This thesis presents a detailed design, calibration, and control of a modular and reconfigurable robot (MRR) system. A MRR system not only includes modular mechanical hardware, but also modular electrical hardware, control algorithms and software. Also, those modular components can be easily constructed into various manipulator configurations to accomplish a wider range of tasks. MRRs represent the next generation of industrial manipulators that cope with the transition from mass to customer-oriented production. The main contributions of this thesis are: 1) mechanical design and calibration of multi-input multi-output (MIMO) joint modules of MRR, and 2) control design to handle multiple configuration and overcome disturbance due to dynamics uncertainty. From the mechanical design point of view, this thesis presents two main topics: 1) each joint is not only modularly designed, but also has multiple-input multiple-output (MIMO) physical connection ports, which contributes to the concept of reconfigurability. Strictly speaking, single-input single-output (SISO) modular joint falls into the category of modular manipulator, and the robot reconfiguration is achieved by integrating different types of modules. For example, with single revolute MIMO joint module, both rotary and pivotal joint can be generated. On the other hand, if you would like to switch from rotary movement to pivotal movement with a SISO joint module, using another pivotal joint module is the only way to achieve this goal, and 2) for precise automation application, joints and links should be accurately connected and oriented when reconfigured. Our proposed modular joint has four connection ports which can be configured as either a rotary joint or a pivotal joint. In addition, key and keyway connection mechanism provides high accuracy in positioning the link onto the joint. Therefore, this structure reduces or eliminates MRRs system calibration time when reconfigured. Furthermore, zero link offset when used as a pivotal joint increases the robot dexterity, maximizes the reachability, and results in kinematics simplicity. The main challenge in the control of an MRR system with harmonic drives (HD) is the significant uncertainties due to friction, unmodelled dynamics, varying payload, gravitation, dynamic coupling between motions of joints, and the configuration changes. In order to compensate all unpredictable effects, we proposed a decentralized saturation-type robust control scheme based on direct-Lyapunov method and backstepping techniques. To better understand the system dynamics behavior, the HD flexspline compliance and friction calibration and results are also provided. The results are used for controller design. The proposed controller is verified through both computer simulation and experimental analysis.

This thesis presents a detailed design, calibration, and control of a modular and reconfigurable robot (MRR) system. A MRR system not only includes modular mechanical hardware, but also modular electrical hardware, control algorithms and software. Also, those modular components can be easily constructed into various manipulator configurations to accomplish a wider range of tasks. MRRs represent the next generation of industrial manipulators that cope with the transition from mass to customer-oriented production. The main contributions of this thesis are: 1) mechanical design and calibration of multi-input multi-output (MIMO) joint modules of MRR, and 2) control design to handle multiple configuration and overcome disturbance due to dynamics uncertainty. From the mechanical design point of view, this thesis presents two main topics: 1) each joint is not only modularly designed, but also has multiple-input multiple-output (MIMO) physical connection ports, which contributes to the concept of reconfigurability. Strictly speaking, single-input single-output (SISO) modular joint falls into the category of modular manipulator, and the robot reconfiguration is achieved by integrating different types of modules. For example, with single revolute MIMO joint module, both rotary and pivotal joint can be generated. On the other hand, if you would like to switch from rotary movement to pivotal movement with a SISO joint module, using another pivotal joint module is the only way to achieve this goal, and 2) for precise automation application, joints and links should be accurately connected and oriented when reconfigured. Our proposed modular joint has four connection ports which can be configured as either a rotary joint or a pivotal joint. In addition, key and keyway connection mechanism provides high accuracy in positioning the link onto the joint. Therefore, this structure reduces or eliminates MRRs system calibration time when reconfigured. Furthermore, zero link offset when used as a pivotal joint increases the robot dexterity, maximizes the reachability, and results in kinematics simplicity. The main challenge in the control of an MRR system with harmonic drives (HD) is the significant uncertainties due to friction, unmodelled dynamics, varying payload, gravitation, dynamic coupling between motions of joints, and the configuration changes. In order to compensate all unpredictable effects, we proposed a decentralized saturation-type robust control scheme based on direct-Lyapunov method and backstepping techniques. To better understand the system dynamics behavior, the HD flexspline compliance and friction calibration and results are also provided. The results are used for controller design. The proposed controller is verified through both computer simulation and experimental analysis.

The purpose of this thesis is to provide an exposition of the \textit{modular theory} of von Neumann algebras. The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and in particular, type III factors. We replace traces with weights, and for a von Neumann algebra $\mathcal{M}$ which admits a weight $\phi$, we show the existence of an automorphic action $\sigma^\phi:\mathbb{R}\rightarrow\text{Aut}(\mathcal{M})$. After showing the existence of these actions we can discuss the crossed product construction, which will then allow us to study the structure of the algebra.

