Physical inactivity is a major contributor to chronic illnesses and mortality globally. However, most interventions to address it rely on static, aggregate models that overlook idiographic (i.e., individual-level) dynamics, limiting intervention effectiveness. Leveraging mobile technology and control systems engineering principles, this dissertation provides a novel, comprehensive framework for personalized behavioral interventions that have been tested experimentally under the Control Optimization Trial (COT) paradigm. Through careful design of experiments, elaborate signal processing and model estimation, and judicious formulation of behavior intervention optimization as a control system problem, this dissertation develops tools to overcome challenges faced in the large-scale dissemination of mobile health (mHealth) interventions. A novel Three-Degrees-of-Freedom Kalman Filter-based Hybrid Model Predictive Control (3DoF-KF HMPC) controller is formulated for physical activity interventions and evaluated in a clinical trial, demonstrating its effectiveness. Furthermore, this dissertation expands on understanding the underlying dynamics influencing behavior change. Engineering principles are applied to develop a conceptual approach to generate dynamic hypotheses and translate these into first-principle dynamic models. The generated models are used in concert with system identification principles to enhance the design of experiments that yield dynamically informative data sets for behavioral medicine applications. Additionally, sophisticated search, filtering, and model estimation algorithms are applied to optimize and personalize model structures and estimate dynamic models that account for nonlinearities and “Just-in-Time” (JIT; moments of need, receptivity, and opportunity) context in behavior change systems. In addition, the pervasive issue of data missingness in interventions is addressed by integrating system identification principles with a Bayesian inference model-based technique for data imputation. The findings in this dissertation extend beyond physical activity, offering insights for promoting healthy behaviors in other applications, such as smoking cessation and weight management. The integration of control systems engineering in behavioral medicine research, as demonstrated in this dissertation, offers broad impacts by advancing the field's understanding of behavior change dynamics, enhancing accessibility to personalized behavioral health interventions, and improving patient outcomes. This research has the potential to radically improve behavioral interventions, increase affordability and accessibility, inspire interdisciplinary collaboration, and provide behavioral scientists with tools capable of addressing societal challenges in mHealth and preventive medicine.

Human-robot interactions can often be formulated as general-sum differential games where the equilibrial policies are governed by Hamilton-Jacobi-Isaacs (HJI) equations. Solving HJI PDEs faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) alleviate CoD in solving PDEs with smooth solutions, they fall short in learning discontinuous solutions due to their sampling nature. This causes PINNs to have poor safety performance when they are applied to approximate values that are discontinuous due to state constraints. This dissertation aims to improve the safety performance of PINN-based value and policy models. The first contribution of the dissertation is to develop learning methods to approximate discontinuous values. Specifically, three solutions are developed: (1) hybrid learning uses both supervisory and PDE losses, (2) value-hardening solves HJIs with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique lifts the value to a higher-dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance. The second contribution is a learning-theoretical analysis of PINN for value and policy approximation. Specifically, by extending the neural tangent kernel (NTK) framework, this dissertation explores why the choice of activation function significantly affects the PINN generalization performance, and why the inclusion of supervisory costate data improves the safety performance. The last contribution is a series of extensions of the hybrid PINN method to address real-time parameter estimation problems in incomplete-information games. Specifically, a Pontryagin-mode PINN is developed to avoid costly computation for supervisory data. The key idea is the introduction of a costate loss, which is cheap to compute yet effectively enables the learning of important value changes and policies in space-time. Building upon this, a Pontryagin-mode neural operator is developed to achieve state-of-the-art (SOTA) safety performance across a set of differential games with parametric state constraints. This dissertation demonstrates the utility of the resultant neural operator in estimating player constraint parameters during incomplete-information games.

Grasping objects in a general household setting is a dexterous task, high compliance is needed to generate a grasp that leads to grasp closure. Standard 6 Degree of Freedom (DoF) manipulators with parallel grippers are naturally incapable of showing such dexterity. This renders many objects in household settings difficult to grasp, as the manipulator cannot access readily available antipodal (planar) grasps. In such scenarios, one must either use a high DoF end effector to learn this compliance or change the initial configuration of the object to find an antipodal grasp. A pipeline that uses the extrinsic forces present in the environment to make up for this lack of compliance is proposed. The proposed method: i) Takes the point cloud input from the environment, and creates a search space with all its available poses. This search space is used to identify the best graspable position for an object with a grasp score network ii) Learn how to approach an object, and generate an appropriate set of motor primitives that converts the current ungraspable pose to a graspable pose. iii) Run a naive grasp detection network to verify the proposed methods and subsequently grasp the initially ungraspable object. By integrating these components, objects that were initially ungraspable, with a standard grasp detection model DexNet, remain no longer ungraspable.

