement in accuracy is one order of magnitude (around1.7984 x 10−5 rad/ sec,8.9987 x 10−6 rad/ sec and1.4222 x 10−5 rad/ sec in three body axes respectively) in terms of standard deviation in steady state estimation error. A new method and algorithm is presented to determine star camera parameters along with satellite attitude with high precision even if these parameters change during long on-orbit operation. Star camera parameters and attitude need to be determined independent of each other as they both can change. An efficient, closed form solution method is developed to estimate star camera parameters (like focal length, principal point offset), lens distortions (like radial distortion) and attitude. The method is based on a two step procedure. In the first step, all parameters (except lens distortion) are estimated using a distortion free camera model. In the second step, lens distortion coefficient is estimated by linear least squares (LS) method. Here the derived camera parameters in first step are used in the camera model that incorporates distortion. However, this method requires identification of observed stars with the catalogue stars. But, on-orbit star identification is difficult as it utilizes the values of camera calibrating parameters that can change in orbit(detector and optical element alignment get change in orbit due to solar pressure or sudden temperature change) from the ground calibrated value. This difficulty is overcome by employing a camera self-calibration technique which only requires four observed stars in three consecutive image frames. Star camera parameters along with lens (radial and decentering) distortion coefficients are determined by camera self calibration technique. Finally Kalman filter is used to refine the estimated data obtained from the LS based method to improve the level of accuracy. We consider the true values of camera parameters as (u0,v0) = (512.75,511.25) pixel, f = 50.5mm; The ground calibrated values of those parameters are (u0,v0) =( 512,512) pixel, f = 50mm; Worst case radial distortion coefficient affecting the star camera lens is considered to be k1 =5 x 10−3 .Our proposed method of attitude determination achieves accuracy of the order of magnitude around 6.2288 x 10−5 rad,3.3712 x 10−5 radand5.8205 x 10−5 rad in attitude angles φ,θ and ψ. Attitude estimation by existing methods in the literature diverges from the true value since they utilize the ground calibrated values of camera parameters instead of true values. To summarize, we developed a formal theory of discrete time Second Order Sliding Mode Observer for uncertain multi-output system. Our methods achieve the desired accuracy while estimating satellite attitude and attitude rate using low fidelity star sensor data. Our methods require lower on-board processing requirement and less memory allocation; thus are suitable for micro-satellite applications. Thus, the objective of using low fidelity star sensor as stand-alone sensor in micro-satellite application is achieved.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction. / AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie, wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence), sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The In the Physiotherapy Division of the Faculty of Health Sciences on the Tygerberg Hospital Campus of the University of Stellenbosch, the challenge arose to develop a portable, affordable and yet accurate 3D measurement machine for the assessment of posture in school children in their classroom environment. Currently Division already uses a state-of-the-art VICON commercial medical measuring machine to measure human posture in 3D in their physiotherapy clinic, but the system is not portable and is too expensive to cart around to different places for testing. To respond to this challenge, this Master’s thesis designed and analyzed a machine and its supporting system through both research on stereo-vision methodologies and empirical appraisal in the field. In the development process, the research was required to overcome the limitations posed by small image resolutions and lens distortions that are typical of cheap cameras. The academic challenge lay in the development of an error prediction model through Jacobian derivation and Error Propagation Law, to predict uncertainties of angular measurement calculated by the system. The research culminated in a system that is comparable in accuracy to the VICON within 3mm, and that has 1.5mm absolute accuracy within its own system for a measurement volume radius of 2.5 m. As such, the developed error model is an exact predictor of the angular error to within 0.02° of arc. These results, for both system accuracy and the error model, exceed the expectations on the basis of the initial challenge of the system. The development of the machine was successful in providing a prototype tool that is suitable for commercial development for use by physiotherapists in human posture measurement and assessment. In its current incarnation, the machine will also serve the Engineering Faculty as the most fundamental form of a three-dimensional