Limited mobility of mobile ground robots in highly unstructured environments is a problem that inhibits the use of such robots in applications with irregular terrain. Furthermore, applications with hazardous environments are good candidates for the use of robotics to reduce the risk of harm to people. Urban search and rescue (USAR) is an application where the environment is irregular, highly unstructured and hazardous to rescuers and survivors. Consequently, it is of interest to effectively use ground robots in applications such as USAR, by employing mobility enhancement techniques, which stem from the robot’s mechanical design. In this case, a robot may go over an obstacle rather than around it. In this thesis the Reconfigurable Robot Team of Mobile Modules with Manipulators (R2TM3) is proposed as a solution to limited mobility in unstructured terrains, specifically aimed at USAR. In this work the conceptualization, mechatronic development, controls, implementation and testing of the system are given. The R2TM3 employs a mobile modular system in which each module is highly functional: self mobile and capable of manipulation with a five degree of freedom (5-DOF) serial manipulator. The manipulator configuration, the docking system and cooperative strategy between the manipulators and track drives enable a system that can perform severe obstacle climbing and also remain highly manoeuvrable. By utilizing modularity, the system may emulate that of a larger robot when the modules are docking to climb obstacles, but may also get into smaller confined spaces by using single robot modules. The use of the 5-DOF manipulator as the docking device allows for module docking that can cope with severe misalignments and offsets – a critical first step in cooperative obstacle management in rough terrain. The system’s concept rationale is outlined, which has been formulated based on a literature review of mobility enhanced systems. Based on the concept, the realization of a low cost prototype is described in detail. Single robot and cooperative robot control methods are given and implemented. Finally, a variety of experiments are conducted with the concept prototype which shows that the intended performance of the concept has been met: mobility enhancement and manoeuvrability.

In this thesis the last two digits of m^k, for different cases of the positive integers m and k, in the base of 10 has been determined. Moreover, using fundamental theory from elementary number theory and abstract algebra, results most helpful in finding the last two digits in any base b has been regarded and developed, such as how to reduce large m and k to more manageable numbers.

When designing analog circuits, we must ultimately perform measurements on the fabricated chips to determine whether they work correctly or not. The test results are compared with simulation results to determine what the differences to the expected results are. Therefore, incremental improvement and redesign becomes possible. We can obtain highly important information from the test results, making circuit testing a very important aspect of the process of analog circuit design. Especially, measurements during the development phase may include internal circuit nodes which will not be accessible in a final design but are pinned out specifically in the development phase. Because the probing tools present capacitive loads to the circuit, these additional loads may affect the analog circuits‟ response, especially in a high frequency range. Therefore, decreasing influence of capacitive loads of the probing tools in the testing environment is very important. We use analog buffers to separate the analog circuit node from the probing tools. Therefore, the buffer becomes a very important block in analog circuit testing [1-3]. For adapting to different testing environments, this thesis examines three different types of buffer which are designed using a partially modular method [4, 5]. All buffers provide a DC to 1 MHz bandwidth. The first buffer module provides a -1.3 V~1.3 V signal range driving 25 pf~85 pf capacitive loads; the second buffer has a -0.8 V~0.8 V range with for 5 pf~25 pf loads; the third buffer yields -0.5 V~0.5 V range with 1 pf~5 pf loads. The circuit design is discussed and simulated results are presented. Finally, measured results are reported for an open-loop output stage with near unity gain (buffer three). This circuit was previously fabricated in 0.35 £gm CMOS technology.

The theory of hypergeometric functions over finite fields was developed in the mid- 1980s by Greene. Since that time, connections between these functions and elliptic curves and modular forms have been investigated by mathematicians such as Ahlgren, Frechette, Koike, Ono, and Papanikolas. In this dissertation, we begin by giving a survey of these results and introducing hypergeometric functions over finite fields. We then focus on a particular family of elliptic curves whose j-invariant gives an automorphism of P1. We present an explicit relationship between the number of points on this family over Fp and the values of a particular hypergeometric function over Fp. Then, we use the same family of elliptic curves to construct a formula for the traces of Hecke operators on cusp forms in level 1, utilizing results of Hijikata and Schoof. This leads to formulas for Ramanujan’s -function in terms of hypergeometric functions.

Computing A^X mod n or A^XB^Y mod n for large X, Y, and n is very important in many ElGamal-like public key cryptosystems. In this paper, we proposed using block method in sparse form to improve the performance of modular exponentiation and analyzing the computational cost by state transition diagram. We also extended the concept of Block Method and make it more general. This method is suitable for some devices with limited storage space, such as smart card.

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Thesis (Ph. D.)--University of Chicago, Department of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.