This thesis lays down a foundation for more advanced work on bipeds by carefully examining cart-inverted pendulum systems (CIPS, often used to approximate each leg of a biped) and associated closed loop performance tradeoffs. A CIPS is characterized by an instability (associated with the tendency of the pendulum to fall) and a right half plane (RHP, non-minimum phase) zero (associated with the cart displacement x). For such a system, the zero is typically close to (and smaller) than the instability. As such, a classical PK control structure would result in very poor sensitivity properties.It is therefore common to use a hierarchical inner-outer loop structure. As such, this thesis examines how such a structure can be used to improve sensitivity properties beyond a classic PK structure and systematically tradeoff sensitivity properties at the plant input/output. While the instability requires a minimum bandwidth at the plant input, the RHP zero imposes a maximum bandwidth on the cart displacement x. Three CIPs are examined – one with a long, short and an intermediately sized pendulum. We show that while the short pendulum system is the most unstable and requires the largest bandwidth at the plant input for stabilization (hardest to control), it also has the largest RHP zero. Consequently, it will permit the largest cart displacement x-bandwidth, and hence, one can argue that the short pendulum system is easiest to control. Similarly, the long pendulum system is the least unstable and requires smallest bandwidth at the plant input for stabilization (easiest to control). However, because this system also possesses the smallest RHP zero it will permit the smallest cart displacement x-bandwidth, and hence, one can argue that the long pendulum system is the hardest to control. Analogous “intermediate conclusions” can be drawn for the system with the “intermediately sized” pendulum. A set of simple academic examples (growing in plant and controller complexity) are introduced to illustrate basic tradeoffs and guide the presentation of the trade studies.

The hexagonal honeycomb is a bio-inspired cellular structure with a high stiffness-to-weight ratio. It has contributed to its use in several engineering applications compared to solid bodies with identical volume and material properties. This characteristic behavior is mainly attributed to the effective nature of stress distribution through the honeycomb beams that manifests as bending, axial, and shear deformation mechanisms. Inspired by the presence of this feature in natural honeycomb, this work focuses on the influence of the corner radius on the mechanical properties of a honeycomb structure subjected to in-plane compression loading. First, the local response at the corner node interface is investigated with the help of finite element simulation of a periodic unit cell within the linear elastic domain and validated against the best available analytical models. Next, a parametric design of experiments (DOE) study with the unit cell is defined with design points of varying circularity and cell length ratios towards identifying the optimal combination of all geometric parameters that maximize stiffness per unit mass while minimizing the stresses induced at the corner nodes. The observed trends are then compared with compression tests of 3D printed Nylon 12 honeycomb specimens of varying corner radii and wall thicknesses. The study concluded that the presence of a corner radius has a mitigating effect on peak stresses but that these effects are dependent on thickness while also increasing specific stiffness in all cases. It also points towards an optimum combination of parameters that achieve both objectives simultaneously while shedding some light on the functional benefit of this radius in wasp and bee nests that employ a hexagonal cell.

Granular materials demonstrate complexity in many physical attributes with various shapes and sizes, varying from several centimeters down to less than a few microns. Some materials are highly cohesive, while others are free-flowing. Despite such complexity in their physical properties, they are extremely important in industries dealing with bulk materials. Through this research, the factors affecting flowability of particulate solids and their interaction with projectiles were explored. In Part I, a novel set of characterization tools to relate various granular material properties to their flow behavior in confined and unconfined environments was investigated. Through this work, a thorough characterization study to examine the effects of particle size, particle size distribution, and moisture on bulk powder flowability were proposed. Additionally, a mathematical model to predict the flow function coefficient (FFC) was developed, based on the surface mean diameter and moisture level, which can serve as a flowability descriptor. Part II of this research focuses on the impact dynamics of low velocity projectiles on granular media. Interaction of granular media with external foreign bodies occurs in everyday events like a human footprint on the beach. Several studies involving numerical and experimental methods have focused on the study of impact dynamics in both dry and wet granular media. However, most of the studies involving impact dynamics considered spherical projectiles under different conditions, while practical models should involve more complex, realistic shapes. Different impacting geometries with conserved density, volume, and velocity on a granular bed may experience contrasting drag forces upon penetration. This is due to the difference in the surface areas coming into contact with the granular media. In this study, a set of non-spherical geometries comprising cuboids, cylinders, hexagonal prisms and triangular prisms with constant density, volume, and impact velocities, were released onto a loosely packed, non-cohesive, dry granular bed. From these experimental results, a model to determine the penetration depth of projectiles upon impact was developed and how it is influenced by the release height and surface area of the projectiles in contact with the granular media was studied.

The way a granular material is transported and handled plays a huge part in the quality of final product and the overall efficiency of the manufacturing process. Currently, there is a gap in the understanding of the basic relationship between the fundamental variables of granular materials such as moisture content, particle shape and size. This can lead to flowability issues like arching and ratholing, which can lead to unexpected downtimes in the whole manufacturing process and considerable wastage of time, energy, and resources. This study specifically focuses on the development of a model based on the surface mean diameter and the moisture content to predict the flow metric flow function coefficient (FFC) to describe the nature of flow of the material. The investigation involved three parts. The first entailed the characterization of the test materials with respect to their physical properties - density, size, and shape distributions. In the second, flowability tests were conducted with the FT4 Powder Rheometer. Shear cell tests were utilized to calculate each test specimen's flow function parameters. Finally, the physical properties were correlated with the results from the flowability tests to develop a reliable model to predict the nature of flow of the test specimens. The model displayed an average error of -6.5%. Predicted values showed great correlation with values obtained from further shear cell tests on the FT4 Rheometer. Additionally, particle shape factors and other flowability descriptors like Carr Index and Hausner Ratio were also evaluated for the sample materials. All size ranges displayed a decreasing trend in the values of Carr Index, Hausner Ratio, and FFC with increasing moisture percentages except the 5-11 micron glass beads, which showed an increasing trend in FFC. The results from this investigation could be helpful in designing equipment for powder handling and avoiding potential flowability issues.

A novel underwater, open source, and configurable vehicle that mimics and leverages advances in quad-copter controls and dynamics, called the uDrone, was designed, built and tested. This vehicle was developed to aid coral reef researchers in collecting underwater spectroscopic data for the purpose of monitoring coral reef health. It is designed with an on-board integrated sensor system to support both automated navigation in close proximity to reefs and environmental observation. Additionally, the vehicle can serve as a testbed for future research in the realm of programming for autonomous underwater navigation and data collection, given the open-source simulation and software environment in which it was developed. This thesis presents the motivation for and design components of the new vehicle, a model governing vehicle dynamics, and the results of two proof-of-concept simulation for automated control.