Robots have the ability to drive with a wide array of freedom, including the freedom to drive past the surface edge, ending in a possible fatal accident. Ultrasonic sensors may be used on robotics with a constant and steady angle of attack relative to the ground. Robots designed as mobile inverted pendulums, such as the MiPs toys, require a method to observe the roaming surface using sensors not directed perpendicularly, or close to it. Cameras, a common addition to robotic hardware, are optical sensors which capture light from all angles. Using image processing techniques, we are able to detect where the edges of the roaming surface exist.

As the number of robotic toys on the market increases, so does the difficulty of differentiating a product from the competition. One approach to this problem is to develop robots that can interact with the user in novel ways. To this end, a relatively small, ball-catching robot was developed with a focus on low-cost components. The two main features that keep the cost low are a mobile inverted pendulum robot design, and low-cost cameras. The focus of this paper is overcoming the challenges that these two features add the the ball-catching task. Linear regression was used for estimating and predicting the ball trajectory using low-cost cameras. Three strategies for intercepting the ball with a non-holonomic robot were compared. The best strategy for the application used nonlinear model predictive control to calculate paths for the robot. A prototype was built and it successfully caught a thrown ball, but only within a limited area. Finally, improvements are suggested to increase the ball catching area of the robot, and to improve catching accuracy.

Mobile robotic systems are increasingly prevalent in several fields of academia, industry, and everyday life. This dissertation outlines the development of several means of locomotion for such systems and the tools created and used to design them. Novel mechanical designs with minimal actuators are combined with advanced control systems to create dynamic locomotion behavior. A single, unified Lagrangian dynamics architecture is used to represent a variety of robotic systems, derived from first principles and applied programmatically. Model-based control methods are heavily used to take advantage of the known dynamics and are also applied programmatically for the automatic generation of control laws and gain scheduling lookup tables. Improvements to encoder velocity estimation across a wide velocity range are described in detail. A number of key hardware advances in different fields are exploited to create low-cost, but capable, mobile robotic systems: additive manufacturing (3D printing), powerful embedded microprocessors (Arduino, ARM, FPGA), solid state sensors (MEMS accelerometers and gyroscopes), and inexpensive brushed DC motors. This dissertation presents both notable results and tactical details of implementation that will be useful to those designing similar systems.

Several novel robotic systems are presented in this dissertation. First, two incarnations of a mobile balancing platform with two coaxial wheels with the center of mass above the center of rotation are presented. Active feedback control is required to stabilize the system. Next, Switchblade is a patent pending treaded inverted pendulum designed for maximum mobility over a wide range of terrain including tight spaces and significant obstacles (e.g. stairs). Multiple variants of the design are explored, which shows that the vehicle concept is broadly applicable across different length scales and use cases. SkySweeper is an under-actuated robotic system designed for multimodal locomotion along wires and cables. Finally, RAPID is a reconfigurable, automated dynamometer for characterizing small DC motors, the primary purpose of which is identifying the operating parameters of motors used in vehicles with model-based control and estimation algorithms.

Adaptive observation seeks to move sensor vehicles in order to accurately estimate and forecast the state of a system. This thesis seeks to formulate an adaptive observation algorithm around the Ensemble Kalman Filter. The Monte Carlo approach of the Ensemble Kalman filter allows for the approximation of the variance of the system estimate, which can be used to move the vehicles in a manner that minimizes this variance. After an introduction to the problem, this thesis gives a brief history of the Ensemble Kalman filter before describing the formulation of the adaptive observation algorithm. It then goes on to describe the numerical simulation setup that is used to perform experiments that test the algorithm’s performance. The results show the success of my adaptive observation algorithm in reducing the variance of the system estimate and therefore the ability of my algorithm to produce an accurate estimate of a model two-dimensional convective flow.

This thesis presents both the control design used to stabilize a small rover on two wheels as a mobile inverted pendulum, as well as the steering design used to achieve a series of unique stable driving modes. Additionally, the rover is assessed as an educational platform for use in teaching various STEM topics at both the high school and undergraduate university levels. The vehicle, termed BeagleRover, uses four DC motors and four servo motors to independently steer each wheel and achieve a total of six different driving modes, four of which are inherently stable four-wheel drive modes while two are unstable two-wheel drives modes. Two of the four stable drive modes implement Ackermann steering geometry to reduce side slip when driving around a turn. Experimental results using measurements from an onboard gyroscope suggest that side slip is indeed reduced by this method. Stability in the two unstable drive modes is achieved through classical control methods including lead and lag control. Complementary filtering of gyroscope and accelerometer measurements is used to derive accurate body position data for use in feedback. In support of current STEM education trends, this thesis provides a detailed solution set to the steering, control and filtering problems for potential use in STEM course material.

