The Inverted Pendulum on a Cart is a classical control theory problem that helps understand the importance of feedback control systems for a coupled plant. In this study, a custom built pendulum system is coupled with a linearly actuated cart and a control system is designed to show the stability of the pendulum. The three major objectives of this control system are to swing up the pendulum, balance the pendulum in the inverted position (i.e. $180^\circ$), and maintain the position of the cart. The input to this system is the translational force applied to the cart using the rotation of the tires. The main objective of this thesis is to design a control system that will help in balancing the pendulum while maintaining the position of the cart and implement it in a robot. The pendulum is made free rotating with the help of ball bearings and the angle of the pendulum is measured using an Inertial Measurement Unit (IMU) sensor. The cart is actuated by two Direct Current (DC) motors and the position of the cart is measured using encoders that generate pulse signals based on the wheel rotation. The control is implemented in a cascade format where an inner loop controller is used to stabilize and balance the pendulum in the inverted position and an outer loop controller is used to control the position of the cart. Both the inner loop and outer loop controllers follow the Proportional-Integral-Derivative (PID) control scheme with some modifications for the inner loop. The system is first mathematically modeled using the Newton-Euler first principles method and based on this model, a controller is designed for specific closed-loop parameters. All of this is implemented on hardware with the help of an Arduino Due microcontroller which serves as the main processing unit for the system.

Vertical take-off and landing (VTOL) systems have become a crucial component of aeronautical and commercial applications alike. Quadcopter systems are rather convenient to analyze and design controllers for, owing to symmetry in body dynamics. In this work, a quadcopter model at hover equilibrium is derived, using both high and low level control. The low level control system is designed to track reference Euler angles (roll, pitch and yaw) as shown in previous work [1],[2]. The high level control is designed to track reference X, Y, and Z axis states [3]. The objective of this paper is to model, design and simulate platooning (separation) control for a fleet of 6 quadcopter units, each comprising of high and low level control systems, using a leader-follower approach. The primary motivation of this research is to examine the ”accordion effect”, a phenomenon observed in leader-follower systems due to which positioning or spacing errors arise in follower vehicles due to sudden changes in lead vehicle velocity. It is proposed that the accordion effect occurs when lead vehicle information is not directly communicated with the rest of the system [4][5] . In this paper, the effect of leader acceleration feedback is observed for the quadcopter platoon. This is performed by first designing a classical platoon controller for a nominal case, where communication within the system is purely ad-hoc (i.e from one quadcopter to it’s immediate successor in the fleet). Steady state separation/positioning errors for each member of the fleet are observed and documented during simulation. Following this analysis, lead vehicle acceleration is provided to the controller (as a feed forward term), to observe the extent of it’s effect on steady state separation, specifically along tight maneuvers. Thus the key contribution of this work is a controller that stabilizes a platoon of quadcopters in the presence of the accordion effect, when employing a leader-follower approach. The modeling shown in this paper builds on previous research to design a low costquadcopter platform, the Mark 3 copter [1]. Prior to each simulation, model nonlinearities and hardware constants are measured or derived from the Mark 3 model, in an effort to observe the working of the system in the presence of realistic hardware constraints. The system is designed in compliance with Robot Operating System (ROS) and the Micro Air Vehicle Link (MAVLINK) communication protocol.

One potential application of multi-robot systems is collective transport, a task in which multiple mobile robots collaboratively transport a payload that is too large or heavy to be carried by a single robot. Numerous control schemes have been proposed for collective transport in environments where robots can localize themselves (e.g., using GPS) and communicate with one another, have information about the payload's geometric and dynamical properties, and follow predefined robot and/or payload trajectories. However, these approaches cannot be applied in uncertain environments where robots do not have reliable communication and GPS and lack information about the payload. These conditions characterize a variety of applications, including construction, mining, assembly in space and underwater, search-and-rescue, and disaster response.
Toward this end, this thesis presents decentralized control strategies for collective transport by robots that regulate their actions using only their local sensor measurements and minimal prior information. These strategies can be implemented on robots that have limited or absent localization capabilities, do not explicitly exchange information, and are not assigned predefined trajectories. The controllers are developed for collective transport over planar surfaces, but can be extended to three-dimensional environments.

