Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Evaluating Alternative Nutrient Sources in Subsistence-Level Aquaponic Systems

Many food production methods are both economically and environmentally unsustainable. Our project investigated aquaponics, an alternative method of agriculture that could address these issues. Aquaponics combines fish and plant crop production in a symbiotic, closed-loop system. We aimed to reduce the initial and operating costs of current aquaponic systems by utilizing alternative feeds. These improvements may allow for sustainable implementation of the system in rural or developing regions. We conducted a multi-phase process to determine the most affordable and effective feed alternatives for use in an aquaponic system. At the end of two preliminary phases, soybean meal was identified as the most effective potential feed supplement. In our final phase, we constructed and tested six full-scale aquaponic systems of our own design. Data showed that soybean meal can be used to reduce operating costs and reliance on fishmeal. However, a more targeted investigation is needed to identify the optimal formulation of alternative feed blends.

Precoder Detection for Cooperative Decode-and-Forward Relaying in OFDMA Systems

We consider an LTE network where a secondary user acts as a relay, transmitting data to the primary user using a decode-and-forward mechanism, transparent to the base-station (eNodeB). Clearly, the relay can decode symbols more reliably if the employed precoder matrix indicators (PMIs) are known. However, for closed loop spatial multiplexing (CLSM) transmit mode, this information is not always embedded in the downlink signal, leading to a need for effective methods to determine the PMI. In this thesis, we consider 2x2 MIMO and 4x4 MIMO downlink channels corresponding to CLSM and formulate two techniques to estimate the PMI at the relay using a hypothesis testing framework. We evaluate their performance via simulations for various ITU channel models over a range of SNR and for different channel quality indicators (CQIs). We compare them to the case when the true PMI is known at the relay and show that the performance of the proposed schemes are within 2 dB at 10% block error rate (BLER) in almost all scenarios. Furthermore, the techniques add minimal computational overhead over existent receiver structure. Finally, we also identify scenarios when using the proposed precoder detection algorithms in conjunction with the cooperative decode-and-forward relaying mechanism benefits the PUE and improves the BLER performance for the PUE. Therefore, we conclude from this that the proposed algorithms as well as the cooperative relaying mechanism at the CMR can be gainfully employed in a variety of real-life scenarios in LTE networks.

Essays on Matching Markets and Their Equilibria

Matching theory and matching markets are a core component of modern economic theory and market design. This dissertation presents three original contributions to this area. The first essay constructs a matching mechanism in an incomplete information matching market in which the positive assortative match is the unique efficient and unique stable match. The mechanism asks each agent in the matching market to reveal her privately known type. Through its novel payment rule, truthful revelation forms an ex post Nash equilibrium in this setting. This mechanism works in one-, two- and many-sided matching markets, thus offering the first mechanism to unify these matching markets under a single mechanism design framework. The second essay confronts a problem of matching in an environment in which no efficient and incentive compatible matching mechanism exists due to matching externalities. I develop a two-stage matching game in which a contracting stage facilitates subsequent conditionally efficient and incentive compatible Vickrey auction stage. Infinite repetition of this two-stage matching game enforces the contract in every period. This mechanism produces inequitably distributed social improvement: parties to the contract receive all of the gains and then some. The final essay demonstrates the existence of prices which stably and efficiently partition a single set of agents into firms and workers, and match those two sets to each other. This pricing system extends Kelso and Crawford's general equilibrium results in a labor market matching model and links one- and two-sided matching markets as well.

EXISTENCE OF UNUSED MANAGED CAPACITY ON DEDICATED LANES AND AN ALTERNATIVE ON HOW TO SELL IT VIA AUCTIONS

This dissertation verifies whether the following two hypotheses are true: (1) High-occupancy/toll lanes (and therefore other dedicated lanes) have capacity that could still be used; (2) such unused capacity (or more precisely, “unused managed capacity”) can be sold successfully through a real-time auction. To show that the second statement is true, this dissertation proposes an auction-based metering (ABM) system, that is, a mechanism that regulates traffic that enters the dedicated lanes. Participation in the auction is voluntary and can be skipped by paying the toll or by not registering to the new system. This dissertation comprises the following four components: a measurement of unused managed capacity on an existing HOT facility, a game-theoretic model of an ABM system, an operational description of the ABM system, and a simulation-based evaluation of the system. Some other and more specific contributions of this dissertation include the following: (1) It provides a definition and a methodology for measuring unused managed capacity and another important variable referred as “potential volume increase”. (2) It proves that the game-theoretic model has a unique Bayesian Nash equilibrium. (3) And it provides a specific road design that can be applied or extended to other facilities. The results provide evidence that the hypotheses are true and suggest that the ABM system would benefit a public operator interested in reducing traffic congestion significantly, would benefit drivers when making low-reliability trips (such as work-to-home trips), and would potentially benefit a private operator interested in raising revenue.