This work presents a new trajectory planning formulation that aims to maximize the probability of finding a target inside a bound domain using a robot over a specified time interval. A preliminary algorithm is developed to detect stationary targets, which is further extended to detect moving targets. Values are assigned at every grid point in the domain based on its distance from the robot; each value represents the probability of not finding the target if it is at that location. A cost function is formulated that computes the likelihood of not finding the target for any given path provided the target is inside the domain.

This cost function is minimized with a set of bound constraints on inputs to obtain an optimal path to find the target. The algorithm incorporates an adjoint-based gradient method to link the input parameters to the cost function. The cost function is nonlinear which makes it hard for most commercial off-the-shelf (COTS) optimization packages to solve it.

For faster convergence the recently developed low storage reduced Hessian box constraint optimization method (LRH-B) was used.

Results show our algorithm outperforms other optimization algorithms, and also explain how this framework is beneficial in terms of application.

The purpose of this thesis is to establish an experimental process by which a structural system may be characterized through modal analysis in an effort to develop and implement disturbance rejection control designs. Throughout this report, a structural test article representing a simplified aircraft model will be the subject of study, referred to as the "Iron Bird." This report discusses how the article was modeled using finite element analysis for the purpose of control design. Then, the report establishes a "dry" wind tunnel testing approach by utilizing readily available testing equipment and hardware as a means of testing aerodynamic control systems as opposed to requiring a wind tunnel facility for the purposes of experimental validation. Reviewing both the experimental setup and design environment, this thesis aims to establish a comprehensive account of how this system was analyzed, designed, and tested. Finally, with the inclusion of plant uncertainty this report analyzes a suite of control design approaches in order to establish methods of implementing more robust controller designs for modal disturbance rejection on this particular system.

The accurate space-time discretization of the partial differential equations (PDEs) governing the dynamic behavior of complex physical phenomena is a core challenge in the field of Computational Fluid Dynamics, and in the simulation of turbulence in particular. However, it appears that over the last 30 years a disproportionate amount of attention has been addressed toward the improvement of spatial discretization techniques, while temporal discretization has relied, in most cases, on old consolidated approaches. Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes Equation (NSE) today often use a mixed implicit/explicit (IMEX) time integration approach developed in the mid 1980s, which combines the second-order implicit Crank-Nicolson (CN) method for the integration of the linear stiff terms and a third-order explicit low-storage Runge-Kutta-Wray (RKW3) method for the nonlinear terms. This hybrid approach, dubbed CN/RKW3, guarantees overall second-order accuracy for the time integration, while allowing an efficient storage implementation.

Our work focuses on the development of new mixed implicit/explicit time integration schemes of the Runge-Kutta type for the simulation of high-dimensional stiff ODEs, with particular attention to the simulation of the NSE. Compared with the venerable CN/RKW3 method, our numerical schemes have better accuracy, improved stability properties, and require the same or slightly increased storage.

We have also developed new relaxation schemes for the iterative solution of linear and, with some modification, nonlinear systems arising from the discretization of PDEs. These schemes prove especially advantageous when applied as the smoothing step in the multigrid solution of elliptic PDEs over stretched grids. A noteworthy application is the iterative solution of the pressure Poisson equation arising when imposing the diverge-free constraint during the simulation of the incompressible NSE using a fractional step method. Compared with the standard approach, our schemes require significantly less computation, while providing comparable converge rates.

We then discuss the implementation of an Ensemble Kalman Filter (EnKF) for the short-term prediction of ocean waves. The approach leverages one of our low-storage IMEX Runge-Kutta schemes for the highly-resolved simulation of the nonlinear equations used to describe wave propagation. We found that, using EnKF for data assimilation of wave measurement data, it is possible to perform accurate wave forecasting up to thirty seconds into the future, provided a sufficient number of ensemble members is employed.

Finally, we introduce a new direct multiple shooting algorithm for Nonlinear Model Predictive Control (NMPC). The new approach allows analytic calculation of the discretized trajectories and associated gradients, which are required when solving the nonlinear programming problem arising within the NMPC formulation. For the discretization of the trajectories, two solutions are proposed: one based on a Runge-Kutta discretization of the continuous-time model, and one leveraging a nonlinear discrete-time model based on Taylor-Lie algebra. This algorithm is then applied to the optimization of the power take-off of a point-absorber wave energy converter (WEC). Results have shown that NMPC improves the WEC power take-off with respect to linear MPC, since the nonlinear viscous forces affecting WEC dynamics are better accounted for. Moreover, the nonlinear formulation also allows the investigation of more complex configurations, such as one-way power flow.