This thesis addresses the above problem for two control objectives. First, decentralized controllers are proposed for velocity control of collective transport, in which the robots must transport a payload at a constant velocity through an unbounded domain that may contain strictly convex obstacles. The robots are provided only with the target transport velocity, and they do not have global localization or prior information about any obstacles in the environment. Second, decentralized controllers are proposed for position control of collective transport, in which the robots must transport a payload to a target position through a bounded or unbounded domain that may contain convex obstacles. The robots are subject to the same constraints as in the velocity control scenario, except that they are assumed to have global localization. Theoretical guarantees for successful execution of the task are derived using techniques from nonlinear control theory, and it is shown through simulations and physical robot experiments that the transport objectives are achieved with the proposed controllers.

Physical activity helps in reducing the risk of many chronic diseases, and plays a key role in maintaining good health of an individual. Just Walk is an intensively adaptive physical activity intervention, which has been designed based on system identification and control engineering principles. The goal of Just Walk is to design interventions that are responsive to an individual's changing needs, and thus encourage the individual to increase the number of steps walked.

Regularization is widely used in the field of machine learning. The goal of this thesis is to see how classical system identification principles in combination with machine learning methods like regularization help towards getting improved model estimates for complex systems. Estimating individual behavioral models using traditional prediction error methods can be done using an order selection. However, this method is can be computationally expensive due to the extensive search performed on a large set of order combination. If order selection is not done properly, it can cause bias (low order) and variance (high order) issues. In such cases regularization plays an important role in addressing the bias-variance trade-off.

One of the most important applications of identifying individual behavioral models is to understand what factors impact most the behavior of the person. Here "factors" can be considered as inputs (designed or environmental) to the participant over the course of the study, and the "behavior" is the step count of the participant under study. This is done by estimating models with different input combinations and then seeing which combinations of inputs (influence behavior most) give the best model estimate (best describe behavior of the person). As a part of this thesis, it is studied how regularized models can give a better estimation of personalized behavioral models, for the Just Walk study, which can further help in designing personalized interventions.

This work is concerned with how best to reconstruct images from limited angle tomographic measurements. An introduction to tomography and to limited angle tomography will be provided and a brief overview of the many fields to which this work may contribute is given.

The traditional tomographic image reconstruction approach involves Fourier domain representations. The classic Filtered Back Projection algorithm will be discussed and used for comparison throughout the work. Bayesian statistics and information entropy considerations will be described. The Maximum Entropy reconstruction method will be derived and its performance in limited angular measurement scenarios will be examined.

Many new approaches become available once the reconstruction problem is placed within an algebraic form of Ax=b in which the measurement geometry and instrument response are defined as the matrix A, the measured object as the column vector x, and the resulting measurements by b. It is straightforward to invert A. However, for the limited angle measurement scenarios of interest in this work, the inversion is highly underconstrained and has an infinite number of possible solutions x consistent with the measurements b in a high dimensional space.

The algebraic formulation leads to the need for high performing regularization approaches which add constraints based on prior information of what is being measured. These are constraints beyond the measurement matrix A added with the goal of selecting the best image from this vast uncertainty space. It is well established within this work that developing satisfactory regularization techniques is all but impossible except for the simplest pathological cases. There is a need to capture the "character" of the objects being measured.

The novel result of this effort will be in developing a reconstruction approach that will match whatever reconstruction approach has proven best for the types of objects being measured given full angular coverage. However, when confronted with limited angle tomographic situations or early in a series of measurements, the approach will rely on a prior understanding of the "character" of the objects measured. This understanding will be learned by a parallel Deep Neural Network from examples.

In the last few decades, with the revolution of availability of low-cost microelectronics, which allow fast and complex computations to be performed on board, there has been increasing attention to aerial vehicles, especially rotary-wing vehicles. This is because of their ability to vertically takeoff and land (VTOL), which make them appropriate for urban environments where no runways are needed. Quadrotors took considerable attention in research and development due to their symmetric body, which makes them simpler to model and control compared to other configurations.

