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In this dissertation we introduce a new class of pursuit-evasion games; the herding problem. Unlike regular pursuit evasion games where the pursuer aims to hunt the evader the objective of the pursuer in this game is to drive the evader to a certain location on the x-y grid. The dissertation deals with this problem using two different methodologies. In the first, the problem is introduced in the continuous-time, continuous-space domain. The continuous time model of the problem is proposed, analyzed and we came up with an optimal control law for the pursuer is obtained so that the evader is driven to the desired destination position in the x-y grid following the local shortest path in the Euler Lagrange sense. Then, a non-holonomic realization of the two agents is proposed. In this and we show that the optimal control policy is in the form of a feedback control law that enables the pursuer to achieve the same objective using the shortest path. The second methodology deals with the discrete model representation of the problem. In this formulation, the system is represented by a finite di-graph. In this di-graph, each state of the system is represented by a node in the graph. Applying dynamic programming technique and shortest path algorithms over the finite graph representing the system, we come up with the optimal control policy that the pursuer should follow to achieve the desired goal. To study the robustness, we formulate the problem in a stochastic setting also. We analyze the stochastic model and derive an optimal control law in this setting. Finally, the case with active evader is considered, the optimal control law for this case is obtained through the application of dynamic programming technique. / Ph. D.

Modern robotics demonstrates the reality of near sci-fi solutions regularly. Swarms of interconnected robotic agents have been proven to have benefits in scalability, robustness, and efficiency. In communication restricted environments, such teams of robots are often required to support their own navigation, planning, and decision making processes, through use of onboard processors and collaboration. Example scenarios that exhibit restriction include unmanned underwater surveys and robots operating in indoor or remote environments without cloud connectivity. We begin this thesis by discussing multi-agent state estimation and it's observability properties, specifically for the case of an agent-to-agent range measurement system. For this case, inspired by navigation requirements underwater, we derive several conditions under which the system's state is guaranteed to be locally weakly observable. Ensuring a state is observable is necessary to maintain an estimate of it via filters, thus observability is required to support higher level navigation and planning. We conclude this section by creating an observability-based planner to control a subset of the agents' inputs. For the next contribution, we discuss scalability for coverage maximizing path planners. Typically planning for many individual robots incurs significant computational complexity which increases exponentially with the number of agents, this is often exacerbated when the objective function is collaborative as in coverage optimization. To maintain feasibility while planning for a large team of robots, we call upon a powerful relation from combinatorics which utilizes the greedy selection algorithm and a matroid condition to create an efficient planner that maintains a fixed performance ratio when compared to the optimal path. We then introduce a motivating example of autonomously assisted search and rescues using multiple aerial agents, and derive planners and models to suit the application. The framework begins by estimating the likely locations of a lost person through a Monte Carlo simulation, yielding a heatmap covering the area of interest. The heatmap is then used in combination with parametrized agent trajectories and a machine learning optimization algorithm to maximize the search efficiency. The search and rescues use case provides an excellent computational testbed for the final portion of the work. We close by discussing a computation architecture to support multi-agent system autonomy. Modern robotic autonomy results, especially computer vision and machine learning algorithms, often require large amounts of processing to yield quality results. With general purpose computing devices reaching a progression barrier, one that is not expected to be solved in the near term, increasingly devices must be designed with their end purposes in mind. To better support autonomy in multi-agent systems, we propose to use a distributed cluster of embedded processors which allows the sharing of computation and storage resources among the component members with minimal communication overhead. Our proposed architecture is composed of mature softwares already well-known in the robotics community, Kubernetes and the robot operating system, allowing ease of use and interoperability with existing algorithms. / Doctor of Philosophy / The traditional approach of robotics typically uses a single large platform capable of accomplishing all tasks assigned to it. However, it has been discovered that deploying multiple smaller platforms, each with their own processor and specific expertise, can have massive performance benefits compared to previous approaches. This development has been driven largely by readily available computing and mobility hardware. Termed as multi-agent systems, they can excel in areas that benefit from multiple perspectives, simultaneous task execution, and redundancy. In addition, planning algorithms developed for previous approaches often can map well onto multi-agent systems, provided there is adequate computational support. In cases where network or cloud connectivity is limited, teams of agents must use their own processors and sensors to make decisions and communicate. However, often an individual agent's computing hardware is limited in mass or size, thus limiting it's processing capabilities. In this work we will first discuss several multi-agent system algorithms, starting with estimation and navigation and ending with area search. We then conclude the work by proposing a novel architecture designed to distribute the computation load across the team in a highly scalable way.