This study consists of two parts, and the first part is the Cable-driven boat motion simulator. In naval operations, vertical take-off and landing (VTOL) drones are widely used as cost-effective assets that are easy to maneuver, enhancing the reconnaissance and surveillance capabilities of ships. Despite their advantages, these drones have limited operational time and need to return to the base platform. To address the challenge of developing drone landing systems, conducting experiments at sea poses significant costs and risks. This dissertation proposes the utilization of a ground-based motion simulator that mimics the 6-DOF motion of a boat. The simulator aims to replicate the sea environment up to sea state 6 on the Doublas scale. To achieve motion control and optimization of the cable-driven boat motion simulator, a Control Lyapunov function-based Quadratic Program (CLF-QP) control method was studied. Given the importance of cable tension in cable-driven robots, the CLF-QP control method facilitates platform movement in the desired 6-DOF motions while ensuring that cable tensions remain within specified limits. In addition to the investigation into designing a boat motion simulator, a related research project focused on camera image-based pose estimation for drone landing. This study is preliminary research on drone landing control and specifically addresses the 3D rotation estimation of a moving platform using 2D images captured by a camera. The research assumes the presence of a circular pattern marker on the flight deck of a ship, with the drone hovering at the center of the platform. Equipped with a camera, the drone captures 2D imagesof the markers and measures the distance between them. As the platform rotates, the circular pattern of markers transforms into an ellipse. The study derives the ellipse equation from the marker positions on the ellipse, utilizing geometry and trigonometric functions to determine the platform’s rotation sequence. By estimating the platform’s rotation, the drone can effectively determine the optimal timing for the platform to rotate within the drone’s capacity to land safely. The proposed method was validated through simulation and hardware testing, with a subsequent discussion on the platform state, and tension tracking errors obtained by a motion capture system and load-cell tension sensors. The second part of this study is the Pipeline exploration and inspection robot. The research introduces a new robot design specifically tailored for inspecting, exploring, and mapping intricate pipe networks featuring multiple curves and joints. The proposed robot, named Model S4, stands out for its simplicity, high maneuverability, and static stability, achieved through the incorporation of four omniwheels arranged in a single plane at the robot center. The robot is equipped with high-torque motors that effectively control roll motions. The robot employs a spring-servo motor integrated series elastic actuator to enhance stability. This mechanism ensures that the robot maintains three or more points of contact with the opposite sidewalls of the pipe, causing the robot’s center plane to consistently align with the centerline of the pipe throughout its operation. This design promotes stable travel within the pipe at any orientation relative to gravity, without the need for constant feedback. Additionally, the robot features mechanisms designed for efficient navigation through pipe curves and T-joints, a capability validated through hardware testing focusing on roll control and maneuvering through pipe curves and joints. The primary contributions of this dissertation are as follows: 1. Control Lyapunov Function-based Quadratic Program (CLF-QP) control for motion control and tension optimization of the cable-driven boat motion simulator. 2. The workspace Analysis for Parameter Optimization of the cable-driven boat motion simulator utilizing static analysis, cable-to-cable and cable-to-platform interference detection algorithm. 3. Hardware model building and testing to verify the performance of CLF-QP control with the discussion of platform pose and tension tracking errors measured by a motion capture system and tension sensors. 4. The simulation and hardware experimental validation of a camera image-based platform rotation estimation. 5. A novel design of a robot for interior exploration and inspection of pipe networks embedding the torsion spring and servo motor integrated series elastic actuator.

A new class of derivative-free optimization algorithms is developed to solve, with remarkable efficiency, a range of practical nonconvex optimization problems whose function evaluations are computationally (or experimentally) expensive. These new algorithms, which are provably convergent under the appropriate assumptions, are response surface methods which iteratively minimize metrics based on an interpolation of existing datapoints and a synthetic model of the uncertainty of this interpolant, which itself is built on the framework of a Delaunay triangulation over the existing datapoints. Unlike other response surface methods, our algorithms can employ any well-behaved interpolation strategy.

An important subproblem in $\alpha$-DOGS is the estimation of the averaging process in stationary ergodic processes. A new approach for determining this quantity is also presented which is mathematically rigorous and numerically accurate.

There are six main algorithms developed in this class thus far (only four of them are presented in this thesis) which address a wide range of practical optimization problems. The first algorithm, dubbed $\Delta$-DOGS, efficiently minimizes expensive objective functions inside linearly-constrained feasible domains. The second algorithm, $\Delta$-DOGS(C), extends $\Delta$-DOGS to handle efficiently more general convex search domains. The third algorithm incorporates a grid into $\Delta$-DOGS to achieve better convergence by performing fewer function evaluations at the boundary of feasibility. The fourth algorithm, dubbed $\alpha$-DOGS, efficiently minimizes objective functions which are noisy, generally derived by taking the statistics of stationary and ergodic random processes. An important subproblem in $\alpha$-DOGS is the estimation of the averaging process in stationary ergodic processes. A new approach for determining this quantity is also presented which is mathematically rigorous and numerically accurate.

Rigorous convergence analyses of all of the algorithms proposed are presented, and necessary conditions to guarantee convergence to the global minimum are provided. For validation, the algorithms proposed have been tested on both well-known benchmark optimization problems as well as some new application-oriented optimization problems in ship design; some illustrative results will be shown.