One contribution of this work is the design of a new open-source based Quadrotor platform for research. This platform is compatible with both HTC Vive Tracking System (HVTS) and OptiTrack Motion Capture System, Robot Operating System (ROS), and MAVLINK communication protocol.

The thesis examined both nonlinear and linear modeling of a 6-DOF rigid-body quadrotor's dynamics along with actuator dynamics. Nonlinear/linear models are used to develop control laws for both low-level and high-level hierarchical control structures. Both HVTS and OptiTrack were used to demonstrate path following for single and multiple quadrotors. Hardware and simulation data are compared. In short, this work establishes a foundation for future work on formation flight of multi-quadrotor.

Unmanned aerial vehicles (UAVs) are widely used in many applications because of their small size, great mobility and hover performance. This has been a consequence of the fast development of electronics, cheap lightweight flight controllers for accurate positioning and cameras. This thesis describes modeling, control and design of an oblique-cross-quadcopter platform for indoor-environments.

One contribution of the work was the design of a new printed-circuit-board (PCB) flight controller (called MARK3). Key features/capabilities are as follows:

(1) a Teensy 3.2 microcontroller with 168MHz overclock –used for communications, full-state estimation and inner-outer loop hierarchical rate-angle-speed-position control,

(2) an on-board MEMS inertial-measurement-unit (IMU) which includes an LSM303D (3DOF-accelerometer and magnetometer), an L3GD20 (3DOF-gyroscope) and a BMP180 (barometer) for attitude estimation (barometer/magnetometer not used),

(3) 6 pulse-width-modulator (PWM) output pins supports up to 6 rotors

(4) 8 PWM input pins support up to 8-channel 2.4 GHz transmitter/receiver for manual control,

(5) 2 5V servo extension outputs for other requirements (e.g. gimbals),

(6) 2 universal-asynchronous-receiver-transmitter (UART) serial ports - used by flight controller to process data from Xbee; can be used for accepting outer-loop position commands from NVIDIA TX2 (future work),

(7) 1 I2C-serial-protocol two-wire port for additional modules (used to read data from IMU at 400 Hz),

(8) a 20-pin port for Xbee telemetry module connection; permits Xbee transceiver on desktop PC to send position/attitude commands to Xbee transceiver on quadcopter.

The quadcopter platform consists of the new MARK3 PCB Flight Controller, an ATG-250 carbon-fiber frame (250 mm), a DJI Snail propulsion-system (brushless-three-phase-motor, electronic-speed-controller (ESC) and propeller), an HTC VIVE Tracker and RadioLink R9DS 9-Channel 2.4GHz Receiver. This platform is completely compatible with the HTC VIVE Tracking System (HVTS) which has 7ms latency, submillimeter accuracy and a much lower price compared to other millimeter-level tracking systems.

The thesis describes nonlinear and linear modeling of the quadcopter’s 6DOF rigid-body dynamics and brushless-motor-actuator dynamics. These are used for hierarchical-classical-control-law development near hover. The HVTS was used to demonstrate precision hover-control and path-following. Simulation and measured flight-data are shown to be similar. This work provides a foundation for future precision multi-quadcopter formation-flight-control.

In this dissertation, we present a H-infinity based multivariable control design methodology that can be used to systematically address design specifications at distinct feedback loop-breaking points. It is well understood that for multivariable systems, obtaining good/acceptable closed loop properties at one loop-breaking point does not mean the same at another. This is especially true for multivariable systems that are ill-conditioned (having high condition number and/or relative gain array and/or scaled condition number). We analyze the tradeoffs involved in shaping closed loop properties at these distinct loop-breaking points and illustrate through examples the existence of pareto optimal points associated with them. Further, we study the limitations and tradeoffs associated with shaping the properties in the presence of right half plane poles/zeros, limited available bandwidth and peak time-domain constraints. To address the above tradeoffs, we present a methodology for designing multiobjective constrained H-infinity based controllers, called Generalized Mixed Sensitivity (GMS), to effectively and efficiently shape properties at distinct loop-breaking points. The methodology accommodates a broad class of convex frequency- and time-domain design specifications. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera parameterization that transforms the nonlinear problem in the controller to an affine one in the Youla et al. parameter. Basis parameters that result in efficient approximation (using lesser number of basis terms) of the infinite-dimensional parameter are studied. Three state-of-the-art subgradient-based non-differentiable constrained convex optimization solvers, namely Analytic Center Cutting Plane Method (ACCPM), Kelley's CPM and SolvOpt are implemented and compared.

