This dissertation presents new fuzzy logic techniques for designing control systems for a wide class of complex systems. The methods are developed in detail for a crane system which contains one rigid-body and one oscillation mode. The crane problem is to transfer the rigid body a given distance such that the pendulation of the oscillation mode is regulated at the final time using a single control input. The investigations include in-depth studies of the time-optimal crane control problem as an integral part of the work. The main contributions of this study are: (1) Development of rule-based systems (both fuzzy and crisp) for the design of optimal controllers. This development involves control variable parametrization, rule derivation with parameter perturbation methods, and the design of rule based controllers, which can be combined with model-based feedback control methods. (2) A thorough investigation and analysis of the solutions for time-optimal control problems of oscillation mode systems, with particular emphasis on the use of phase-plane interpretation. (3) Development of fuzzy logic control system methodology using expert rules obtained through energy reducing considerations. In addition, dual mode control is a "spin-off" design method which, although no longer time optimal, can be viewed as a near-optimal control method which may be easier to implement. In both types of design optimization of the fuzzy logic controller can be used to improve performance. / Ph. D.

A method utilizing H2 control concepts and the numerical method of Polynomial Chaos was developed in order to create a novel robust probabilistically optimal control approach. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. As such, the development of new methods utilizing probability density functions (PDFs) was desired. From a more theoretical viewpoint, the utilization of Polynomial Chaos for studying and designing control systems has not been very thoroughly investigated. The current work looks at expanding the H2 and related Linear Quadratic Regulator (LQR) control problems for systems with parametric uncertainty. This allows solving deterministic linear equations that represent probabilistic linear differential equations. The application of common LTI (Linear Time Invariant) tools to these expanded systems are theoretically justified and investigated. Examples demonstrating the utilized optimization process for minimizing the H2 norm and parallels to LQR design are presented. The dissertation begins with a thorough background section that reviews necessary probability theory. Also, the connection between Polynomial Chaos and dynamic systems is explained. Next, an overview of related control methods, as well as an in-depth review of current Polynomial Chaos literature is given. Following, formal analysis, related to the use of Polynomial Chaos, is provided. This lays the ground for the general method of control design using Polynomial Chaos and H2. Then an experimental section is included that demonstrates controller synthesis for a constructed probabilistic system. The experimental results lend support to the method. / Ph. D.

Falls from heights (FFH) are one of the leading causes of fatalities in skilled labor divisions such as construction, mining, agriculture/forestry, and manufacturing. Previous research has established that localized muscle fatigue (LMF) increases center of mass (COM)- and center of pressure (COP)-based measures of quiet stance. This is important because these increases have been linked to elevated risk of falls, and workers in the construction industry frequently engage in fatiguing activities while working at heights. In addition, the rate of fatality due to an occupational fall increases exponentially with age. Improved methods of fall prevention may be obtained through increased understanding of factors that have a deleterious effect on balance and postural control such as LMF and aging. An initial study was conducted to investigate the effects of LMF and aging on balance recovery from a postural perturbation without stepping. Sagittal plane postural perturbations were administered to young and older groups of participants before and after exercises to fatigue the lumbar extensors or ankle plantar flexors. Measures of balance recovery were based on the COM and COP trajectories and the maximum perturbation that could be withstood without stepping. Balance recovery measures were consistent with an LMF-induced decrement to recover from perturbations without stepping. Aging was also associated with an impaired ability to recover from the perturbations. The second study in the series investigated the effects of aging and LMF on the neural control of upright stance during small postural perturbations. Small magnitude postural perturbations were administered to young and older groups before and after fatiguing exercises. A single degree of freedom (DOF) model of the human body was developed that accurately simulated the experimentally collected kinematics during recovery from the perturbations. The model was controlled by invariant feedback gains that operated on the time-delayed kinematics. Feedback gains and time-delay were optimized for each participant, and a novel delay margin analysis was performed to assess system robustness toward instability. Results indicated that older individuals had a longer "effective" time-delay and exhibited greater reliance on afferent velocity information. No changes in feedback controller gains, time-delay, or delay margins were found with LMF in either age group. The final study investigated the use of a nonlinear controller to simulate responses to large magnitude postural perturbations. A three DOF model of the human body was developed and controlled with the state-dependent Riccati equation (SDRE). Parameters of the SDRE were optimized to fit the experimentally recorded kinematics. Unlike other forms of nonlinear control, the SDRE provides meaningful parameters for interpretation in the system identification. The SDRE approach was successful at stabilizing the dynamical system; however, accurate results were not obtained. Reasons for these errors are discussed, and an alternative formulation to the time-delayed optimal control problem using Roesser state space equations is presented. / Ph. D.