Self-Organizing Map Neural Architectures Based on Limit Cycle Attractors

Recent efforts to develop large-scale neural architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason is that most conventional SOMs use a static encoding representation: Each input is typically represented by the fixed activation of a single node in the map layer. This not only carries information in an inefficient and unreliable way that impedes building robust multi-SOM neural architectures, but it is also inconsistent with rhythmic oscillations in biological neural networks. Here I develop and study an alternative encoding scheme that instead uses limit cycle attractors of multi-focal activity patterns to represent input patterns/sequences. Such a fundamental change in representation raises several questions: Can this be done effectively and reliably? If so, will map formation still occur? What properties would limit cycle SOMs exhibit? Could multiple such SOMs interact effectively? Could robust architectures based on such SOMs be built for practical applications? The principal results of examining these questions are as follows. First, conditions are established for limit cycle attractors to emerge in a SOM through self-organization when encoding both static and temporal sequence inputs. It is found that under appropriate conditions a set of learned limit cycles are stable, unique, and preserve input relationships. In spite of the continually changing activity in a limit cycle SOM, map formation continues to occur reliably. Next, associations between limit cycles in different SOMs are learned. It is shown that limit cycles in one SOM can be successfully retrieved by another SOM’s limit cycle activity. Control timings can be set quite arbitrarily during both training and activation. Importantly, the learned associations generalize to new inputs that have never been seen during training. Finally, a complete neural architecture based on multiple limit cycle SOMs is presented for robotic arm control. This architecture combines open-loop and closed-loop methods to achieve high accuracy and fast movements through smooth trajectories. The architecture is robust in that disrupting or damaging the system in a variety of ways does not completely destroy the system. I conclude that limit cycle SOMs have great potentials for use in constructing robust neural architectures.

Microfabricated elastomer tactile sensors for robotic fingertip systems

Tactile sensing is an important aspect of robotic systems, and enables safe, dexterous robot-environment interaction. The design and implementation of tactile sensors on robots has been a topic of research over the past 30 years, and current challenges include mechanically flexible “sensing skins”, high dynamic range (DR) sensing (i.e.: high force range and fine force resolution), multi-axis sensing, and integration between the sensors and robot. This dissertation focuses on addressing some of these challenges through a novel manufacturing process that incorporates conductive and dielectric elastomers in a reusable, multilength-scale mold, and new sensor designs for multi-axis sensing that improve force range without sacrificing resolution. A single taxel was integrated into a 1 degree of freedom robotic gripper for closed-loop slip detection. Manufacturing involved casting a composite silicone rubber, polydimethylsiloxane (PDMS) filled with conductive particles such as carbon nanotubes, into a mold to produce microscale flexible features on the order of 10s of microns. Molds were produced via microfabrication of silicon wafers, but were limited in sensing area and were costly. An improved technique was developed that produced molds of acrylic using a computer numerical controlled (CNC) milling machine. This maintained the ability to produce microscale features, and increased the sensing area while reducing costs. New sensing skins had features as small as 20 microns over an area as large as a human hand. Sensor architectures capable of sensing both shear and normal force sensing with high dynamic range were produced. Using this architecture, two sensing modalities were developed: a capacitive approach and a contact resistive approach. The capacitive approach demonstrated better dynamic range, while the contact resistive approach used simpler circuitry. Using the contact resistive approach, normal force range and resolution were 8,000 mN and 1,000 mN, respectively, and shear force range and resolution were 450 mN and 100 mN, respectively. Using the capacitive approach, normal force range and resolution were 10,000 mN and 100 mN, respectively, and shear force range and resolution were 1,500 mN and 50 mN, respectively.

Effects of Drive Speed Modulation on Dynamics of Slender Rotating Structures

Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied. Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.