The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.

Toward the ambitious long-term goal of a fleet of cooperating Flexible Autonomous Machines operating in an uncertain Environment (FAME), this thesis addresses various perception and control problems in autonomous aerial robotics. The objective of this thesis is to motivate the use of perspective cues in single images for the planning and control of quadrotors in indoor environments. In addition to providing empirical evidence for the abundance of such cues in indoor environments, the usefulness of these perspective cues is demonstrated by designing a control algorithm for navigating a quadrotor in indoor corridors. An Extended Kalman Filter (EKF), implemented on top of the vision algorithm, serves to improve the robustness of the algorithm to changing illumination.

In this thesis, vanishing points are the perspective cues used to control and navigate a quadrotor in an indoor corridor. Indoor corridors are an abundant source of parallel lines. As a consequence of perspective projection, parallel lines in the real world, that are not parallel to the plane of the camera, intersect at a point in the image. This point is called the vanishing point of the image. The vanishing point is sensitive to the lateral motion of the camera and hence the quadrotor. By tracking the position of the vanishing point in every image frame, the quadrotor can navigate along the center of the corridor.

Experiments are conducted using the Augmented Reality (AR) Drone 2.0. The drone is equipped with the following componenets: (1) 720p forward facing camera for vanishing point detection, (2) 240p downward facing camera, (3) Inertial Measurement Unit (IMU) for attitude control , (4) Ultrasonic sensor for estimating altitude, (5) On-board 1 GHz Processor for processing low level commands. The reliability of the vision algorithm is presented by flying the drone in indoor corridors.

Microbial fuel cells(MFC) use micro-organisms called anode-respiring bacteria(ARB) to convert chemical energy into electrical energy. This process can not only treat wastewater but can also produce useful byproduct hydrogen peroxide(H2O2). Process variables like anode potential and pH play important role in the MFC operation and the focus of this dissertation are pH and potential control problems.

Most of the adaptive pH control solutions use signal-based-norms as cost functions, but their strong dependency on excitation signal properties makes them sensitive to noise, disturbances, and modeling errors. System-based-norm( H-infinity) cost functions provide a viable alternative for the adaptation as they are less susceptible to the signal properties. Two variants of adaptive pH control algorithms that use approximate H-infinity frequency loop-shaping (FLS) cost metrics are proposed in this dissertation.

A pH neutralization process with high retention time is studied using lab scale experiments and the experimental setup is used as a basis to develop a first-principles model. The analysis of such a model shows that only the gain of the process varies significantly with operating conditions and with buffering capacity. Consequently, the adaptation of the controller gain (single parameter) is sufficient to compensate for the variation in process gain and the focus of the proposed algorithms is the adaptation of the PI controller gain. Computer simulations and lab-scale experiments are used to study tracking, disturbance rejection and adaptation performance of these algorithms under different excitation conditions. Results show the proposed algorithm produces optimum that is less dependent on the excitation as compared to a commonly used L2 cost function based algorithm and tracks set-points reasonably well under practical conditions. The proposed direct pH control algorithm is integrated with the combined activated sludge anaerobic digestion model (CASADM) of an MFC and it is shown pH control improves its performance.

Analytical grade potentiostats are commonly used in MFC potential control, but, their high cost (>$6000) and large size, make them nonviable for the field usage. This dissertation proposes an alternate low-cost($200) portable potentiostat solution. This potentiostat is tested using a ferricyanide reactor and results show it produces performance close to an analytical grade potentiostat.