This dissertation introduces and examines Soft Curved Reconfigurable Anisotropic Mechanisms (SCRAMs) as a solution to address actuation, manufacturing, and modeling challenges in the field of soft robotics, with the aim of facilitating the broader implementation of soft robots in various industries. SCRAM systems utilize the curved geometry of thin elastic structures to tackle these challenges in soft robots. SCRAM devices can modify their dynamic behavior by incorporating reconfigurable anisotropic stiffness, thereby enabling tailored locomotion patterns for specific tasks. This approach simplifies the actuation of robots, resulting in lighter, more flexible, cost-effective, and safer soft robotic systems. This dissertation demonstrates the potential of SCRAM devices through several case studies. These studies investigate virtual joints and shape change propagation in tubes, as well as anisotropic dynamic behavior in vibrational soft twisted beams, effectively demonstrating interesting locomotion patterns that are achievable using simple actuation mechanisms. The dissertation also addresses modeling and simulation challenges by introducing a reduced-order modeling approach. This approach enables fast and accurate simulations of soft robots and is compatible with existing rigid body simulators. Additionally, this dissertation investigates the prototyping processes of SCRAM devices and offers a comprehensive framework for the development of these devices. Overall, this dissertation demonstrates the potential of SCRAM devices to overcome actuation, modeling, and manufacturing challenges in soft robotics. The innovative concepts and approaches presented have implications for various industries that require cost-effective, adaptable, and safe robotic systems. SCRAM devices pave the way for the widespread application of soft robots in diverse domains.

Low back pain (LBP) is the most common symptom leading to hospitalization and medical assistance. In the US, LBP is the fifth most prevalent case for visiting hospitals. Approximately 2.06 million LBP incidents were reported during the timeline between 2004 and 2008. Globally, LBP occurrence increased by almost 200 million from 1990 to 2017. This problem is further implicated by physical and financial constraints that impact the individual’s quality of life. The medical cost exceeded $87.6 billion, and the lifetime prevalence was 84%. This indicates that the majority of people in the US will experience this symptom. Also, LBP limits Activities of Daily Living (ADL) and possibly affects the gait and postural stability. Prior studies indicated that LBP patients have slower gait speed and postural instability. To alleviate this symptom, the epidural injection is prescribed to treat pain and improve mobility function. To evaluate the effectiveness of LBP epidural injection intervention, gait and posture stability was investigated before and after the injection. While these factors are the fundamental indicator of LBP improvement, ADL is an element that needs to be significantly considered. The physical activity level depicts a person’s dynamic movement during the day, it is essential to gather activity level that supports monitoring chronic conditions, such as LBP, osteoporosis, and falls. The objective of this study was to assess the effects of Epidural Steroid Injection (ESI) on LBP and related gait and postural stability in the pre and post-intervention status. As such, the second objective was to assess the influence of ESI on LBP, and how it influences the participant’s ADL physical activity level. The results indicated that post-ESI intervention has significantly improved LBP patient’s gait and posture stability, however, there was insufficient evidence to determine the significant disparity in the physical activity levels. In conclusion, ESI depicts significant positive effects on LBP patients’ gait and postural parameters, however, more verification is required to indicate a significant effect on ADL physical activity levels.

This thesis presents a study on the user adaptive variable impedance control of a wearable ankle robot for robot-aided rehabilitation with a primary focus on enhancing accuracy and speed. The controller adjusts the impedance parameters based on the user's kinematic data to provide personalized assistance. Bayesian optimization is employed to minimize an objective function formulated from the user's kinematic data to adapt the impedance parameters per user, thereby enhancing speed and accuracy. Gaussian process is used as a surrogate model for optimization to account for uncertainties and outliers inherent to human experiments. Student-t process based outlier detection is utilized to enhance optimization robustness and accuracy. The efficacy of the optimization is evaluated based on measures of speed, accuracy, and effort, and compared with an untuned variable impedance controller during 2D curved trajectory following tasks. User effort was measured based on muscle activation data from the tibialis anterior, peroneus longus, soleus, and gastrocnemius muscles. The optimized controller was evaluated on 15 healthy subjects and demonstrated an average increase in speed of 9.85% and a decrease in deviation from the ideal trajectory of 7.57%, compared to an unoptimized variable impedance controller. The strategy also reduced the time to complete tasks by 6.57%, while maintaining a similar level of user effort.