The field of unmanned aerial vehicle, or UAV, navigation has been moving towards collision inclusive path planning, yet work has not been done to consider what a UAV is colliding with, and if it should or not. Therefore, there is a need for a framework that allows a UAV to consider what is around it and find the best collision candidate. The following work presents a framework that allows UAVs to do so, by considering what an object is and the properties associated with it. Specifically, it considers an object’s material and monetary value to decide if it is good to collide with or not. This information is then published on a binary occupancy map that contains the objects’ size and location with respect to the current position of the UAV. The intent is that the generated binary occupancy map can be used with a path planner to decide what the UAV should collide with. The framework was designed to be as modular as possible and to work with conventional UAV's that have some degree of crash resistance incorporated into their design. The framework was tested by using it to identify various objects that could be collision candidates or not, and then carrying out collisions with some of the objects to test the framework’s accuracy. The purpose of this research was to further the field of collision inclusive path planning by allowing UAVs to know, in a way, what they are intending to collide with and decide if they should or not in order to make safer and more efficient collisions.

Walking and mobility are essential aspects of our daily lives, enabling us to engage in various activities. Gait disorders and impaired mobility are widespread challenges faced by older adults and people with neurological injuries, as these conditions can significantly impact their quality of life, leading to a loss of independence and an increased risk of mortality. In response to these challenges, rehabilitation, and assistive robotics have emerged as promising alternatives to conventional gait therapy, offering potential solutions that are less labor-intensive and costly. Despite numerous advances in wearable lower-limb robotics, their current applicability remains confined to laboratory settings. To expand their utility to broader gait impairments and daily living conditions, there is a pressing need for more intelligent robot controllers. In this dissertation, these challenges are tackled from two perspectives: First, to improve the robot's understanding of human motion and intentions which is crucial for assistive robot control, a robust human locomotion estimation technique is presented, focusing on measuring trunk motion. Employing an invariant extended Kalman filtering method that takes sensor misplacement into account, improved convergence properties over the existing methods for different locomotion modes are shown. Secondly, to enhance safe and effective robot-aided gait training, this dissertation proposes to directly learn from physical therapists' demonstrations of manual gait assistance in post-stroke rehabilitation. Lower-limb kinematics of patients and assistive force applied by therapists to the patient's leg are measured using a wearable sensing system which includes a custom-made force sensing array. The collected data is then used to characterize a therapist's strategies. Preliminary analysis indicates that knee extension and weight-shifting play pivotal roles in shaping a therapist's assistance strategies, which are then incorporated into a virtual impedance model that effectively captures high-level therapist behaviors throughout a complete training session. Furthermore, to introduce safety constraints in the design of such controllers, a safety-critical learning framework is explored through theoretical analysis and simulations. A safety filter incorporating an online iterative learning component is introduced to bring robust safety guarantees for gait robotic assistance and training, addressing challenges such as stochasticity and the absence of a known prior dynamic model.

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.

Robotic technology can be broadly categorized into two main approaches based on the compliance of the robot's materials and structure: hard and soft. Hard, traditional robots, with mechanisms to transmit forces, provide high degrees of freedom (DoFs) and precise manipulation, making them commonly used in industry and academic research. The field of soft robotics, on the other hand, is a new trend from the past three decades of robotics that uses soft materials such as silicone or textiles as the body or material base instead of the rigid bodies used in traditional robots. Soft robots are typically pre-programmed with specific geometries, and perform well at tasks such as human-robot interaction, locomotion in complex environments, and adaptive reconfiguration to the environment, which reduces the cost of future programming and control. However, full soft robotic systems are often less mobile due to their actuation --pneumatics, high-voltage electricity or magnetics -- even if the robot itself is at a millimeter or centimeter scale. Rigid or hard robots, on the other hand, can often carry the weight of their own power, but with a higher burden of cost for control and sensing. A middle ground is thus sought, to combine soft robotics technologies with rigid robots, by implementing mechanism design principles with soft robots to embed functionalities or utilize soft robots as the actuator on a rigid robotic system towards an affordable robotic system design. This dissertation showcases five examples of this design principle with two main research branches: locomotion and wearable robotics. In the first research case, an example of how a miniature swimming robot can navigate through a granular environment using compliant plates is presented, compared to other robots that change their shape or use high DoF mechanisms. In the second pipeline, mechanism design is implemented using soft robotics concepts in a wearable robot. An origami-inspired, soft "exo-shell", that can change its stiffness on demand, is introduced. As a follow-up to this wearable origami-inspired robot, a geometry-based, ``near" self-locking modular brake is then presented. Finally, upon combining the origami-inspired wearable robot and brake design, a concept of a modular wearable robot is showcased for the purpose of answering a series of biomechanics questions.

