Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.

Simulating Granite Emplacement and Deformation with Centrifuge Analogue Modelling

The Greater Himalayan leucogranites are a discontinuous suite of intrusions emplaced in a thickened crust during the Miocene southward ductile extrusion of the Himalayan metamorphic core. Melt-induced weakening is thought to have played a critical role in strain localization that facilitated the extrusion. Recent advancements in centrifuge analogue modelling techniques allow for the replication of a broader range of crustal deformation behaviors, enhancing our understanding of large hot orogens. Polydimethylsiloxane (PDMS) is commonly used in centrifuge experiments to model weak melt zones. Difficulties in handling PDMS had, until now, limited its emplacement in models prior to any deformation. A new modelling technique has been developed where PDMS is emplaced into models that have been subjected to some shortening. This technique aims to better understand the effects of melt on strain localization and potential decoupling between structural levels within an evolving orogenic system. Models are subjected to an early stage of shortening, followed by the introduction of PDMS, and then a final stage of shortening. Theoretical percentages of partial melt and their effect on rock strength are considered when adding a specific percentage of PDMS in each model. Due to the limited size of the models, only PDMS sheets of 3 mm thickness were used, which varied in length and width. Within undeformed packages, minimal surface and internal deformation occurred when PDMS is emplaced in the lower layer of the model, showing a vertical volume increase of ~20% within the package; whereas the emplacement of PDMS into the middle layer showed internal dragging of the middle laminations into the lower layer and a vertical volume increase ~30%. Emplacement of PDMS results in ~7% shortening for undeformed and deformed models. Deformed models undergo ~20% additional shortening after two rounds of deformation. Strain localization and decoupling between units occur in deformed models where the degree of deformation changes based on the amount of partial melt present. Surface deformation visible by the formation of a bulge, mode 1 extension cracks and varying surface strain ellipses varies depending if PDMS is present. Better control during emplacement is exhibited when PDMS is added into cooler models, resulting in reduced internal deformation within the middle layer.

An investigation of lower limb joint powers as a predictive measure of countermovement vertical jump height.

Measuring and tracking athletic performance is crucial to an athlete’s development and the countermovement vertical jump is often used to measure athletic performance, particularly lower limb power. The linear power developed in the lower limb is estimated through jump height. However, the relationship between angular power, produced by the joints of the lower limb, and jump height is not well understood. This study examined the contributions of the kinetic value of angular power, and its kinematic component, angular velocity, of the lower limb joints to jump height in the countermovement vertical jump. Kinematic and kinetic data were gathered from twenty varsity-level basketball and volleyball athletes as they performed six maximal effort jumps in four arm swing conditions: no-arm involvement, single-non-dominant arm swing, single-dominant arm swing, and two-arm swing. The displacement of the whole body centre of mass, peak joint powers, peak angular velocity, and locations of the peaks as a percentage of the jump’s takeoff period, were computed. Linear regressions assessed the relationship of the variables to jump height. Results demonstrated that knee peak power (p = 0.001, ß = 0.363, r = 0.363), its location within takeoff period (p = 0.023, ß = -0.256, r = 0.256), and peak knee peak angular velocity (p = 0.005, ß = 0.310, r = 0.310) were moderately linked to increased jump height. Additionally, the location, within the takeoff period, of the peak angular velocities of the hip (p = 0.003, ß = -0.318, r = 0.419) and ankle (p = 0.011, ß = 0.270, r = 0.419) were positively linked to jump height. These results highlight the importance of training the velocity and timing of joint motion beyond traditional power training protocols as well as the importance of further investigation into appropriate testing protocol that is sensitive to the contributions by individual joints in maximal effort jumping.

On the feasibility of time-lapse superconducting gravimetry for reservoir monitoring

The feasibility of monitoring fluid flow subsurface processes that result in density changes, using the iGrav superconducting gravimeter, is investigated. Practical targets include steam-assisted gravity drainage (SAGD) bitumen depletion and water pumping from aquifers, for which there is currently a void in low-impact, inexpensive monitoring techniques. This study demonstrates that the iGrav has the potential to be applied to multi-scale and diverse reservoirs. Gravity and gravity gradient signals are forward modeled for a real SAGD reservoir at two time steps, and for surface-fed and groundwater-fed aquifer pumping models, to estimate signal strength and directional dependency of water flow. Time-lapse gravimetry on small-scale reservoirs exhibits two obstacles, namely, a µgal sensitivity requirement and high noise levels in the vicinity of the reservoir. In this study, both limitations are overcome by proposing (i) a portable superconducting gravimeter, and (ii) a pair of instruments under various baseline geometries. This results in improved spatial resolution for locating depletion zones, as well as the cancellation of noise common in both instruments. Results indicate that a pair of iGrav superconducting gravimeters meet the sensitivity requirements and the spatial focusing desired to monitor SAGD bitumen migration at the reservoir scales. For SAGD reservoirs, the well pair separation, reservoir depth, and survey sampling determine the resolvability of individual well pair depletion patterns during the steam chamber rising phase, and general reservoir depletion patterns during the steam chamber spreading phase. Results show that monitoring water table elevation changes due to pumping and tracking whether groundwater or surface water is being extracted are feasible.

Towards Mapping of Rock Walls Using a UAV-Mounted 2D Laser Scanner in GPS Denied Environments

In geotechnical engineering, the stability of rock excavations and walls is estimated by using tools that include a map of the orientations of exposed rock faces. However, measuring these orientations by using conventional methods can be time consuming, sometimes dangerous, and is limited to regions of the exposed rock that are reachable by a human. This thesis introduces a 2D, simulated, quadcopter-based rock wall mapping algorithm for GPS denied environments such as underground mines or near high walls on surface. The proposed algorithm employs techniques from the field of robotics known as simultaneous localization and mapping (SLAM) and is a step towards 3D rock wall mapping. Not only are quadcopters agile, but they can hover. This is very useful for confined spaces such as underground or near rock walls. The quadcopter requires sensors to enable self localization and mapping in dark, confined and GPS denied environments. However, these sensors are limited by the quadcopter payload and power restrictions. Because of these restrictions, a light weight 2D laser scanner is proposed. As a first step towards a 3D mapping algorithm, this thesis proposes a simplified scenario in which a simulated 1D laser range finder and 2D IMU are mounted on a quadcopter that is moving on a plane. Because the 1D laser does not provide enough information to map the 2D world from a single measurement, many measurements are combined over the trajectory of the quadcopter. Least Squares Optimization (LSO) is used to optimize the estimated trajectory and rock face for all data collected over the length of a light. Simulation results show that the mapping algorithm developed is a good first step. It shows that by combining measurements over a trajectory, the scanned rock face can be estimated using a lower-dimensional range sensor. A swathing manoeuvre is introduced as a way to promote loop closures within a short time period, thus reducing accumulated error. Some suggestions on how to improve the algorithm are also provided.