Roth, Zvi S.

Sorensen's model of glucose metabolism and regulation is reconstructed using SimulinkRTM. Most of the existing glucose metabolism models consist of several mass balance equations that interact with each others. Graphical format used by SimulinkRTM provides a visualized perspective of such relations so that it is easier to modify the model on ad hoc basis. Type-I and Type-II diabetes with relevant clinical details are simulated. Further, a control strategy is introduced in order to simulate the control of exogenous insulin pump. Simulated results are consistent with available clinical data. Living systems in general, exhibit both stochastical and deterministic characteristics. Activities such as glucose metabolism traditionally modeled do not include stochastical properties, nor that they are viewed in the large framework of complex system with explicit interaction details. Currently, a complexity system model is developed to describe the glucose metabolism related activities. The simulation results obtained thereof illustrate the bounding domain of variations in some clinically observed details.

Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom, making the class a rich one from a control standpoint. The double inverted pendulum is a particular underactuated system and a well-known benchmark case for which many solutions have been offered in the literature. The control objective is to bring the system to its unstable top equilibrium point. The underactuated horizontal double pendulum is a two-link planar robot with only one actuator either at the shoulder or the elbow. Almost no work was done on the underactuated horizontal pendulum, mainly due to the lack of controllability of such a system. The fundamental difference between a double inverted pendulum and an underactuated horizontal double pendulum is that in the latter gravity effects do not exist. Gravity is important to the controllability of the system. Thus, in search for a "gravity substitute," we added springs in the underactuated horizontal double pendulum in order to create a source of potential energy. Two different types of such systems are analyzed: spring coupled underactuated horizontal double pendulums and underactuated horizontal double pendulums with spring-loaded sliding bar constraint. The main contribution of the thesis is in proving that the zero state of the spring coupled systems is globally asymptotically stabilizable. Explicit control laws were developed.

To assess and evaluate the performance of robots and machine tools dynamically, it
is desirable to have a precision measuring device that performs dynamic measurement
of end-effector positions of such robots and machine tools. Among possible
measurement techniques, Laser Tracking Systems (LTSs) exlnbit the capability of high
accuracy, large workspace, high sampling rate, and automatic target-tracking,. and thus
are well-suited for robot calibration both kinematically and dynamically.
In this dissertation, the design and implementation of a control system for a homemade
laser tracking measurement systems is addressed and calibration of a robot using
the laser tracking system is demonstrated Design and development of a control system for a LTS is a challenging task. It
involves a deep understanding of laser interferometry,. controls, mechanics and optics,.
both in theoretical perspective and in implementation aspect. One of the most important
requirements for a successful design and implementation of a control system for the
LTS is proper installation and alignment of the laser and optical system,. or laser
transducer system. The precision of measurement using the LTS depends highly on the
accuracy of the laser transducer system, as well as the accuracy of the installation and
alignment of the optical system. Hence, in reference to the experimental alignment
method presented in this dissertation, major error sources affecting the system
measurement accuracy are identified and analyzed. A manual compensation method is
developed to eliminate the effects of these error sources effectively in the measurement
system. Considerations on proper design and installation of laser and optical
components are indicated in this dissertation.
As a part of the conventional control system design, a dynamic system model of the
LTS is required. In this study, a detailed derivation and analysis of the dynamic model
of the motor gimbal system using Lagrange-Euler equations of motion is developed for
both ideal and complete gimbal systems. Based on this system model,. a conventional
controller is designed.
Fuzzy Logic Controllers (FLC) are designed in order to suppress noise or
disturbances that exist in the motor driver subsystem. By using the relevant control
strategies. noise and disturbances present in the electrical control channels are shown to
reduce significantly. To improve the system performance further, a spectrum analysis of the error sources and disturbances existing in the system is conducted. Major noise
sources are effectively suppressed by using a two-stage fuzzy logic control strategy. A
comparison study on the performances of different control strategies is given in this
dissertation, in reference to the following: An ideal system model, a system with a long
time delay, a system with various noise sources and a system model with uncertainties.
Both simulation and experimental results are furnished to illustrate the advantages of
the FLC in respect of its transient response, steady-state response, and tracking
performance. Furthermore, noise reduction in the laser tracking system is demonstrated.
Another important issue concerning a successful application of the LTS in the
calibration of a robot is the estimation of system accuracy. Hence, a detailed analysis of
system accuracy of the LTS is presented in this worL This analysis is also verified by
experimental methods by means of tracking a Coordinate Measuring Machine available
in the FAU Robotics Center. Using the developed LTS, a PUMA robot in the FAU
Robotics Center is calibrated. The results obtained are confirmative with the data
available in the literature.
In summary, the proposed methodology towards the design and implementation of a
control system for LTSs has been shown to be successful by performing experimental
tracking and calibration studies at the FAU Robotics Center.

