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.

Unmanned aerial vehicles (UAVs) have reshaped the world of aviation. With the emergence of different types of UAVs, a multitude of mission critical applications, e.g., aerial photography, package delivery, grasping and manipulation, aerial reconnaissance and surveillance have been accomplished successfully. All of the aforementioned applications require the UAVs to be robust to external disturbances and safe while flying in cluttered environments and these factors are of paramount importance for task completion. In the first phase, this dissertation starts by presenting the synthesis and experimental validation of real-time low-level estimation and robust attitude and position controllers for multirotors. For the task of reliable position estimation, a hybrid low-pass de-trending filter is proposed for attenuating noise and drift in the velocity and position estimates respectively. Subsequently, a disturbance observer (DOB) approach with online Q-filter tuning is proposed for disturbance rejection and precise position control. Finally, a non-linear disturbance observer (NDOB) approach, along with a parameter optimization framework, is proposed for robust attitude control of multirotors. Multiple simulation and experimental flight tests are performed to demonstrate the efficacy of the proposed algorithms. Aerial grasping and collection is a type of mission-critical task which requires vision based sensing and robust control algorithms for successful task completion. In the second phase, this dissertation initially explores different object grasping approaches utilizing soft and rigid graspers. Additionally, vision based control paradigms are developed for object grasping and collection applications, specifically from water surfaces. Autonomous object collection from water surfaces presents a multitude of challenges: i) object drift due to propeller outwash, ii) reflection and glare from water surfaces makes object detection extremely challenging and iii) lack of reliable height sensors above water surface (for autonomous landing on water). Finally, a first of its kind aerial manipulation system, with an integrated net system and a robust vision based control structure, is proposed for floating object collection from water surfaces. Objects of different shapes and sizes are collected, through multiple experimental flight tests, with a success rate of 91.6%. To the best of the author's knowledge, this is the first work demonstrating autonomous object collection from water surfaces.

The field of prostheses and rehabilitation devices has seen tremendous advancement since the ’90s. However, the control aspect of the said devices is lacking. The need for mathematical theories to improve the control strategies is apparent. This thesis attempts to bridge the gap by introducing some dynamic system analysis and control strategies.Firstly, the human gait dynamics are assumed to be periodic. Lyapunov Floquet theory and Invariant manifold theory are applied. A transformation is obtained onto a simple single degree of freedom oscillator system. The said system is transformed back into the original domain and compared to the original system. The results are discussed and critiqued. Then the technique is applied to the kinematic and kinetic data collected from healthy human subjects to verify the technique’s feasibility. The results show that the technique successfully reconstructed the kinematic and kinetic data. Human gait dynamics are not purely periodic, so a quasi-periodic approach is adopted. Techniques to reduce the order of a quasi-periodic system are studied. Lyapunov-Peron transformation (a surrogate of Lyapunov Floquet transformation for quasi-periodic systems) is studied. The transformed system is easier to control. The inverse of the said transformation is obtained to transform back to the original domain. The application of the techniques to different cases (including externally forced systems) is studied. The reduction of metabolic cost is presented as a viable goal for applying the previously studied control techniques. An experimental protocol is designed and executed to understand periodic assistive forces' effects on human walking gait. Different tether stiffnesses are used to determine the best stiffness for a given subject population. An estimation technique is introduced to obtain the metabolic cost using the center of mass's kinematic data. Lastly, it is concluded that the mathematical techniques can be utilized in a robotic tail-like rehabilitation device. Some possible future research ideas are provided to implement the techniques mentioned in this dissertation.