Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Modeling and Control of the Power Conversion Unit in a Solid Oxide Fuel Cell Environment

In this doctoral thesis, a power conversion unit for a 10 kWsolid oxide fuel cell is modeled, and a suitable control system is designed. The need for research was identified based on an observation that there was no information available about the characteristics of the solid oxide fuel cell from the perspective of power electronics and the control system, and suitable control methods had not previously been studied in the literature. In addition, because of the digital implementation of the control system, the inherent characteristics of the digital system had to be taken into account in the characteristics of the solid oxide fuel cell (SOFC). The characteristics of the solid oxide fuel cell as well the methods for the modeling and control of the DC/DC converter and the grid converter are studied by a literature survey. Based on the survey, the characteristics of the SOFC as an electrical power source are identified, and a solution to the interfacing of the SOFC in distributed generation is proposed. A mathematical model of the power conversion unit is provided, and the control design for the DC/DC converter and the grid converter is made based on the proposed interfacing solution. The limit cycling phenomenon is identified as a source of low-frequency current ripple, which is found to be insignificant when connected to a grid-tied converter. A method to mitigate a second harmonic originating from the grid interface is proposed, and practical considerations of the operation with the solid oxide fuel cell plant are presented. At the theoretical level, the thesis discusses and summarizes the methods to successfully derive a model for a DC/DC converter, a grid converter, and a power conversion unit. The results of this doctoral thesis can also be used in other applications, and the models and methods can be adopted to similar applications such as photovoltaic systems. When comparing the results with the objectives of the doctoral thesis, we may conclude that the objectives set for the work are met. In this doctoral thesis, theoretical and practical guidelines are presented for the successful control design to connect a SOFC-based distributed generation plant to the utility grid.

Modeling, optimizing and simulating robot calibration with accuracy improvement

This work describes techniques for modeling, optimizing and simulating calibration processes of robots using off-line programming. The identification of geometric parameters of the nominal kinematic model is optimized using techniques of numerical optimization of the mathematical model. The simulation of the actual robot and the measurement system is achieved by introducing random errors representing their physical behavior and its statistical repeatability. An evaluation of the corrected nominal kinematic model brings about a clear perception of the influence of distinct variables involved in the process for a suitable planning, and indicates a considerable accuracy improvement when the optimized model is compared to the non-optimized one.

Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Modeling a Network of Heat Exchangers

This research work addresses the problem of building a mathematical model for the given system of heat exchangers and to determine the temperatures, pressures and velocities at the intermediate positions. Such model could be used in nding an optimal design for such a superstructure. To limit the size and computing time a reduced network model was used. The method can be generalized to larger network structures. A mathematical model which includes a system of non-linear equations has been built and solved according to the Newton-Raphson algorithm. The results obtained by the proposed mathematical model were compared with the results obtained by the Paterson approximation and Chen's Approximation. Results of this research work in collaboration with a current ongoing research at the department will optimize the valve positions and hence, minimize the pumping cost and maximize the heat transfer of the system of heat exchangers.

Modeling and kinetic study of bio-ethanol production from soy protein concentrate by-product

Abstract The aim of this work was to evaluate a non-agitated process of bioethanol production from soybean molasses and the kinetic parameters of fermentation using a strain of Saccharomyces cerevisiae (ATCC® 2345). Kinetic experiment was conducted in medium with 30% (w v-1) of soluble solids without supplementation or pH adjustment. The maximum ethanol concentration was in 44 hours, the ethanol productivity was 0.946 g L-1 h-1, the yield over total initial sugars (Y1) was 47.87%, over consumed sugars (Y2) was 88.08% and specific cells production rate was 0.006 h-1. The mathematical polynomial was adjusted to the experimental data and provided very similar parameters of yield and productivity. Based in this study, for one ton of soybean molasses can be produced 103 kg of anhydrous bioethanol.

An Eigenfunction Approach for Volatility Modeling.

In this paper, we introduce a new approach for volatility modeling in discrete and continuous time. We follow the stochastic volatility literature by assuming that the variance is a function of a state variable. However, instead of assuming that the loading function is ad hoc (e.g., exponential or affine), we assume that it is a linear combination of the eigenfunctions of the conditional expectation (resp. infinitesimal generator) operator associated to the state variable in discrete (resp. continuous) time. Special examples are the popular log-normal and square-root models where the eigenfunctions are the Hermite and Laguerre polynomials respectively. The eigenfunction approach has at least six advantages: i) it is general since any square integrable function may be written as a linear combination of the eigenfunctions; ii) the orthogonality of the eigenfunctions leads to the traditional interpretations of the linear principal components analysis; iii) the implied dynamics of the variance and squared return processes are ARMA and, hence, simple for forecasting and inference purposes; (iv) more importantly, this generates fat tails for the variance and returns processes; v) in contrast to popular models, the variance of the variance is a flexible function of the variance; vi) these models are closed under temporal aggregation.