Laser tracking coordinate measuring machines have the potential of continuously measuring three dimensional target coordinates in a large workspace with a fast sampling rate and high accuracy. Proper calibration of a laser tracking measurement system is essential prior to use of such a device for metrology. In the absence of a more accurate instrument for system calibration, one has to rely on self-calibration strategies. In this dissertation, a kinematic model that describes not only the motion but also geometric variations of a multiple-beam laser tracking system was developed. The proposed model has the following features: (1) Target positions can be computed from both distance and angular measurements. (2) Through error analysis it was proven that even rough angular measurement may improve the overall system calibration results. A self-calibration method was proposed to calibrate intelligent machines with planar constraints. The method is also applied to the self-calibration of the laser tracking system and a standard PUMA 560 robot. Various calibration strategies utilizing planar constraints were explored to deal with different system setups. For each calibration strategy, issues about the error parameter estimation of the system were investigated to find out under which conditions these parameters can be uniquely estimated. These conditions revealed the applicability of the planar constraints to the system self-calibration. The observability conditions can serve as a guideline for the experimental setup when planar constraint is utilized in the machine calibration including the calibration of the laser tracking systems. Intensive simulation studies were conducted to check validity of the theoretical results. Realistic noise values were injected to the system models to statistically assess the behavior of the self-calibration system under real-world conditions. Various practical calibration issues were also explored in the simulations and therefore to pave ways for experimental investigation. The calibration strategies were also applied experimentally to calibrate a laser tracking system constructed at the Robotics Center in Florida Atlantic University.

Robot calibration using a vision system and moving cameras is the focus of this dissertation. The dissertation contributes in the areas of robot modeling, kinematic identification and calibration measurement. The effects of perspective distortion of circular camera calibration points is analyzed. A new modified complete and parametrically continuous robot kinematic model, an evolution of the complete and parametrically continuous (CPC) model, is proposed. It is shown that the model's error-model can be developed easily as the structure of this new model is very simple and similar to the Denavit-Hartenbert model. The derivation procedure of the error-model follows a systematic method that can be applied to any kind of robot arms. Pose measurement is the most crucial step in robot calibration. The use of stereo as well as mono mobile camera measurement system for collection of pose data of the robot end-effector is investigated. The Simulated Annealing technique is applied to the problem of optimal measurement configuration selection. Joint travel limits can be included in the cost function. It is shown that trapping into local minimum points can be effectively avoided by properly choosing an initial point and a temperature schedule. The concept of simultaneous calibration of camera and robot is developed and implemented as an automated process that determines the system model parameters using only the system's internal sensors. This process uses a unified mathematical model for the entire robot/camera system. The results of the kinematic identification, optimal configuration selection, and simultaneous calibration of robot and camera using the PUMA 560 robot arm have demonstrated that the modified complete and parametrically continuous model is a viable and simple modeling tool, which can achieve desired accuracy. The systematic way of modeling and performing of different kinds of vision-based robot applications demonstrated in this dissertation will pave the way for industrial standardizing of robot calibration done by the robot user on the manufacturing floor.

Parallel manipulators have their special characteristics in contrast to the traditional serial type of robots. Stewart platform is a typical six degree of freedom fully parallel robot manipulator. The goal of this research is to enhance the accuracy and the restricted workspace of the Stewart platform. The first part of the dissertation discusses the effect of three kinematic constraints: link length limitation, joint angle limitation and link interference, and kinematic parameters on the workspace of the platform. An algorithm considering the above constraints for the determination of the volume and the envelop of Stewart platform workspace is developed. The workspace volume is used as a criterion to evaluate the effects of the platform dimensions and kinematic constraints on the workspace and the dexterity of the Stewart platform. The analysis and algorithm can be used as a design tool to select dimensions, actuators and joints in order to maximize the workspace. The remaining parts of the dissertation focus on the accuracy enhancement. Manufacturing tolerances, installation errors and link offsets cause deviations with respect to the nominal parameters of the platform. As a result, if nominal parameters are being used, the resulting platform pose will be inaccurate. An accurate kinematic model of Stewart platform which accommodates all manufacturing and installation errors is developed. In order to evaluate the effects of the above factors on the accuracy, algorithms for the forward and inverse kinematics solutions of the accurate model are developed. The effects of different manufacturing tolerances and installation errors on the platform accuracy are investigated based on this model. Simulation results provide insight into the expected accuracy and indicate the major factors contributing to the inaccuracies. In order to enhance the accuracy, there is a need to calibrate the platform, or to determine the actual values of the kinematic parameters (Parameter Identification) and to incorporate these into the inverse kinematic solution (Accuracy Compensation). An error-model based algorithm for the parameter identification is developed. Procedures for the formulation of the identification Jacobian and for accuracy compensation are presented. The algorithms are tested using simulated measurements in which the realistic measurement noise is included. As a result, pose error of the platform are significantly reduced.

