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In this paper the popup height of rising buoyant spheres is studied over a range of distinct release depths along with the accompanying velocities and accelerations near the free surface. In the past, regimes of motion due to vortex induced vibrations have been classified based on trajectories below the free surface. This study focuses on the popup height, velocity and acceleration at free surface exit, and vortex shedding in order to further define regimes of motion experienced by a rising buoyant sphere. Varying the release depth below the free surface reveals varying exit angles, velocities, accelerations, and popup heights at surface exit. Vortex shedding prior to free surface exit causes decelerations contributing to the variation in exit velocities and resulting popup heights. Using high-speed imaging and particle image velocimetry, we examine the trajectories, accelerations, velocities and vortex shedding events for spheres of different mass ratios over a range of Reynolds number (2e4 >Re> 6e5). At lower Re, spheres released from shallow release depths result in greater accelerations and velocities at free surface exit along with greater popup heights compared to releases from deeper depths. After reaching a depth which results in a minimum popup height, further increasing the release depth reveals an increase in popup height demonstrating an oscillatory pattern due to the sphere being released from vortex forces after shedding. This pattern is repeated as the popup height again decreases with greater release depths. For spheres of greater Re, popup height increases linearly with release depth, demonstrating continued accelerations at free surface exit.

In trajectory optimization, a common objective is to minimize propellant mass via multiple gravity assist maneuvers (MGAs). Some computer programs have been developed to analyze MGA trajectories. One of these programs, Parallel Global Multiobjective Optimization (PaGMO), uses an interesting technique known as the Island Model Paradigm. This work provides the community with a MATLAB optimizer, STOpS, that utilizes this same Island Model Paradigm with five different optimization algorithms. STOpS allows optimization of a weighted combination of many parameters. This work contains a study on optimization algorithm performance and how each algorithm is affected by its available settings. STOpS successfully found optimal trajectories for the Mariner 10 mission and the Voyager 2 mission that were similar to the actual missions flown. STOpS did not necessarily find better trajectories than those actually flown, but instead demonstrated the capability to quickly and successfully analyze/plan trajectories. The analysis for each of these missions took 2-3 days each. The final program is a robust tool that has taken existing techniques and applied them to the specific problem of trajectory optimization, so it can repeatedly and reliably solve these types of problems.

The information presented in the thesis is a continuation of the Spacecraft Trajectory Optimization Suite (STOpS). This suite was originally designed and developed by Timothy Fitzgerald and further developed by Shane Sheehan, both graduate students at California Polytechnic State University, San Luis Obispo. Spacecraft utilizing low-thrust transfers are becoming more and more common due to their efficiency on interplanetary trajectories, and as such, finding the most optimal trajectory between two planets is something of interest. The version of STOpS presented in this thesis uses Multiple Gravity-Assist Low-Thrust (MGALT) trajectories paired with the island model paradigm to accomplish this goal. The island model utilizes four different global search algorithms: a Genetic Algorithm, Differential Evolution, Particle Swarm Optimization, and Monotonic Basin Hopping. The first three algorithms were featured in the initial version of STOpS written by Fitzgerald [1], and were subsequently modified by Sheehan [2] to work with a low-thrust adaptation of STOpS. For this work, Monotonic Basin Hopping was added to aid the suite with the MGALT trajectory search. Monotonic Basin Hopping was successfully validated against four different test functions which had been used to validate the other three algorithms. The purpose of this validation was to ensure Monotonic Basin Hopping would work as intended, ensuring it would work in cooperation with the other three algorithms to produce a near optimal solution. After verifying the addition of Monotonic Basin Hopping, all four algorithms were used in the island model paradigm to verify MGALT STOpS’ ability to solve two known orbital transfer problem. The first verification case involved an Earth to Mars transfer with fixed thruster parameters and a predetermined time of flight. The second verification case involved a transfer from Earth to Jupiter via a Mars gravity assist; two different versions of the verification case were solved against trajectories produced by industry optimization software, the Satellite Tour Design Program Low-Thrust Gravity Assist and the Gravity Assisted Low-thrust Local Optimization Program. In the first verification case, MGALT STOpS successfully validated the Earth to Mars trajectory problem and found results agreeable to literature. In the second verification case, MGALT STOpS was partially successful in validating the Earth to Mars to Jupiter trajectory problems, and found results similar to literature. The final software produced for this work is a trajectory optimization suite implemented in MATLAB, which can solve interplanetary low-thrust trajectories with or without the inclusion of gravity assists.

