This dissertation presents a comprehensive study of modeling and control issues associated with nonholonomic differential drive mobile robots. The first part of dissertation focuses on modeling using Lagrangian mechanics. The dynamics is modeled as a two-input two-output (TITO) nonlinear model. Motor dynamics are also modeled. Trade studies are conducted to shed light on critical vehicle design parameters, and how they impact static properties, dynamic properties, directional stability, coupling and overall vehicle design. An aspect ratio based dynamic decoupling condition is also presented. The second part of dissertation addresses design of linear time-invariant (LTI), multi-input multi-ouput (MIMO) fixed-structure H∞ controllers for the inner-loop velocity (v, ω) tracking system of the robot, motivated by a practical desire to design classically structured robust controllers. The fixed-structure H∞-optimal controllers are designed using Generalized Mixed Sensitivity(GMS) methodology to systematically shape properties at distinct loop breaking points. The H∞-control problem is solved using nonsmooth optimization techniques to compute locally optimal solutions. Matlab’s Robust Control toolbox (Hinfstruct and Systune) is used to solve the nonsmooth optimization. The dissertation also addresses the design of fixed-structure MIMO gain-scheduled H∞ controllers via GMS methodology. Trade-off studies are conducted to address the effect of vehicle design parameters on frequency and time domain properties of the inner-loop control system of mobile robot. The third part of dissertation focuses on the design of outer-loop position (x, y, θ) control system of mobile robot using real-time model predictive control (MPC) algorithms. Both linear time-varying (LTV) MPC and nonlinear MPC algorithms are discussed.The outer-loop performance of mobile robot is studied for two applications - 1) single robot trajectory tracking and multi-robot coordination in presence of obstacles, 2) maximum progress maneuvering on racetrack. The dissertation specifically addresses the impact of variation of c.g. position w.r.t. wheel-axle on directional maneuverability, peak control effort required to perform aggressive maneuvers, and overall position control performance. Detailed control relevant performance trade-offs associated with outer-loop position control are demonstrated through simulations in discrete time. Optimizations packages CPLEX(convex-QP in LTV-MPC) and ACADO(NLP in nonlinear-MPC) are used to solve the OCP in real time. All simulations are performed on Robot Operating System (ROS).

This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck) regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current (DC-AC) inverter. These are widely used for power transfer in a variety of industrial and personal applications. This motivates the precise quantification of conditions under which existing modeling and design methods yield satisfactory designs, and the study of alternatives when they don’t. This dissertation describes a method utilizing Fourier components of the input square wave and the inductor-capacitor (LC) filter transfer function, which doesn’t require the small ripple approximation. Then, trade-offs associated with the choice of the filter order are analyzed for integrated buck converters with a constraint on their chip area. Design specifications which would justify using a fourth or sixth order filter instead of the widely used second order one are examined. Next, sampled-data (SD) control of a buck converter is analyzed. Three methods for the digital controller design are studied: analog design followed by discretization, direct digital design of a discretized plant, and a “lifting” based method wherein the sampling time is incorporated in the design process by lifting the continuous-time design plant before doing the controller design. Specifically, controller performance is quantified by studying the induced-L2 norm of the closed loop system for a range of switching/sampling frequencies. In the final segment of this dissertation, the inner-outer control loop, employed in inverters with an inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the loop broken at the error and the control are examined, demonstrating that traditional methods only address these properties for one loop-breaking point. New controllers are then provided for improving both sets of properties.

