Origami, the Japanese art of paper folding, has come a long way from its traditionalroots. It’s now being used in modern engineering and design. In this thesis, I explored multi-stable origami structures. These structures can hold multiple stable shapes, which could have a big impact on various technologies. I aim to break down the complex ideas behind these structures and explain their potential applications in a way that’s easy to understand. In this research, I looked at the history of origami and recent developments in computational design to create and study multi-stable origami structures. I used computer tools like parametric modeling software and finite element analysis to come up with new origami designs. These tools helped me create, improve, and test these designs with a level of accuracy and speed that hadn’t been possible before. The process begins with the formulation of design principles rooted in the fundamental geometry and mechanics of origami. Leveraging mathematical algorithms and optimization techniques, diverse sets of origami crease patterns are generated, each tailored to exhibit specific multi-stable behaviors. Through iterative refinement and simulation-driven design, optimal solutions are identified, leading to the realization of intricate origami morphologies that defy traditional design constraints. Furthermore, the technological implications of multi-stable origami structures are explored across a spectrum of applications. In robotics, these structures serve as foundational building blocks for reconfigurable mechanisms capable of adapting to dynamic environments and tasks. In aerospace engineering, they enable the development of lightweight, deployable structures for space exploration and satellite deployment. In architecture, they inspire innovative approaches to adaptive building envelopes and kinetic facades, enhancing sustainability and user experience. In summary, this thesis presents a comprehensive exploration of multi-stable origami structures, from their generation through computational design methodologies to their application across diverse technological domains. By pushing the boundaries of traditional design paradigms and embracing the synergy between art, science, and technology, this research opens new frontiers for innovation and creativity in the realm of origami-inspired engineering.

The Endoscopic Submucosal Dissection (ESD) method is increasingly becoming the method of choice for surgeons attempting to remove precancerous and early-stage cancerous lesions in the lining of the Gastrointestinal (GI) tract. Being an endoscopic procedure, it is less invasive than most other procedures used for tumor removal. However, this procedure has a steep learning curve and a high number of surgical complications. The primary reason for this is the limited ability of the surgeon to retract mucosal (stomach lining) tissue while they dissect under it. Unlike in traditional surgery, the surgeon lacks a second hand to leverage tissue during dissection in endoscopic procedures. This study proposed the deployment of an endoscopic clip to the surface of the lesion. The clip had a permanent magnet connected to it. In addition, a large permanent external magnet mounted to the end-effector of a robotic arm was positioned above the magnetic clip to pull the internal magnet and retract tissue. Magnetic Force simulations were conducted in the design processes for the magnets to determine whether sufficient force for tissue retraction was being achieved. The use of fiber optic shape sensors to track and localize the internal magnet was also explored. Experimental validations of the external and internal magnet designs as well as tracking of the internal magnet were performed in surgical trials on ex-vivo and live porcine models. Compared to traditional ESD, the use of magnetic retraction in ESD significantly improved tissue exposure for dissection, decreased the required time for the dissection stage of the ESD procedure, and reduced the incidence of surgical complications. Therefore, this technology holds substantial potential for enhancing ESD procedures, advancing the non-invasive treatment of colorectal cancer, and potentially improving patient outcomes significantly.

This thesis presents a study on the optimization of friction pads, centered around a custom friction setup designed to enhance the operational efficiency of tube inspection robots. By surface texturing of Polydimethylsiloxane (PDMS) pads, inspired by the remarkable design of lizards' toes, this research pioneers the development of friction pads aimed at significantly elevating the adaptability and effectiveness of robotic systems in the challenging domain of industrial tube inspection. A cornerstone of this study is the novel friction setup, which has been carefully engineered to simulate real-world operational conditions with high precision. This custom-built apparatus, capable of exerting variable normal loads and accommodating diverse surface textures on curved pipe surfaces, has been instrumental in uncovering the intricate behavior of friction pads. Notably, the setup's capacity to measure forces on curved surfaces with a 6-axis load cell, providing critical insights into frictional forces in multiple directions, stands out as a pivotal contribution to the field. Through exhaustive experimentation facilitated by this advanced friction setup, the research has demonstrated that the design and texture of PDMS pads, particularly those featuring triangular grooves at a depth of 1 mm, markedly influence their frictional performance. These pads exhibit superior traction, especially under higher loads and on corroded surfaces, underscoring the importance of angular groove geometries in enhancing mechanical interlocking with surface irregularities. The inverse relationship observed between the coefficient of friction and applied normal force across various textures further highlights the nuanced mechanical behavior of PDMS friction pads under stress, accentuating the critical role of the custom friction setup in enabling these discoveries. This insight necessitates a refined approach to load application, ensuring optimal frictional engagement. This thesis not only advances the understanding of PDMS pad frictional behavior but also introduces a new frictional device testing method through its innovative friction setup. Future explorations will build on this foundation, probing the effects of different PDMS compositions, surface treatments, and environmental conditions on frictional performance, propelled by the capabilities of the custom friction setup.