Timing verification in transaction modeling

Les systèmes Matériels/Logiciels deviennent indispensables dans tous les aspects de la vie quotidienne. La présence croissante de ces systèmes dans les différents produits et services incite à trouver des méthodes pour les développer efficacement. Mais une conception efficace de ces systèmes est limitée par plusieurs facteurs, certains d'entre eux sont: la complexité croissante des applications, une augmentation de la densité d'intégration, la nature hétérogène des produits et services, la diminution de temps d’accès au marché. Une modélisation transactionnelle (TLM) est considérée comme un paradigme prometteur permettant de gérer la complexité de conception et fournissant des moyens d’exploration et de validation d'alternatives de conception à des niveaux d’abstraction élevés. Cette recherche propose une méthodologie d’expression de temps dans TLM basée sur une analyse de contraintes temporelles. Nous proposons d'utiliser une combinaison de deux paradigmes de développement pour accélérer la conception: le TLM d'une part et une méthodologie d’expression de temps entre différentes transactions d’autre part. Cette synergie nous permet de combiner dans un seul environnement des méthodes de simulation performantes et des méthodes analytiques formelles. Nous avons proposé un nouvel algorithme de vérification temporelle basé sur la procédure de linéarisation des contraintes de type min/max et une technique d'optimisation afin d'améliorer l'efficacité de l'algorithme. Nous avons complété la description mathématique de tous les types de contraintes présentées dans la littérature. Nous avons développé des méthodes d'exploration et raffinement de système de communication qui nous a permis d'utiliser les algorithmes de vérification temporelle à différents niveaux TLM. Comme il existe plusieurs définitions du TLM, dans le cadre de notre recherche, nous avons défini une méthodologie de spécification et simulation pour des systèmes Matériel/Logiciel basée sur le paradigme de TLM. Dans cette méthodologie plusieurs concepts de modélisation peuvent être considérés séparément. Basée sur l'utilisation des technologies modernes de génie logiciel telles que XML, XSLT, XSD, la programmation orientée objet et plusieurs autres fournies par l’environnement .Net, la méthodologie proposée présente une approche qui rend possible une réutilisation des modèles intermédiaires afin de faire face à la contrainte de temps d’accès au marché. Elle fournit une approche générale dans la modélisation du système qui sépare les différents aspects de conception tels que des modèles de calculs utilisés pour décrire le système à des niveaux d’abstraction multiples. En conséquence, dans le modèle du système nous pouvons clairement identifier la fonctionnalité du système sans les détails reliés aux plateformes de développement et ceci mènera à améliorer la "portabilité" du modèle d'application.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Statistical modeling on (α, +∞)

Observations in daily practice are sometimes registered as positive values larger then a given threshold α. The sample space is in this case the interval (α,+∞), α > 0, which can be structured as a real Euclidean space in different ways. This fact opens the door to alternative statistical models depending not only on the assumed distribution function, but also on the metric which is considered as appropriate, i.e. the way differences are measured, and thus variability

Statistical modeling on coordinates

This paper is a first draft of the principle of statistical modelling on coordinates. Several causes —which would be long to detail—have led to this situation close to the deadline for submitting papers to CODAWORK’03. The main of them is the fast development of the approach along the last months, which let appear previous drafts as obsolete. The present paper contains the essential parts of the state of the art of this approach from my point of view. I would like to acknowledge many clarifying discussions with the group of people working in this field in Girona, Barcelona, Carrick Castle, Firenze, Berlin, G¨ottingen, and Freiberg. They have given a lot of suggestions and ideas. Nevertheless, there might be still errors or unclear aspects which are exclusively my fault. I hope this contribution serves as a basis for further discussions and new developments

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Modeling chemotaxis reveals the role of reversed phosphotransfer and a bi-functional kinase-phosphatase

Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY6, aided by its specific phosphatase, the bifunctional kinase CheA3, acts as a phosphate sink for the other RRs; and (2) a phosphorelay pathway involving CheB2 connects the cytoplasmic cluster kinase CheA3 with the polar localised kinase CheA2, and allows CheA3-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA3 to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources.

Kinematic modeling of head-neck movements

The main objective is to generate kinematic models for the head and neck movements. The motivation comes from our study of individuals with quadriplegia and the need to design rehabilitation aiding devices such as robots and teletheses that can be controlled by head-neck movements. It is then necessary to develop mathematical models for the head and neck movements. Two identification methods have been applied to study the kinematics of head-neck movements of able-body as well as neck-injured subjects. In particular, sagittal plane movements are well modeled by a planar two-revolute-joint linkage. In fact, the motion in joint space seems to indicate that sagittal plane movements may be classified as a single DOF motion. Finally, a spatial three-revolute-joint system has been employed to model 3D head-neck movements.