Over the past few decades, there is an increase in demand for various ground robot applications such as warehouse management, surveillance, mapping, infrastructure inspection, etc. This steady increase in demand has led to a significant rise in the nonholonomic differential drive vehicles (DDV) research. Albeit extensive work has been done in developing various control laws for trajectory tracking, point stabilization, formation control, etc., there are still problems and critical questions in regards to design, modeling, and control of DDV’s - that need to be adequately addressed. In this thesis, three different dynamical models are considered that are formed by varying the input/output parameters of the DDV model. These models are analyzed to understand their stability, bandwidth, input-output coupling, and control design properties. Furthermore, a systematic approach has been presented to show the impact of design parameters such as mass, inertia, radius of the wheels, and center of gravity location on the dynamic and inner-loop (speed) control design properties. Subsequently, extensive simulation and hardware trade studies have been conductedto quantify the impact of design parameters and modeling variations on the performance of outer-loop cruise and position control (along a curve). In addition to this, detailed guidelines are provided for when a multi-input multi-output (MIMO) control strategy is advisable over a single-input single-output (SISO) control strategy; when a less stable plant is preferable over a more stable one in order to accommodate performance specifications. Additionally, a multi-robot trajectory tracking implementation based on receding horizon optimization approach is also presented. In most of the optimization-based trajectory tracking approaches found in the literature, only the constraints imposed by the kinematic model are incorporated into the problem. This thesis elaborates the fundamental problem associated with these methods and presents a systematic approach to understand and quantify when kinematic model based constraints are sufficient and when dynamic model-based constraints are necessary to obtain good tracking properties. Detailed instructions are given for designing and building the DDV based on performance specifications, and also, an open-source platform capable of handling high-speed multi-robot research is developed in C++.

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.

Toward the ambitious long-term goal of developing a robotic circus, this thesis addresses key steps toward the development of a ground robot that can catch a ball. Toward this end, we examine nonlinear quadratic drag trajectories for a tossed ball. Relevant least square error fits are provided. It is also shown how a Kalman filter and Extended Kalman filter can be used to generate estimates for the ball trajectory.

Several simple ball intercept policies are examined. This includes open loop and closed loop policies. It is also shown how a low-cost differential-drive research grade robot can be built, modeled and controlled. Directions for developing more complex xy planar intercept policies are also briefly discussed. In short, the thesis establishes a foundation for future work on developing a practical ball catching robot.

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.

Swarms of low-cost, autonomous robots can potentially be used to collectively perform tasks over large domains and long time scales. The design of decentralized, scalable swarm control strategies will enable the development of robotic systems that can execute such tasks with a high degree of parallelism and redundancy, enabling effective operation even in the presence of unknown environmental factors and individual robot failures. Social insect colonies provide a rich source of inspiration for these types of control approaches, since they can perform complex collective tasks under a range of conditions. To validate swarm robotic control strategies, experimental testbeds with large numbers of robots are required; however, existing low-cost robots are specialized and can lack the necessary sensing, navigation, control, and manipulation capabilities.

To address these challenges, this thesis presents a formal approach to designing biologically-inspired swarm control strategies for spatially-confined coverage and payload transport tasks, as well as a novel low-cost, customizable robotic platform for testing swarm control approaches. Stochastic control strategies are developed that provably allocate a swarm of robots around the boundaries of multiple regions of interest or payloads to be transported. These strategies account for spatially-dependent effects on the robots' physical distribution and are largely robust to environmental variations. In addition, a control approach based on reinforcement learning is presented for collective payload towing that accommodates robots with heterogeneous maximum speeds. For both types of collective transport tasks, rigorous approaches are developed to identify and translate observed group retrieval behaviors in Novomessor cockerelli ants to swarm robotic control strategies. These strategies can replicate features of ant transport and inherit its properties of robustness to different environments and to varying team compositions. The approaches incorporate dynamical models of the swarm that are amenable to analysis and control techniques, and therefore provide theoretical guarantees on the system's performance. Implementation of these strategies on robotic swarms offers a way for biologists to test hypotheses about the individual-level mechanisms that drive collective behaviors. Finally, this thesis describes Pheeno, a new swarm robotic platform with a three degree-of-freedom manipulator arm, and describes its use in validating a variety of swarm control strategies.

Toward the ambitious long-term goal of a fleet of cooperating Flexible Autonomous Machines operating in an uncertain Environment (FAME), this thesis addresses several critical modeling, design and control objectives for ground vehicles. One central objective is formation of multi-robot systems, particularly, longitudinal control of platoon of ground vehicle. In this thesis, the author use low-cost ground robot platform shows that with leader information, the platoon controller can have better performance than one without it.

Based on measurement from multiple vehicles, motor-wheel system dynamic model considering gearbox transmission has been developed. Noticing the difference between on ground vehicle behavior and off-ground vehicle behavior, on ground vehicle-motor model considering friction and battery internal resistance has been put forward and experimentally validated by multiple same type of vehicles. Then simplified longitudinal platoon model based on on-ground test were used as basis for platoon controller design.