While wearable soft robots have successfully addressed many inherent design limitations faced by wearable rigid robots, they possess a unique set of challenges due to their soft and compliant nature. Some of these challenges are present in the sensing, modeling, control and evaluation of wearable soft robots. Machine learning algorithms have shown promising results for sensor fusion with wearable robots, however, they require extensive data to train models for different users and experimental conditions. Modeling soft sensors and actuators require characterizing non-linearity and hysteresis, which complicates deriving an analytical model. Experimental characterization can capture the characteristics of non-linearity and hysteresis but requires developing a synthesized model for real-time control. Controllers for wearable soft robots must be robust to compensate for unknown disturbances that arise from the soft robot and its interaction with the user. Since developing dynamic models for soft robots is complex, inaccuracies that arise from the unmodeled dynamics lead to significant disturbances that the controller needs to compensate for. In addition, obtaining a physical model of the human-robot interaction is complex due to unknown human dynamics during walking. Finally, the performance of soft robots for wearable applications requires extensive experimental evaluation to analyze the benefits for the user. To address these challenges, this dissertation focuses on the sensing, modeling, control and evaluation of soft robots for wearable applications. A model-based sensor fusion algorithm is proposed to improve the estimation of human joint kinematics, with a soft flexible robot that requires compact and lightweight sensors. To overcome limitations with rigid sensors, an inflatable soft haptic sensor is developed to enable gait sensing and haptic feedback. Through experimental characterization, a mathematical model is derived to quantify the user's ground reaction forces and the delivered haptic force. Lastly, the performance of a wearable soft exosuit in assisting human users during lifting tasks is evaluated, and the benefits obtained from the soft robot assistance are analyzed.

Acrobatic maneuvers of quadrotors present unique challenges concerning trajectorygeneration, control, and execution. Specifically, the flip maneuver requires dynamically feasible trajectories and precise control. Various factors, including rotor dynamics, thrust allocation, and control strategies, influence the successful execution of flips. This research introduces an approach for tracking optimal trajectories to execute flip maneuvers while ensuring system stability autonomously. Model Predictive Control (MPC) designs the controller, enabling the quadrotor to plan and execute optimal trajectories in real-time, accounting for dynamic constraints and environmental factors. The utilization of predictive models enables the quadrotor to anticipate and adapt to changes during aggressive maneuvers. Simulation-based evaluations were conducted in the ROS and Gazebo environments. These evaluations provide valuable insights into the quadrotor’s behavior, response time, and tracking accuracy. Additionally, real-time flight experiments utilizing state- of-the-art flight controllers, such as the PixHawk 4, and companion computers, like the Hardkernel Odroid, validate the effectiveness of the proposed control algorithms in practical scenarios. The conducted experiments also demonstrate the successful execution of the proposed approach. This research’s outcomes contribute to quadrotor technology’s advancement, particularly in acrobatic maneuverability. This opens up possibilities for executing maneuvers with precise timing, such as slingshot probe releases during flips. Moreover, this research demonstrates the efficacy of MPC controllers in achieving autonomous probe throws within no-fly zone environments while maintaining an accurate desired range. Field application of this research includes probe deployment into volcanic plumes or challenging-to-access rocky fault scarps, and imaging of sites of interest. along flight paths through rolling or pitching maneuvers of the quadrotor, to use sensorsuch as cameras or spectrometers on the quadrotor belly.

Navigation and mapping in GPS-denied environments, such as coal mines ordilapidated buildings filled with smog or particulate matter, pose a significant challenge due to the limitations of conventional LiDAR or vision systems. Therefore there exists a need for a navigation algorithm and mapping strategy which do not use vision systems but are still able to explore and map the environment. The map can further be used by first responders and cave explorers to access the environments. This thesis presents the design of a collision-resilient Unmanned Aerial Vehicle (UAV), XPLORER that utilizes a novel navigation algorithm for exploration and simultaneous mapping of the environment. The real-time navigation algorithm uses the onboard Inertial Measurement Units (IMUs) and arm bending angles for contact estimation and employs an Explore and Exploit strategy. Additionally, the quadrotor design is discussed, highlighting its improved stability over the previous design. The generated map of the environment can be utilized by autonomous vehicles to navigate the environment. The navigation algorithm is validated in multiple real-time experiments in different scenarios consisting of concave and convex corners and circular objects. Furthermore, the developed mapping framework can serve as an auxiliary input for map generation along with conventional LiDAR or vision-based mapping algorithms. Both the navigation and mapping algorithms are designed to be modular, making them compatible with conventional UAVs also. This research contributes to the development of navigation and mapping techniques for GPS-denied environments, enabling safer and more efficient exploration of challenging territories.