The poetics of an architecture of a moment is explored through design of a contemplative room (wherin the geometric transformation of a cubic base to a cone) demonstrates the rhythmn and proportion of the construction of the room and the relative motion of the sun in the space. The relationship of the sun rays on the walls of the room passing through a reflecting pool are shown using demonstrative and constructive means of descriptive geometry as both the design generator and poetic expression.The composition of the buildings reveals the play of light on form. / Master of Architecture / An exploration to understand the relationship of architecture and the material sensible world. The work seeks to reveal that through the tangible architectural strategies of form, structure, material and light, the intangible qualities of architecture are defined.

Pursuit-evasion games are the subject of a variety of research initiatives seeking to provide some level of autonomy to mobile, robotic vehicles with on-board controllers. Applications of these controllers include defense topics such as unmanned aerial vehicle (UAV) and unmanned underwater vehicle (UUV) navigation for threat surveillance, assessment, or engagement. Controllers implementing pursuit-evasion algorithms are also used for improving everyday tasks such as driving in traffic when used for collision avoidance maneuvers. Currently, pursuit-evasion tactics are incorporated into the control by solving the Hamilton-Jacobi-Isaacs (HJI) equation explicitly, simplifying the solution using approximate dynamic programming, or using a purely finite-horizon approach. Unfortunately, these methods are either subject to difficulties of long computational times or having no guarantees of succeeding in the pursuit-evasion game. This leads to more difficulties of implementing these tactics on-line in a real robotic scenario where the opposing agent may not be known before the maneuver is required. This dissertation presents a novel method of solving the HJI equation by partitioning the state space into regions of local, finite horizon control laws. As a result, the HJI equation can be reduced to solving the Hamilton-Jacobi-Bellman equation recursively as information is received about an opposing agent. Adding complexity to the problem structure results in a decreased calculation time to allow pursuit-evasion tactics to be calculated on-board an agent during a scenario. The algorithms and implementation methods are given explicitly and illustrated with an example of two robotic vehicles in a collision avoidance maneuver. / Ph. D.

The use of autonomous underwater vehicles (AUVs) for oceanic observation and research is becoming more common. Underwater gliders are a specific class of AUV that do not use conventional propulsion. Instead they change their buoyancy and center of mass location to control attitude and trajectory. The vehicles spend most of their time in long, steady glides, so even minor improvements in glide range can be magnified over multiple dives. This dissertation presents a rigid-body dynamic system for a generic vehicle operating in a moving fluid (ocean current or wind). The model is then reduced to apply to underwater gliders. A reduced-order point-mass model is analyzed for optimal gliding in the presence of a current. Different numerical method solutions are compared while attempting to achieve maximum glide range. The result, although approximate, provides good insight into how the vehicles may be operated more effectively. At the end of each dive, the gliders must change their buoyancy and pitch to transition to a climb. Improper scheduling of the buoyancy and pitch change may cause the vehicle to stall and lose directional stability. Optimal control theory is applied to the buoyancy and angle of attack scheduling of a point-mass model. A rigid-body model is analyzed on a singular arc steady glide. An analytical solution for the control required to stay on the arc is calculated. The model is linearized to calculate possible perturbation directions while remaining on the arc. The nonlinear model is then propagated in forward and reverse time with the perturbations and analyzed. Lastly, one of the numerical solutions is analyzed using the singular arc equations for verification. This work received support from the Office of Naval Research under Grant Number N00014-08-1-0012. / Ph. D.

The re-use of any architecture site, whether it is empty or still holding a presence in remaining elements, creates a connection with the past. Formed by a retaining wall and smokestack, an outdoor room is the destination from which two paths direct the inhabitant. This room divides the site and is surrounded by two buildings designed as a library. Through the use of additional architectural elements, frame and column, the inhabitant is guided along the two paths through visual and physical markers. The inhabitant can either move through the building and find framed views of the smokestack and outdoor room, or move around the building, descending the site towards the outdoor room. This project uses a series of perspective drawings to show the designated paths from the street to the outdoor room. / Master of Architecture

In this thesis, we describe a method for controlling the cycle-averaged velocity direction of a fixed-wing aircraft in an unpowered, helical descent. While the aircraft propulsion system is disabled, either intentionally or due to a failure, the aerodynamic control surfaces (aileron, elevator, and rudder) are assumed to be functional. Our approach involves two steps: (i) establishing a stable, steady, helical motion for which the control surfaces are not fully deflected and (ii) modulating the aircraft control surfaces about their nominal positions to ``slant'' the helical flight path in a desired direction relative to the atmosphere, whether to attain a desired impact location, to counter a steady wind, or both. The effectiveness of the control law was evaluated in numerical simulations of a general transport model (GTM). / Master of Science