Accurately simulating human motions is a major function of and challenge to digital human models and integrating humans in computer-aided design systems. Numerous successful applications of human motion simulation have already demonstrated their ability to improve occupational efficiency, effectiveness, and safety. In this dissertation, a novel motion simulation model using fuzzy logic control is presented. This model was motivated by the fact that humans use linguistic terms to guide their behaviors while fuzzy logic provides mathematical representations of linguistic terms. Specifically in this model, fuzzy logic was used to specify a neural controller which was generally considered as the part in the postural control system that plans human motions. Fuzzy rules were generated according to certain trends observed from actual human motions. An optimization procedure was performed to specify the parameters of the membership functions by minimizing the differences between the simulated and actual final postures. This research contributed to the field of human movement science by providing a motion simulation model that can accurately predict novel human motions and provide interpretations of potential human motion planning strategies. Understanding balance control is another research focus in this dissertation. Investigating balance control may aid in preventing unnecessary fall-related incidents and understanding the postural control system. Since human behaviors are generally effective and efficient, balance control models (both two- and three-dimensional) based on an optimal control strategy were developed to aid in better understanding balance control. Specifically, the neural controller was considered as an optimal controller that minimizes a performance index defined by physical quantities relevant to sway. Free model parameters, such as weights of relevant physical quantities and sensory delay time, were determined by an optimization procedure whose objective was to minimize a scalar error between simulated and experimental center-of-pressure (COP) based measures. Many factors, such as aging, localized muscle fatigue, and external loads, have been found to adversely affect balance control. At the same time, behaviors during upright stance are commonly characterized by COP-based measures. Thus, changes in COP based measures with aging, LMF, and external loads were addressed by using the proposed models, and possible postural control mechanisms were identified by interpreting these changes. Findings from these studies demonstrated that the proposed models were able to accurately simulate human sway behaviors and provide plausible mechanisms regarding how the postural control system works when maintaining upright balance. / 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.

Spacecraft relative motion modeling and control promises to enable or augment a wide range of missions for scientific research, military applications, and space situational awareness. This dissertation focuses on the development of novel, optimization-based, control design for some representative relative-motion-enabled missions. Spacecraft relative motion refers to two (or more) satellites in nearly identical orbits. We examine control design for relative configurations on the scale of meters (for the purposes of proximity operations) as well as on the scale of tens of kilometers (representative of science gathering missions). Realistic control design for satellites is limited by accurate modeling of the relative orbital perturbations as well as the highly constrained nature of most space systems. We present solutions to several types of optimal orbital maneuvers using a variety of different, realistic assumptions based on the maneuver objectives. Initially, we assume a perfectly circular orbit with a perfectly spherical Earth and analytically solve the under-actuated, minimum-energy, optimal transfer using techniques from optimal control and linear operator theory. The resulting open-loop control law is guaranteed to be a global optimum. Then, recognizing that very few, if any, orbits are truly circular, the optimal transfer problem is generalized to the elliptical linear and nonlinear systems which describe the relative motion. Solution of the minimum energy transfer for both the linear and nonlinear systems reveals that the resulting trajectories are nearly identical, implying that the nonlinearity has little effect on the relative motion. A continuous-time, nonlinear, sliding mode controller which tracks the linear trajectory in the presence of a higher fidelity orbit model shows that the closed-loop system is both asymptotically stable and robust to disturbances and un-modeled dynamics. Next, a novel method of computing discrete-time, multi-revolution, finite-thrust, fuel-optimal, relative orbit transfers near an elliptical, perturbed orbit is presented. The optimal control problem is based on the classical, continuous-time, fuel-optimization problem from calculus of variations, and we present the discrete-time analogue of this problem using a transcription-based method. The resulting linear program guarantees a global optimum in terms of fuel consumption, and we validate the results using classical impulsive orbit transfer theory. The new method is shown to converge to classical impulsive orbit transfer theory in the limit that the duration of the zero-order hold discretization approaches zero and the time horizon extends to infinity. Then the fuel/time optimal control problem is solved using a hybrid approach which uses a linear program to solve the fuel optimization, and a genetic algorithm to find the minimizing time-of-flight. The method developed in this work allows mission planners to determine the feasibility for realistic spacecraft and motion models. Proximity operations for robotic inspection have the potential to aid manned and unmanned systems in space situational awareness and contingency planning in the event of emergency. A potential limiting factor is the large number of constraints imposed on the inspector vehicle due to collision avoidance constraints and limited power and computational resources. We examine this problem and present a solution to the coupled orbit and attitude control problem using model predictive control. This control technique allows state and control constraints to be encoded as a mathematical program which is solved on-line. We present a new thruster constraint which models the minimum-impulse bit as a semi-continuous variable, resulting in a mixed-integer program. The new model, while computationally more expensive, is shown to be more fuel-efficient than a sub-optimal approximation. The result is a fuel efficient, trajectory tracking, model predictive controller with a linear-quadratic attitude regulator which tracks along a pre-computed ``safe'' trajectory in the presence of un-modeled dynamics on a higher fidelity orbital and attitude model. / Ph. D.

