A numerical simulation for evaluating methods of predicting and controlling the response of an elastic wing in an airstream is discussed. The technique employed interactively and simultaneously solves for the response in the time domain by considering the air, wing, and controller as elements of a single dynamical system. The method is very modular, allowing independent modifications to the aerodynamic, structural, or control subsystems and it is not restricted to periodic motions or simple geometries. To illustrate the technique, we use a High Altitude, Long Endurance aircraft wing. The wing is modeled structurally as a linear Euler-Bernoulli beam that includes dynamic coupling between the bending and torsional oscillations. The governing equations of motion are derived and extended to allow for rigid-body motions of the wing. The exact solution to the unforced linear problem is discussed as well as a Galerkin and finite-element approximations. The finite-element discretization is developed and used for the simulations. A general, nonlinear, unsteady vortex-lattice method, which is capable of simulating arbitrary subsonic maneuvers of the wing and accounts for the history of the motion, is employed to model the flow around the wing and provide the aerodynamic loads. Two methods of incorporating gusts in the aerodynamic model are also discussed. Control of the wing is effected via a distributed torque actuator embedded in the wing and two strategies for actuating the wing are described: a classical linear proportional integral strategy and a novel nonlinear feedback strategy based on the phenomenon of saturation that may exist in nonlinear systems with two-to-one internal resonances. Both control strategies can suppress the flutter oscillations of the wing, but the nonlinear controller must be actively tuned to be effective; gust control proved to be more difficult. / Master of Science

The aim of this dissertation is to systematically construct a hierarchical framework that allows for robust multi-agent collaborative legged locomotion. More specifically, this work provides a detailed derivation of a torque controller that is theoretically justifiable in the context of Hybrid Zero Dynamics at the lowest level of control to produce highly robust locomotion, even when subject to uncertainty. The torque controller is based on virtual constraints and partial feedback linearization and is cast into the form of a strictly convex quadratic program. This partial feedback linearization is then relaxed through the use of a defect variable, where said defect variable is allowed only to change in a manner that is consistent with rapidly exponentially stable output dynamics through the use of a Control Lyapunov Function. The torque controller is validated in both simulation and on hardware to demonstrate the efficacy of the approach. In particular, the robot is subject to payload and push disturbances and is still able to remain stable. Furthermore, the continuity of the torque controller, in addition to robustness analysis of the periodic orbit, is also provided. At the next level of control, we consider emulating the Single Rigid Body model through the use of Behavioral Systems Theory, resulting in a data-driven model that adequately describes a quadruped at the reduced-order level. Still, due to the complexity and a considerable number of variables in the problem, the model further undergoes a $2$-norm approximation, resulting in a model that is computationally efficient enough to be used in a real-time manner for trajectory planning. In order to test the method rigorously, we consider a series of experiments to examine how the planner works when using different gait parameters than that which was used during data collection. Furthermore, the planner is compared to the traditional Single Rigid Body model to test its efficacy for reference tracking. This data-driven model is then extended to the multi-agent case, where each agent is rigidly holonomically constrained to one another. In this case, the model is used in a distributed manner using a one-step communication delay such that the coupling between agents can be adequately considered while spreading the computational demand. The trajectory planner is evaluated through various hardware experiments with three agents, and simulations are also used to display the scalability of the approach by considering five robots. Finally, this dissertation examines how traditional reduced-order models can be used in tandem with data-based models to reap the benefits of both methods. More specifically, an interconnected Single Rigid Body model is considered, where the interaction forces are described via a data-driven model. Simulations are provided to display the efficacy of this approach at the reduced order level and show that the interaction forces can be reduced by considering them in the trajectory planner. As in the previous cases, this is followed by experimental evaluation subject to external forces and different terrains. / Doctor of Philosophy / The goal of this dissertation is to create a layered control scheme for teams of quadrupeds that results in stable and robust locomotion, including a high-level trajectory planner and a low-level controller. More specifically, this work outlines an optimal torque-based whole-body controller that operates at the joint level to track desired trajectories. These trajectories are obtained by a high-level trajectory planner, which utilizes a data-driven predictive controller to create an optimal trajectory without explicitly requiring knowledge of a model. The hierarchical control scheme is then extended to consider collaborative locomotion. Namely, this work considers teams of quadrupeds that are rigidly connected to one another such that there is no relative motion between them. There are potentially large interaction forces that are applied between the robots that cannot be measured, which can result in instability. Furthermore, the models used to describe the interconnected system are prohibitively complex when being used for trajectory planning. For this reason, the data-driven model considered for a single robot is extended to create a centralized model that encapsulates not only the motion of a single robot but also its connection constraints. The resulting model is very large, making it difficult to use in a real-time manner. Therefore, this work outlines how to distribute the model such that each robot can locally plan for its own motion while also considering the coupling between them. Finally, this work provides one additional extension that combines a traditional physics-based model with a data-driven model to capitalize on the strengths of each. In particular, a physics-based model is considered as a baseline, while a data-driven model is used to describe the interaction forces between robots. In using this final extension, both improved solve times and smoother locomotion are achieved. Each of the aforementioned methods is tested thoroughly through both simulations and experiments.

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Magnetic properties of ferrite structures are known to cause fluctuations in Earth's magnetic field around the object. These fluctuations are known as the object's magnetic signature and are unique based on the object's geometry and material. It is a common practice to neutralize magnetic signatures periodically after certain time intervals, however there is a growing interest to develop real time degaussing systems for various applications. Development of real time degaussing system is a challenging problem because of magnetic hysteresis and difficulties in measurement or estimation of near-field flux data. The goal of this research is to develop a real time feedback control system that can be used to minimize magnetic signatures for ferrite structures. Experimental work on controlling the magnetic signature of a cylindrical steel shell structure with a magnetic disturbance provided evidence that the control process substantially increased the interior magnetic flux. This means near field estimation using interior sensor data is likely to be inaccurate. Follow up numerical work for rectangular and cylindrical cross sections investigated variations in shell wall flux density under a variety of ambient excitation and applied disturbances. Results showed magnetic disturbances could corrupt interior sensor data and magnetic shielding due to the shell walls makes the interior very sensitive to noise. The magnetic flux inside the shell wall showed little variation due to inner disturbances and its high base value makes it less susceptible to noise. This research proceeds to describe a nonlinear controller to use the shell wall data as an input. A nonlinear plant model of magnetics is developed using a constant to represent domain rotation lag and a gain function to describe the magnetic hysteresis curve for the shell wall. The model is justified by producing hysteresis curves for multiple materials, matching experimental data using a particle swarm algorithm, and observing frequency effects. The plant model is used in a feedback controller and simulated for different materials as a proof of concept. / Electrical and Computer Engineering