Ferrofluidic microrobots have emerged as promising tools for minimally invasive medical procedures, leveraging their unique properties to navigate through complex fluids and reach otherwise inaccessible regions of the human body, thereby enabling new applications in areas such as targeted drug delivery, tissue engineering, and diagnostics. This dissertation develops a model-predictive controller for the external magnetic manipulation of ferrofluid microrobots. Several experiments are performed to illustrate the adaptability and generalizability of the control algorithm to changes in system parameters, including the three-dimensional reference trajectory, the velocity of the workspace fluid, and the size, orientation, deformation, and velocity of the microrobotic droplet. A linear time-invariant control system governing the dynamics of locomotion is derived and used as the constraints of a least squares optimal control algorithm to minimize the projected error between the actual trajectory and the desired trajectory of the microrobot. The optimal control problem is implemented after time discretization using quadratic programming. In addition to demonstrating generalizability and adaptability, the accuracy of the control algorithm is analyzed for several different types of experiments. The experiments are performed in a workspace with a static surrounding fluid and extended to a workspace with fluid flowing through it. The results suggest that the proposed control algorithm could enable new capabilities for ferrofluidic microrobots, opening up new opportunities for applications in minimally invasive medical procedures, lab-on-a-chip, and microfluidics.

The objective of this thesis is to propose two novel interval observer designs for different classes of linear and hybrid systems with nonlinear observations. The first part of the thesis presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations. The observer is constructed using mixed-monotone decompositions, which ensures correctness and positivity without additional constraints/assumptions. The proposed design also involves additional degrees of freedom that may improve the performance of the observer design. The proposed observer is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. The observer gains are computed using mixed-integer (linear) programs. The second part of the thesis addresses the problem of designing a novel asymptotically stable interval estimator design for hybrid systems with nonlinear dynamics and observations under the assumption of known jump times. The proposed architecture leverages mixed-monotone decompositions to construct a hybrid interval observer that is guaranteed to frame the true states. Moreover, using common Lyapunov analysis and the positive/cooperative property of the error dynamics, two approaches were proposed for constructing the observer gains to achieve uniform asymptotic stability of the error system based on mixed-integer semidefinite and linear programs, and additional degrees of freedom are incorporated to provide potential advantages similar to coordinate transformations. The effectiveness of both observer designs is demonstrated through simulation examples.

Humans possess the ability to entrain their walking to external pulses occurring atperiods similar to their natural walking cadence. Expanding the basin of entrainment has become a promising option for gait rehabilitation for those affected by hemiparesis. Efforts to expand the basin have utilized either conventional fixed-speed treadmill setups, which require significant alteration to natural walking biomechanics; or overground walking tracks, which are largely impractical. In this study, overground walking was simulated using an actively self-pacing variable speed treadmill, and periodic hip flexion perturbations (≈ 12 Nm) were applied about a subject using a Soft Robotic Hip Exoskeleton. This study investigated the effectiveness of conducting gait entrainment rehabilitation with simulated overground walking to improve the success rate of entrainment at high frequency conditions. This study also investigated whether simulated overground walking can preserve natural biomechanics by examining stride length and normalized propulsive impulse at various conditions. Participants in this study were subjected to four perturbation frequencies, ranging from their naturally preferred gait frequency up to 30% faster. Each subject participated in two days of testing: one day subjects walked on a conventional fixed-speed treadmill, and another day on a variable speed treadmill. Results showed that subjects were more frequently able to entrain to the fastest perturbation frequency on the variable speed treadmill. Results also showed that natural biomechanics were preserved significantly better on the variable speed treadmill across all accelerated perturbation frequencies. This study showed that simulated overground walking can aid in extending the basin of entrainment while preserving natural biomechanics during gait entrainment, which is a promising development for gait rehabilitation. However, a comparative study on neurologically disordered individuals is necessary to quantify the clinical relevance of these findings.