This thesis aims to address the real-time planning and nonlinear control of quadrupedal locomotion such that the resulting gaits are robust to various kinds of disturbances. Specifically, this work addresses two scenarios. Namely, a quasi-static formulation in which an inertial appendage (i.e., a tail) is used to assist the quadruped in negating external push disturbances, and an agile formulation which is derived in a manner such that an appendage could easily be added in future work to examine the affect of tails on agile and high-speed motions. Initially, this work presents a unified method in which bio-inspired articulated serpentine robotic tails may be integrated with walking robots, specifically quadrupeds, in order to produce stable and highly robust locomotion. The design and analysis of a holonomically constrained 2 degree of freedom (DOF) tail is shown and its accompanying nonlinear dynamic model is presented. The model created is used to develop a hierarchical control scheme which consists of a high-level path planner and a full-order nonlinear low-level controller. The high-level controller is based on model predictive control (MPC) and acts on a linear inverted pendulum (LIP) model which has been extended to include the forces produced by the tail by augmenting the LIP model with linearized tail dynamics. The MPC is used to generate center of mass (COM) and tail trajectories and is subject to the net ground reaction forces of the system, tail shape, and torque saturation of the tail in order to ensure overall feasibility of locomotion. At the lower level, a full-order nonlinear controller is implemented to track the generated trajectories using quadratic program (QP) based input-output (I-O) feedback linearization which acts on virtual constraints. The analytical results of the proposed approach are verified numerically through simulations using a full-order nonlinear model for the quadrupedal robot, Vision60, augmented with a tail, totaling at 20 DOF. The simulations include a variety of disturbances to show the robustness of the presented hierarchical control scheme. The aforementioned control scheme is then extended in the latter portion of this thesis to achieve more dynamic, agile, and robust locomotion. In particular, we examine the use of a single rigid body model as the template model for the real-time high-level MPC, which is linearized using variational based linearization (VBL) and is solved at 200 Hz as opposed to an event-based manner. The previously defined virtual constraints controller is also extended so as to include a control Lyapunov function (CLF) which contributes to both numerical stability of the QP and aids in stability of the output dynamics. This new hierarchical scheme is validated on the A1 robot, with a total of 18 DOF, through extensive simulations to display agility and robustness to ground height variations and external disturbances. The low-level controller is then further validated through a series of experiments displaying the ability for this algorithm to be readily transferred to hardware platforms. / Master of Science / This thesis aims to address the real-time planning and nonlinear control of four legged walking robots such that the resulting gaits are robust to various kinds of disturbances. Initially, this work presents a method in which a robotic tail can be integrated with legged robots to produce very stable walking patterns. A model is subsequently created to develop a multi-layer control scheme which consists of a high-level path planner, based on a reduced-order model and model predictive control techniques, that determines the trajectory for the quadruped and tail, followed by a low-level controller that considers the full-order dynamics of the robot and tail for robust tracking of the planned trajectory. The reduced-order model considered here enforces quasi-static motions which are slow but generally stable. This formulation is validated numerically through extensive full-order simulations of the Vision60 robot. This work then proceeds to develop an agile formulation using a similar multi-layer structure, but uses a reduced-order model which is more amenable to dynamic walking patterns. The low-level controller is also augmented slightly to provide additional robustness and theoretical guarantees. The latter control algorithm is extensively numerically validated in simulation using the A1 robot to show the large increase in robustness compared to the quasi-static formulation. Finally, this work presents experimental validation of the low-level controller formulated in the latter half of this work.