Online consolidation fiber placement is emerging as an automated manufacturing process for the fabrication of large composite material complex structures. While traditional composite manufacturing techniques limited the products' size, geometrical shapes and laminate patterns, robotic automation of the fiber placement process allows the manufacture of complex bodies with any desired surface pattern or towpreg's direction. Therefore, a complete understanding of the robot kinematic capabilities should be made to accurately position the structure's substrate in the workcell and to compute the feasible product dimensions and sizes. A Matlab algorithm is developed to verify the feasibility of straight-line trajectory paths and to locate all valid towpreg segments in the workspace, with no focus on optimization. The algorithm is applied preliminary to a three-link planar arm; and a 6-dof Merlin robot is subsequently considered to verify the towpreg layouts in the three-dimensional space. The workspace is represented by the longest feasible segments and plotted on parallel two-dimensional planes. The analysis is extended to locate valid square areas with predetermined dimensions. The fabrication of isotropic circular coupons is then tested with two different compaction heads. The results allow the formulation of a geometric correlation between the end-effector dimensional measures and the orientation of the end-effector with respect to the towpreg segments. / Master of Science

As progress pushes the boundaries of both the performance of new hardware components and the computational capacity of modern computers, the requirements on the performance of robotic systems are becoming more and more demanding. The objective of this thesis is to demonstrate that concurrent design (Co-Design) is the approach to follow to design hardware and control for such high-performance robots. In particular, this work proposes a co-design framework and an algorithm to tackle two main issues: i) how to use Co-Design to benchmark different robotic systems, and ii) how to effectively warm-start the trajectory optimization (TO) problem underlying the co-design problem aiming at global optimality. The first contribution of this thesis is a co-design framework for the energy efficiency analysis of a redundant actuation architecture combining Quasi-Direct Drive (QDD) motors and Series Elastic Actuators (SEAs). The energy consumption of the redundant actuation system is compared to that of Geared Motors (GMs) and SEAs alone. This comparison is made considering two robotic systems performing different tasks. The results show that, using the redundant actuation, one can save up to 99% of energy with respect to SEA for sinusoidal movements. This efficiency is achieved by exploiting the coupled dynamics of the two actuators, resulting in a latching-like control strategy. The analysis also shows that these large energy savings are not straightforwardly extendable to non-sinusoidal movements, but smaller savings (e.g., 7%) are nonetheless possible. The results highlight that the combination of complex hardware morphologies and advanced numerical Co-Design can lead to peak hardware performance that would be unattainable by human intuition alone. Moreover, it is also shown how to leverage Stochastic Programming (SP) to extend a similar co-design framework to design robots that are robust to disturbances by combining TO, morphology and feedback control optimization. The second contribution is a first step towards addressing the non-convexity of complex co-design optimization problems. To this aim, an algorithm for the optimal control of dynamical systems is designed that combines TO and Reinforcement Learning (RL) in a single framework. This algorithm tackles the two main limitations of TO and RL when applied to continuous-space non-linear systems to minimize a non-convex cost function: TO can get stuck in poor local minima when the search is not initialized close to a “good” minimum, whereas the RL training process may be excessively long and strongly dependent on the exploration strategy. Thus, the proposed algorithm learns a “good” control policy via TO-guided RL policy search. Using this policy to compute an initial guess for TO, makes the trajectory optimization process less prone to converge to poor local optima. The method is validated on several reaching problems featuring non-convex obstacle avoidance with different dynamical systems. The results show the great capabilities of the algorithm in escaping local minima, while being more computationally efficient than the state-of-the-art RL algorithms Deep Deterministic Policy Gradient and Proximal Policy Optimization. The current algorithm deals only with the control side of a co-design problem, but future work will extend it to include also hardware optimization. All things considered, this work advanced the state of the art on Co-Design, providing a framework and an algorithm to design both hardware and control for high-performance robots and aiming to the global optimality.

<p> The topic of study within includes the development and application of nonlinear control technologies on sampled systems. Discrete control structures are introduced that expand on existing differential geometric and predictive control methods. The differential geometric techniques are described from the error trajectory context, which are typically only derived for continuous application. The discrete error trajectory controllers introduced have one of two configurations. The first configuration requires satisfaction of the error trajectory objective at the next sampling interval through prediction of system behaviour over the controller sampling interval. This objective found limited success and it is observed that satisfaction of the error trajectory objective at discrete intervals does not generally result in the intended response. The second configuration minimizes the integrated distance from the error manifold defined by the error trajectory objective over the entire controller sampling interval. It is observed that this integrated error trajectory controller best emulates the intent of the continuous controller in the discrete domain. Techniques borrowed from predictive control are incorporated into the integrated error trajectory controller such as input move suppression and constraints to produce an optimal error trajectory controller, further improving performance.</p> <p> The predictive control method introduced utilizes a transformation of the input space. The differentiating property of input transformation predictive control (ITPC) from other methods is the prediction technique that is capable of estimating the future behaviour of nonlinear systems through elementary matrix operations similar to the dynamic matrix control (DMC) prediction technique. This is achieved by separation of the steady state and dynamic system properties and the introduction of an intermediate state prediction layer. This allows for the nonlinear prediction of system behaviour without the need to numerically integrate the system model.</p> <p> Two example systems are used to demonstrate application of the discrete error trajectory and ITPC on nonlinear controllers. Performance for these control structures is compared to technologies accepted within the control community for a broad range for characteristics including, computation efficiency, design effort and other nonlinear performance criteria, with favourable results.</p> / Thesis / Master of Engineering (MEngr)