The dissertation focuses on robot manipulator dynamic modeling, and inertial
and kinematic parameters identification problem. An automatic dynamic parameters
derivation symbolic algorithm is presented. This algorithm provides the linearly
independent dynamic parameters set. It is shown that all the dynamic parameters are
identifiable when the trajectory is persistently exciting. The parameters set satisfies
the necessary condition of finding a persistently exciting trajectory. Since in practice the system data matrix is corrupted with noise, conventional
estimation methods do not converge to the true values. An error bound is given for
Kalman filters. Total least squares method is introduced to obtain unbiased
estimates.
Simulations studies are presented for five particular identification methods.
The simulations are performed under different noise levels.
Observability problems for the inertial and kinematic parameters are
investigated. U%wer certain conditions all L%wearly Independent Parameters
derived from are observable.
The inertial and kinematic parameters can be categorized into three parts
according to their influences on the system dynamics. The dissertation gives an
algorithm to classify these parameters.

Theoretical and practical issues of kinematic modeling, measurement, identification and compensation are addressed in this dissertation. A comprehensive robot calibration methodology using a new Complete and Parametrically Continuous (CPC) kinematic model is presented. The dissertation focuses on model-based robot calibration techniques. Parametric continuity of a kinematic model is defined and discussed to characterize model singularity. Irreducibility is defined to facilitate error model reduction. Issues of kinematic parameter identification are addressed by utilizing generic forms of linearized kinematic error models. The CPC model is a complete and parametrically continuous kinematic model capable of describing geometry and motion of a robot manipulator. Owing to the completeness of the CPC model, the transformation from the base frame to the world frame and from the tool frame to the last link frame can be modeled with the same modeling convention as the one used for internal link transformations. Due to the parametric continuity of the CPC model, numerical difficulties in kinematic parameter identification using error models are reduced. The CPC model construction, computation of the link parameters from a given link transformation, inverse kinematics, transformations between the CPC model and the Denavit-Hartenberg model, and linearized CPC error model construction are investigated. New methods for self-calibration of a laser tracking coordinate-measuring-machine are reported. Two calibration methods, one based on a four-tracker system and the other based on three trackers with a precision plane, are proposed. Iterative estimation algorithms along with simulation results are presented. Linear quadratic regulator (LQR) theory is applied to design robot accuracy compensators. In the LQR algorithm, additive corrections of joint commands are found without explicitly solving the inverse kinematic problem for an actual robot; a weighting matrix and coefficients in the cost function can be chosen systematically to achieve specific objective such as emphasizing the positioning accuracy of the end-effector over its orientation accuracy and vice versa and taking into account joint travelling limits as well as singularity zones of the robot. The results of the kinematic identification and compensation experiments using the PUMA robot have shown that the CPC modeling technique presented in this dissertation is a convenient and effective means for accuracy improvements of industrial robots.

Developing on-line methods for detecting and locating process malfunctions is an important goal towards full automation of systems. Model-based methods, which check the consistency of the observations using the known functional relationships among the process variables seem to have the potential of early detection of slowly developing failures in complex systems. This dissertation deals with nonlinear filtering as a method for failure detection in dynamic processes. The failure detection problem is presented here as an Identification Problem, where no jumps between the possible operating modes are assumed, i.e. there is only uncertainty with regard to which is the present mode. The identification filter consists of parallel Kalman filters, each tuned to a different system mode of operation, whose estimates parametrize the conditional probability equations. An extension of the filter is derived for the case of different measurement noise coefficients in different modes for the continuous-discrete case. In the continuous-time case with different measurement noise intensities the likelihood function is shown to be ill-defined as the induced measures become singular. The average performance of the continuous-descrete as well as the continuous-time identification filters are studied. It is shown that on the average and after a sufficiently long time a correct decision is expected for any decision threshold level. An alternative identification filter structure is derived using the maximum-likelihood estimation philosophy. The filter reduces to parallel Kalman filters, feeding the state estimates to a maximum likelihood generator which then chooses a set of indicator functions to maximize the total likelihood. Some aspects of interpreting a sequence of decisions, choosing a decision threshold and reinitializing the filter are discussed qualitatively using simulation examples. Furthermore, a new approach based on scaling of the likelihood functions is presented. Scaling is shown to be equivalent to choosing a threshold level for the conditional probabilities.