This thesis presents collision avoidance integrated with lane keeping and adaptive cruise control for a car. Collision avoidance is the ability to avoid obstacles that are in the vehicle's path, without causing damage to the obstacle or car. There are three types of collision avoidance controllers, passive, active, and semi-active. This thesis is designed using active collision avoidance controllers. There are two controllers developed for collision avoidance in this paper. They are an optimal controller and a fuzzy controller. The optimal vehicle trajectory, which maximizes the distance to an obstacle and changes lanes, is derived. The optimal collision avoidance controller is a closed loop controller; with the decisions based on the current state. The fuzzy controller makes decisions based on the system rules. A simulation environment was created to compare these two controllers as viable solutions for collision avoidance. The environment uses MATLAB/Simulink for simulation of the vehicle as well as the optimal and fuzzy controllers. The simulation incorporates system blocks of the kinematics of a car, navigation, states, control law, and velocity controller. Once the controllers are fully developed and tested in the simulation environment, they are implemented and tested on the platform vehicle. This verifies the real world performance of the controllers. The platform vehicle is a modified radio controlled car. This car is completely autonomous. The car has onboard sensors that allow it to follow a white piece of tape as well as detect obstacles. / Master of Science

A compact model representing the dynamics between piezoelectric voltage inputs and cantilever probe positioning, including nonlinear surface interaction forces, for atomic force microscopes (AFM) is considered. By considering a relatively large cantilever stiffness, singular perturbation methods reduce complexity in the model and allows for faster responses to Van der Waals interaction forces experienced by the cantilever's tip and measurement sample. In this study, we outline a nonlinear near-optimal feedback control approach for non-contact mode imaging designed to move the cantilever tip laterally about a desired trajectory and maintain the tip vertically about the equilibrium point of the attraction and repulsion forces. We also consider the universal instance when the tip-sample interaction force is unknown, and we construct cascaded high-gain observers to estimate these forces and multiple AFM dynamics for the purpose of output feedback control. Our proposed output feedback controller is used to accomplish the outlined control objective with only the piezotube position available for state feedback. / Master of Science / In this thesis, the idea of an atomic force microscope (AFM), specifically the applications of the non-contact mode, will be discussed. An atomic force microscope (AFM) is a tool that measures the surface height of nanometer sized samples. To improve the speed and precision of the machine under a non-contact mode objective, a controller is designed based on optimality and is applied to the system. The system contains a series of equations designed to steer the system towards a desired trajectory and minimal vibrations. Given the complexity of the system, resulting from nonlinearities, we will apply singular perturbation principles on the system's stiffness property to separate the larger problem into two smaller ones. These two problems are inserted into a near-optimal controller and a series of simulations are conducted to demonstrate performance. Alongside this, we will outline an observer to estimate the unknown dynamics of the system. These estimates are then applied to our controller to demonstrate that only the AFM's piezotube position is to be known in order to estimate and control the remaining dynamics of the system.

<p> The abort mission refers to the mission where the landing vehicle needs to terminate the landing mission when an anomaly happens and be safely guided to the desired orbit. Missions involving crew on board demands for a robust and efficient abort strategy. This thesis focuses on solving the time-optimal abort guidance (TOAG) problem in real-time via the feature-based learning method. First, according to the optimal control theory, the features are identified to represent the optimal solutions of TOAG using a few parameters. After that, a sufficiently large dataset of time-optimal abort trajectories is generated offline by solving the TOAG problems with different initial conditions. Then the features are extracted for all generated cases. To find the implicit relationships between the initial conditions and identified features, neural networks are constructed to map the relationships based on the generated dataset. A successfully trained neural network can generate solution in real time for a reasonable initial condition. Finally, experimental flight tests are conducted to demonstrate the onboard computation capability and effectiveness of the proposed method. </p>