<p> The unique features of the Interrupted Thorium Cycle owing to Pa-233 have been examined including possible implications for practical implementation of the cycle. Generalized trajectories for the fuel inventories of fusion-fission symbionts are derived through a comprehensive parametric analysis. The resultant formulations are then applied to a specific example. It is concluded that this formulation and analysis leads to more exact fissile and fusile fuel characterizations than suggested by conventional procedures. </p> / Thesis / Master of Engineering (MEngr)

Title: Borderline personality disorder: examining trajectories of development among adolescents Background: Borderline personality disorder (BPD) tends to be highly comorbid with other disorders. In adolescence, information about the classification and development of BPD is in its early stages. There is limited empirical research available that investigates predictors of clinically significant symptom trajectories of the disorder using data collected in childhood. Given the enormous personal and societal costs associated with BPD, early detection and prevention is important. Clinical implications of this research include an improved understanding of risk factors and possible mechanisms for development of BPD symptomatology. Objectives: To identify trajectories of BPD symptomatology in a Canadian sample of adolescents (N = 703) assessed at ages 13, 14, 15 and 16, while examining predictors of trajectory group membership assessed at age 12. Methods: Data from the McMaster Teen Study was used to examine trajectories of BPD symptoms using group-based trajectory modeling. The influence of gender, depression, ADHD, family functioning and various sociodemographic variables as predictors of an individual’s group membership was tested. Chi-square, analysis of variance and multinomial logistic regression was used to analyze the data. Results: A four-group trajectory model was most robust at describing BPD symptomatology in this age group. Univariate analyses supported female gender, depression and ADHD at baseline, parental age, marital status, education, and income as significant predictors of group membership. Female gender, depression and ADHD severity at baseline were significant predictors of group membership when adopting a multivariate approach. There is a greater prevalence of girls with higher depression and ADHD scores in the high-increasing features and BPD group. Conclusion: Findings demonstrate four various developmental trajectories of BPD features. Results further the understanding of the factors associated with development of the disorder across time. / Thesis / Master of Science (MSc) / Information about the classification and development of borderline personality disorder (BPD) in adolescence is in its early stages. While evidence for similar construct validity to the adult disorder exists for adolescents, major gaps in knowledge regarding the stability in course of BPD symptoms and predictors of clinically significant symptom trajectories in this age group remain. As most clinicians will assess youth already having significant features of the disorder, early detection requires knowledge of the indicators that precede an unfavourable trajectory. This dissertation will help address these gaps by modeling trajectories of BPD symptoms in youth across ages 13-16, whilst examining factors influencing trajectory group membership.

This thesis presents a novel architecture for human-in-the-loop control of multiple drones. The design of such systems must address several challenges at the same time. The drones must avoid collisions with each other and with obstacles in their task environment while following operator's command as closely as possible to navigate their environment. To this end, they should be able to adjust their pre-defined desired formation and, if needed, transition to alternative formations to ensure collision-free operation in their task environment while following the operator's commands. The proposed control strategy is a central algorithm with multiple stages and relies on formulating and solving convex optimization problems in real time to achieve the control objectives. The operator provides reference velocity commands for the flock of drones to move them in the task environment. The algorithm creates linear collision avoidance constraints and distributes the operator's commands among the drones through a number of intermediate steps. It generates reference trajectories for the drones motion by solving a model-based optimization problem over a receding horizon. Conventional trajectory controllers generate the control inputs for individual drones. Prospective formation shapes are obtained for the drones by formulating and solving parallel convex optimizations, considering the operator's reference command and the obstacle-free space. While keeping the convexity of the optimization problem, the proposed algorithm allows for the presence of obstacles in the middle of the formation. This is achieved by properly assigning obstacle-free regions to each agent separately in the formation. In addition, safe convex regions in the form of linear inequality constraints are generated in the direction of the operator's commanded velocity. Moreover, constraints are introduced to avoid inter-drone collisions at each step. Trajectory optimization is formulated as a quadratic programming problem similar to model predictive control schemes to minimize deviation from human operator's command. The effectiveness of the proposed control algorithm is initially verified by simulating two different operational scenarios. Furthermore, the algorithm is implemented on actual hardware to operate a flock of three drones in a laboratory setting. The implementation of the algorithm in C++ utilizes high-performance computation techniques to achieve sufficiently high real-time control update rates for smooth and stable operation of the drones. / Thesis / Master of Applied Science (MASc) / The rise of unmanned aerial vehicle technology and the increase in their accessibility have made them viable solutions for serious missions such as search and rescue operations. Complex cooperative tasks can be conducted via a collection of drones which can show higher levels of robustness and agility as a system. Although repetitive and simple actions can be easily automated, real-world problems are unpredictable in which complex decision-making is involved. Such scenarios can be tackled by the presence of a human supervisor to empower the system with strong cognitive capabilities. This thesis presents a multi-layer control framework for human-in-the-loop operation of a flock of unmanned aerial vehicles. This method continuously optimizes the drones trajectories to adhere as closely as possible to operator's motion commands while avoiding collisions among them and with obstacles in their task environment. This new control framework is successfully validated in both simulations and experiments in a laboratory environment.