Hardware and software has been updated to facilitate the goal of control a platoon of ground vehicles. Based on previous work of Lin on low-cost differential-drive

(DD) RC vehicles called Thunder Tumbler, new robot platform named Enhanced

Thunder Tumbler (ETT 2) has been developed with following improvement: (1) optical wheel-encoder which has 2.5 times higher resolution than magnetic based one,

(2) BNO055 IMU can read out orientation directly that LSM9DS0 IMU could not,

(3) TL-WN722N Wifi USB Adapter with external antenna which can support more stable communication compared to Edimax adapter, (4) duplex serial communication between Pi and Arduino than single direction communication from Pi to Arduino, (5) inter-vehicle communication based on UDP protocol.

All demonstrations presented using ETT vehicles. The following summarizes key hardware demonstrations: (1) cruise-control along line, (2) longitudinal platoon control based on local information (ultrasonic sensor) without inter-vehicle communication, (3) longitudinal platoon control based on local information (ultrasonic sensor) and leader information (speed). Hardware data/video is compared with, and corroborated by, model-based simulations. Platoon simulation and hardware data reveals that with necessary information from platoon leader, the control effort will be reduced and space deviation be diminished among propagation along the fleet of vehicles. In short, many capabilities that are critical for reaching the longer-term FAME goal are demonstrated.

With recent advances in missile and hypersonic vehicle technologies, the need for being able to accurately simulate missile-target engagements has never been greater. Within this research, we examine a fully integrated missile-target engagement environment. A MATLAB based application is developed with 3D animation capabilities to study missile-target engagement and visualize them. The high fidelity environment is used to validate miss distance analysis with the results presented in relevant GNC textbooks and to examine how the kill zone varies with critical engagement parameters; e.g. initial engagement altitude, missile Mach, and missile maximum acceleration. A ray-based binary search algorithm is used to estimate the kill zone region; i.e. the set of initial target starting conditions such that it will be "killed". The results show what is expected. The kill zone increases with larger initial missile Mach and maximum acceleration & decreases with higher engagement altitude and higher target Mach. The environment is based on (1) a 6DOF bank-to-turn (BTT) missile, (2) a full aerodynamic-stability derivative look up tables ranging over Mach number, angle of attack and sideslip angle (3) a standard atmosphere model, (4) actuator dynamics for each of the four cruciform fins, (5) seeker dynamics, (6) a nonlinear autopilot, (7) a guidance system with three guidance algorithms (i.e. PNG, optimal, differential game theory), (8) a 3DOF target model with three maneuverability models (i.e. constant speed, Shelton Turn & Climb, Riggs-Vergaz Turn & Dive). Each of the subsystems are described within the research. The environment contains linearization, model analysis and control design features. A gain scheduled nonlinear BTT missile autopilot is presented here. Autopilot got sluggish as missile altitude increased and got aggressive as missile mach increased. In short, the environment is shown to be a very powerful tool for conducting missile-target engagement research - a research that could address multiple missiles and advanced targets.

Scarcity of potable water is one of the major problems faced in the world today. Majority of this problem can be solved if technology is developed to obtain potable water from brackish or saline water. The present desalination methods face challenges such as high costs in terms of energy consumption and infrastructure, physical size of the system, requirement of membrane and high pressure systems and hence have been facing various issues in implementation of the same.

This research provides a new low pressure, low energy, portable method to desalinate water without the need for separation membranes, heat or chemical reactions. This method is energy efficient, cost effective, compact, environment friendly and suitable for portable desalination units. This technology, named as Polyphase Alternating current Bi-Ionic Propulsion System (PACBIPS) makes use of polyphase alternating current source to create a gradient in salt concentration. The gradient in salt concentration is achieved due to the creation of a traveling wave which attracts anions on its positive peak (crests) and cations on its negative peak (troughs) and travels along a central pipe thereby flushing the ions down.

Another method of PACBIPS is based on Helmholtz capacitor which involves the formation of an electric double layer between the electrode and electrolyte consisting of equal and opposite ions which can be approximated as a capacitor. Charging and discharging this capacitor helps adsorb the ions onto a carbon electrode which has high surface area and electrical conductivity. This desalinates seawater and provides pure water. Mathematical modeling, analysis and implementation of the two methods have

been presented in this work. The effects of zeta potential, electric field screening, electric mobility on desalination have been discussed.