Aerospace Engineering Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2737
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Item Analysis of the Stochastic Stability and Asymptotically Stationary Statistics for a Class of Nonlinear Attitude Estimation Algorithms(2018) Galante, Joseph Marshall; Sanner, Robert M; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Attitude estimation algorithms are critical components of satellite control systems, aircraft autopilots, and other applications. Attitude estimation systems perform their task by fusing attitude and gyroscope measurements; however, such measurements are typically corrupted by random noise and gyroscopes may have significant bias. Variations of the extended Kalman filter are commonly used, but this technique relies on instantaneous linearization of the underlying nonlinear dynamics and global stability cannot be guaranteed. Nonlinear attitude observers with guaranteed global stability have been derived and experimentally demonstrated, but only for the deterministic setting where no stochastic effects are present. The first part of this thesis extends a deterministic nonlinear attitude estimator by introducing additional dynamics that allow learning variations of gyro bias as a function of operating temperature, a common source of bias variation in rate gyro readings. The remainder of the thesis formally addresses the problem of stochastic stability and asymptotic performance for this family of estimators when the measurements contain random noise. Analysis tools from stochastic differential equation theory and stochastic Lyapunov analysis are used together to demonstrate convergence of the filter states to a stationary distribution, and to bound the associated steady-state statistics as a function of filter gains and sensor parameters. In many cases these bounds are conservative, but solutions have been found for the associated stationary Fokker-Planck PDEs for two cases. When only the gyro measurement contains noise, the attitude estimation errors are shown to converge to a bipolar Bingham distribution. When the gyro measurement is further assumed to have constant bias, the estimation errors are shown to converge to a joint bipolar Bingham and multivariate Gaussian distribution. Knowledge of the stationary distributions allow for exact computation of steady-state statistics. Further, the analysis suggests a method for modeling a continuous quaternion noise process with specified statistics on SO(3); this model is used for analyzing estimator performance when both the gyro and the attitude measurements contain noise. Bounds and exact predictions for the different noise models are validated using a high fidelity numerical integration method for nonlinear stochastic differential equations.Item Quaternion-Based Control for Aggressive Trajectory Tracking with a Micro-Quadrotor UAV(2014) Kehlenbeck, Andrew Gale; Humbert, James S; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)With potential missions for quadrotor micro-air vehicles (MAVs) calling for smaller, more agile vehicles, it is important to implement attitude controllers that allow the vehicle to reach any desired attitude without encountering computational singularities, as is the case when using an Euler angle representation. A computationally efficient quaternion-based state estimator is presented that enables the Army Research Laboratory's (ARL) 100-gram micro-quadrotor to determine its attitude during agile maneuvers using only an on-board gyroscope and accelerometer and a low-power processor. Inner and outer loop attitude and position controllers are also discussed that use the quaternion attitude representation to control the vehicle along aggressive trajectories with the assistance of an outside motion capture system. A trajectory generation algorithm is then described that leverages the quadrotor's inherent dynamics to allow it to reach extreme attitudes for applications such as perching on walls or ceilings and flying through small openings.