Institute for Systems Research

Bluetooth is a promising new wireless technology that enables portable devices to form short-range wireless ad hoc networks and is based on a frequency hopping physical layer. This fact implies that hosts are not able to communicate unless they have previously discovered each other by synchronizing their frequency hopping patterns. Thus, even if all nodes are within direct communication range of each other, only those nodes which are synchronized with the transmitter can hear the transmission.

To support any-to-any communication, nodes must be synchronized so that the pairs of nodes (which can communicate with each other) together form a connected graph.

Using Bluetooth as an example, this paper first provides deeper insights into the issue to link establishment in frequency hopping wireless systems. It then introduces the Bluetooth Topology Costruction Protocol (BTCP), an asynchronous distributed protocol for constructing scatternets which starts with nodes that have no knowledge of their surroundings and terminates with the formation of a connected network satisfying all connectivity constraints posed by the Bluetooth technology.

To the best of our knowledge, the work presented in this paper is the first attempt at building Bluetooth scatternets using distributed logic and is quite "practical" in the sense that it can be implemented using the communication primitives offered by the Bluetooth 1.0 specifications.

Our approach to this problem is based on plant diagonalization.To do this, we search for basis transformations for the vector of outputs coming from the sensors and the vector of inputs applied to the actuators so that, in the new bases, the MIMOsystem becomes a collection of decoupled SISO systems.This formulation provides a number of advantages for the synthesis and implementation of a feedback control law,particularly for systems where the number of inputs and outputs is large.

Of course, in order for this idea to be feasible,the required basis transformations must have properties which allow them to be implemented on a distributed control network. Namely, they must be computed in a distributed manner which respects the spatial distribution of the data(to reduce communication overhead) and takes advantage of the massive parallel processing capability of the network (to reduce computation time).

In this thesis, we present some tools which can be used to find suitable transforms which achieve "approximate"plant diagonalization. We begin by showing how to search the large collection of orthogonal transforms which are contained in the wavelet packet to find the one which most nearly, or approximately, diagonalizes a given real valued matrix.Wavelet packet transforms admit a natural distributed implementation,making them suitable for use on a control network.We then introduce a class of linear operators called recursive orthogonal transforms (ROTs) which we have developed specifically for the purpose of signal processing on distributed control networks.

We show how to use ROTs to approximately diagonalize fixed real and complex matricesas well as transfer function matrices which exhibit a spatial invariance property. Numerical examples of allproposed diagonalization methods are presented and discussed.

Recognizing the challenge to produce multiple prototypes, this thesisresearch aims to integrate three state-of-the-art technologies: 3D solid modeling, rapid prototyping, and vacuum casting. A system architecture combining hardwareand computer software is designed and implemented.

The system utilizes computergraphics to construct a 3D model of an object through visualitzion. A softwaresystem, Maestro, processes a CAD file, generates support structures, and creates slice data to build prototypes by a stereolithography process. Thebuilt part serves as a master pattern for creation of a silicone rubber mold in a vacuum environment. This vacuum environment creates a material flow ratethat ensures replicas with superior quality in regards to surface finish anddimensional accuracy. This mold is then used to cast multiple replicas ofthe master pattern.

The unique contribution of this research is the application of thedeveloped system to meet a specific need in medical research - an effort torestore sight in blind individuals by implanting electordes in the visualcortex. Six replcas of a monkey skull are produced for surgeions to practicesurgical procedures. Image data obtained from CT scans of a mondkey head are successfully used to contruct a 3D solid model to fabricate a batch of six functional prototypes. The superior quality of these replicas hasoffered a unique opportunity for exploratory surgery in efforts to restoresight.