Shape memory alloys (SMAs) are a class of smart materials that can recover their predetermined shape when subjected to an appropriate thermal cycle. This unique property makes SMAs attractive for actuator applications, where the material’s phase transformation can be used to generate controlled motion or force. The actuator design leverages the one-way shape memory effect of NiTi (Nickel-Titanium) alloy wire, which contracts upon heating and recovers its original length when cooled. A bias spring opposes the SMA wire contraction, enabling a cyclical actuation motion. Thermal actuation is achieved through joule heating by passing an electric current through the SMA wire. This thesis presents the design of a compact, lightweight SMA-based actuator, providing controlled and precise motion in various engineering applications. A design of a soft actuator is presented exploiting the responses of the shape memory alloy (SMA) to trigger intrinsically mono-stable shape reconfiguration. The proposed class of soft actuators will perform bending actuation by selectively activating the SMA. The transition sequences were optimized by geometric parameterizations and energy-based criteria. The reconfigured structure is capable of arbitrary bending, which is reported here. The proposed class of robots has shown promise as a fast actuator or shape reconfigurable structure, which will bring new capabilities in future long-duration missions in space or undersea, as well as in bio-inspired robotics.

In this thesis, I investigate a subset of reinforcement learning (RL) tasks where the objective for the agent is to achieve temporally extended goals. A common approach, in this setting, is to represent the tasks using deterministic finite automata (DFA) and integrate them in the state space of the RL algorithms, yet such representations often disregard causal knowledge pertinent to the environment. To address this limitation, I introduce the Temporal-Logic-based Causal Diagram (TL-CD) in RL.TL-CD encapsulates temporal causal relationships among diverse environmental properties. We leverage the TL-CD to devise an RL algorithm that significantly reduces environment exploration requirements. By synergizing TL-CD with task-specific DFAs, I identify scenarios wherein the agent can efficiently determine expected rewards early during the exploration phases. Through a series of case studies, I empirically demonstrate the advantages of TL-CDs, particularly highlighting the accelerated convergence of the algorithm towards an optimal policy facilitated by diminished exploration of the environment.

When solving analysis, estimation, and control problems for Partial Differential Equations (PDEs) via computational methods, one must resolve three main challenges: (a) the lack of a universal parametric representation of PDEs; (b) handling unbounded differential operators that appear as parameters; and (c), enforcing auxiliary constraints such as Boundary conditions and continuity conditions. To address these challenges, an alternative representation of PDEs called the `Partial Integral Equation' (PIE) representation is proposed in this work. Primarily, the PIE representation alleviates the problem of the lack of a universal parametrization of PDEs since PIEs have, at most, $12$ Partial Integral (PI) operators as parameters. Naturally, this also resolves the challenges in handling unbounded operators because PI operators are bounded linear operators. Furthermore, for admissible PDEs, the PIE representation is unique and has no auxiliary constraints --- resolving the last of the $3$ main challenges. The PIE representation for a PDE is obtained by finding a unique unitary map from the states of the PIE to the states of the PDE. This map shows a PDE and its associated PIE have equivalent system properties, including well-posedness, internal stability, and I/O behavior. Furthermore, this unique map also allows us to construct a well-defined dual representation that can be used to solve optimal control problems for a PDE. Using the equivalent PIE representation of a PDE, mathematical and computational tools are developed to solve standard problems in Control theory for PDEs. In particular, problems such as a test for internal stability, Input-to-Output (I/O) $L_2$-gain, $\hinf$-optimal state observer design, and $\hinf$-optimal full state-feedback controller design are solved using convex-optimization and Lyapunov methods for linear PDEs in one spatial dimension. Once the PIE associated with a PDE is obtained, Lyapunov functions (or storage functions) are parametrized by positive PI operators to obtain a solvable convex formulation of the above-stated control problems. Lastly, the methods proposed here are applied to various PDE systems to demonstrate the application.