Chronic ankle instability (CAI) is caused by the failure to seek treatment and rehabilitation after an acute ankle sprain. Typically, clinical assessment of ankle sprains is done under unloaded conditions, despite the fact that ankle sprains occur during weight loading. Characterization of ankle stiffness, a representation of ankle stability during weight loading, is crucial to quantify ankle stability. Patients with CAI suffer from gait asymmetry, and the descriptions of the asymmetry ratio vary widely throughout the research community. Bilateral ankle stiffness could be a systematic metric to describe the gait asymmetry of CAI patients. Additionally, women generally have higher ankle joint and ligamentous laxity than men, and lower ankle stiffness, which has been thoroughly investigated in previous literature. However, differences in bilateral ankle stiffness between sexes still need to be investigated. Using twin dual-axis robotic platforms, this study investigated the weight loading effect on ankle stiffness in the frontal plane during standing, the bilateral difference in stiffness between the dominant and non-dominant ankle, and the sex difference in bilateral ankle stiffness during standing for varying weight distribution. The group average results of 20 healthy subjects showed that ankle stiffness increased with increasing weight loading on the ankle, which is speculated to be caused by active muscle contraction and changes in passive structure due to weight loading. For the bilateral difference of the group, the statistical analysis showed that there was no significant difference between dominant and non-dominant ankle stiffness for all the weight distributions considered. Although the group average result of the difference in bilateral ankle stiffness was statistically insignificant, individual analysis confirmed the importance of subject-specific investigation of bilateral ankle stiffness, as there were more cases of dominant ankle stiffness being larger than non-dominant ankle stiffness, and the bilateral difference was subject-specific. Investigations into sex differences in bilateral ankle stiffness showed that ankle stiffness in males is significantly greater than in females, even after normalizing the stiffness by weight, which is speculated to be caused by higher joint and ligamentous laxity in females regardless of laterality.

The introduction of assistive/autonomous features in cyber-physical systems, e.g., self-driving vehicles, have paved the way to a relatively new field of system analysis for safety-critical applications, along with the topic of controlling systems with performance and safety guarantees. The different works in this thesis explore and design methodologies that focus on the analysis of nonlinear dynamical systems via set-membership approximations, as well as the development of controllers and estimators that can give worst-case performance guarantees, especially when the sensor data containing information on system outputs is prone to data drops and delays. For analyzing the distinguishability of nonlinear systems, building upon the idea of set membership over-approximation of the nonlinear systems, a novel optimization-based method for multi-model affine abstraction (i.e., simultaneous set-membership over-approximation of multiple models) is designed. This work solves for the existence of set-membership over-approximations of a pair of different nonlinear models such that the different systems can be distinguished/discriminated within a guaranteed detection time under worst-case uncertainties and approximation errors. Specifically, by combining mesh-based affine abstraction methods with T-distinguishability analysis in the literature yields a bilevel bilinear optimization problem, whereby leveraging robust optimization techniques and a suitable change of variables result in a sufficient linear program that can obtain a tractable solution with T-distinguishability guarantees. Moreover, the thesis studied the designs of controllers and estimators with performance guarantees, and specifically, path-dependent feedback controllers and bounded-error estimators for time-varying affine systems are proposed that are subject to delayed observations or missing data. To model the delayed/missing data, two approaches are explored; a fixed-length language and an automaton-based model. Furthermore, controllers/estimators that satisfy the equalized recovery property (a weaker form of invariance with time-varying finite bounds) are synthesized whose feedback gains can be adapted based on the observed path, i.e., the history of observed data patterns up to the latest available time step. Finally, a robust kinodynamic motion planning algorithm is also developed with collision avoidance and probabilistic completeness guarantees. In particular, methods based on fixed and flexible invariant tubes are designed such that the planned motion/trajectories can reject bounded disturbances using noisy observations.