measuring apparatus using only basic theories and algorithms of stereo-vision, thereby providing a basic experimental platform from which further scientific research on the theory and application of computer vision can be conducted. / AFRIKAANSE OPSOMMING: Die Fisioterapie Afdeling van die Fakulteit Gesondheidswetenskappe op die Tygerberg kampus van die Universiteit van Stellenbosch gebruik ’n allernuutste VICON kommersiële mediese meettoestel om menslike postuur in drie dimensies te meet. Vanuit hierdie Afdeling het die uitdaging ontstaan om ’n draagbare, bekostigbare, maar tog akkurate, drie-dimensionele meetapparaat geskik vir die meet van die postuur van skoolkinders in die klaskamer te ontwikkel. In aanvaarding van hierdie uitdaging, het hierdie Magistertesis ’n toestel en ondersteuningstels ontwerp en ontleed deur beide navorsing in stereo-visie metodiek en terplaatse beoordeling. In die ontwikkelingsproses moes die navorsing die beperkings wat deur klein-beeld resolusie en lens-distorsie (tipies van goedkoop kameras) meegebring word, oorkom. Die akademiese uitdaging lê in die ontwikkeling van ’n voorspellende foutmodel deur van die Jacobianse-afleiding en die Fout Propageringswet gebruik te maak om onsekerheid van hoeksberekening deur die stelsel te voorspel. Die navorsing het gelei tot ’n stelsel wat binne 3mm vergelykbaar is in akkuraatheid met dié van die VICON en ook 1.5mm absolute interne akkuraatheid het in ’n meet-volume radius van 2.5m radius. Die ontwikkelde foutmodel is dus ’n presiese voorspeller van hoekfout tot binne 0.02° van boog. Die resultate met betrekking tot beide die akkuraatheid en die foutmodel het die oorspronklike verwagtinge van die uitdaging oortref. Die ontwikkeling was suksesvol in die skep van ’n prototipe-toestel geskik vir kommersiële ontwikkeling, vir gebruik deur fisioterapeute in die meting en evaluering van menslike postuur. Die stelsel is in sy fundamentele vorm, deur die gebruik van slegs basiese teorieë en algoritmes van stereo-visie, funksioneer as ’n drie-dimensionele meetapparaat. In die fundamentele vorm sal die stelsel die Ingenieursfakulteit dien as ’n basiese eksperimentele platform waarop verdere wetenskaplike navorsing in die teorie en toepassing van rekenaar-visie gedoen kan word.

With the rising popularity of ROVs and other UV solutions, more robust and high performance controllers have become a necessity. A model of the ROV or UV can be a valuable tool during control synthesis. The main objective of this thesis was to use a model in design and development of controllers for an ROV. In this thesis, an ROV from Blue Robotics was used. The ROV was equipped with 6 thrusters placed such that the ROV was capable of moving in 6-DOFs. The ROV was further equipped with an IMU, two pressure sensors and a magnetometer. The ROV platform was further developed with EKF-based sensor fusion, a control system and manual control capabilities. To model the ROV, the framework of Fossen (2011) was used. The model was estimated using two different methods, the prediction-error method and an EKF-based method. Using the prediction-error method, it was found that the initial states of the quaternions had a large impact on the estimated parameters and the overall fit to validation data. A Kalman smoother was used to estimate the initial states. To circumvent the problems with the initial quaternions, an \abbrEKF was implemented to estimate the model parameters. The EKF estimator was less sensitive to deviations in the initial states and produced a better result than the prediction-error method. The resulting model was compared to validation data and described the angular velocities well with around 70 % fit. The estimated model was used to implement feedback linearisation which was used in conjunction with an attitude controller and an angular velocity controller. Furthermore, a depth controller was developed and tuned without the use of the model. Performance of the controllers was tested both in real tests and simulations. The angular velocity controller using feedback linearisation achieved good reference tracking. However, the attitude controller could not stabilise the system while using feedback linearisation. Both controllers' performance could be improved further by tuning the controllers' parameters during tests. The fact that the feedback linearisation made the ROV unstable, indicates that the attitude model is not good enough for use in feedback linearisation. To achieve stability, the magnitude of the parameters in the feedback linearisation were scaled down. The assumption that the ROV's center of rotation coincides with the placement of the ROV's center of gravity was presented as a possible source of error. In conclusion, good performance was achieved using the angular velocity controller. The ROV was easier to control with the angular velocity controller engaged compared to controlling it in open loop. More work is needed with the model to get acceptable performance from the attitude controller. Experiments to estimate the center of rotation and the center of gravity of the ROV may be helpful when further improving the model.