Animals have always been a source of inspiration for real-life problems. The octopus is one such animal that has a lot of untapped potential. The octopus’s arm is without solid joints or bone structure and despite this it can achieve many complicated movements with virtually infinite degrees of freedom. This ability is made possible through the unique morphology of the arm. The octopus’s arm is divided into transverse, longitudinal, oblique, and circular muscle groups and each one has a unique muscle fiber orientation. The octopus’s arm is classified as a hydrostat because it maintains a constant volume while contracting with the help of its different muscle groups. These muscle groups allow elongation, shortening, bending, and twisting of the arm when they work in combination with each other. To confirm the role of transverse and longitudinal muscle groups, an electromyography (EMG) recording of these muscle groups was performed while an amputated arm of an Octopus bimaculoides was stimulated with an electrical signal to induce movement. Statistical analysis was performed on these results to confirm the roles of each muscle group quantitatively. Octopus arm morphology was previously assumed to be uniform along the arm. Through a magnetic resonance imaging (MRI) study at the proximal, middle, and distal sections of the arm this notion was disproven, and a new pattern was discovered. Drawing inspiration from this finding and previous octopus arm prototypes, 4 bio-inspired designs were conceived and tested in finite element analysis (FEA) simulations. Four tests in elongation, shortening, bending, and transverse-assisted bending movements were performed on all designs to compare each design’s performance. The findings in this study have applications in engineering and soft robotics fields for use cases such as, handling fragile objects, minimally invasive surgeries, difficult-to-access areas that require squeezing through small holes, and other novel cases.

Soft robotics has garnered attention for its substantial prospective in various domains, such as manipulation and interactions with humans, by offering competitive advantages against rigid robotic systems, including inherent compliance and variable stiffness. Despite these benefits, their theoretically infinite degrees of freedom and prominent nonlinearities pose significant challenges in developing dynamic models and guiding the robots along desired paths. Additionally, soft robots may exhibit rigid behaviors and potentially collide with their surroundings during path tracking tasks, particularly when possible contact points are unknown. In this dissertation, reduced-order models are used to describe the behaviors of three different soft robot designs, including both linear parameter varying (LPV) and augmented rigid robot (ARR) models. While the reduced-order model captures the majority of the soft robot's dynamics, modeling uncertainties notably remain. Non-repeated modeling uncertainties are addressed by categorizing them as a lumped disturbance, employing two methodologies, $H_\infty$ method and nonlinear disturbance observer (NDOB) based sliding mode control, for its rejection. For repeated disturbances, an iterative learning control (ILC) with a P-type learning function is implemented to enhance trajectory tracking efficacy. Furthermore,for non-repeated disturbances, the NDOB facilitates the contact estimation, and its results are jointly used with a switching algorithm to modify the robot trajectories. The stability proof of all controllers and corresponding simulation and experimental results are provided. For a path tracking task of a soft robot with multi-segments, a robust control strategy that combines a LPV model with an innovative improved nonlinear disturbance observer-based adaptive sliding mode control (INASMC). The control framework employs a first-order LPV model for dynamic representation, leverages an improved disturbance observer for accurate disturbance forecasting, and utilizes adaptive sliding mode control to effectively counteract uncertainties. The tracking error under the proposed controller is proven to be asymptotically stable, and the controller's effectiveness is is validated with simulation and experimental results. Ultimately, this research mitigates the inherent uncertainty in soft robot modeling, thereby enhancing their functionality in contact-intensive tasks.

Tire blowout often occurs during driving, which can suddenly disturb vehicle motions and seriously threaten road safety. Currently, there is still a lack of effective methods to mitigate tire blowout risks in everyday traffic, even for automated vehicles. To fundamentally study and systematically resolve the tire blowout issue for automated vehicles, a collaborative project between General Motors (GM) and Arizona State University (ASU) has been conducted since 2018. In this dissertation, three main contributions of this project will be presented. First, to explore vehicle dynamics with tire blowout impacts and establish an effective simulation platform for close-loop control performance evaluation, high-fidelity tire blowout models are thoroughly developed by explicitly considering important vehicle parameters and variables. Second, since human cooperation is required to control Level 2/3 partially automated vehicles (PAVs), novel shared steering control schemes are specifically proposed for tire blowout to ensure safe vehicle stabilization via cooperative driving. Third, for Level 4/5 highly automated vehicles (HAVs) without human control, the development of control-oriented vehicle models, controllability study, and automatic control designs are performed based on impulsive differential systems (IDS) theories. Co-simulations Matlab/Simulink® and CarSim® are conducted to validate performances of all models and control designs proposed in this dissertation. Moreover, a scaled test vehicle at ASU and a full-size test vehicle at GM are well instrumented for data collection and control implementation. Various tire blowout experiments for different scenarios are conducted for more rigorous validations. Consequently, the proposed high-fidelity tire blowout models can correctly and more accurately describe vehicle motions upon tire blowout. The developed shared steering control schemes for PAVs and automatic control designs for HAVs can effectively stabilize a vehicle to maintain path following performance in the driving lane after tire blowout. In addition to new research findings and developments in this dissertation, a pending patent for tire blowout detection is also generated in the tire blowout project. The obtained research results have attracted interest from automotive manufacturers and could have a significant impact on driving safety enhancement for automated vehicles upon tire blowout.