Abstract

State estimation is an essential part of any robotic autonomy solution. Continuous-time trajectory estimation is an attractive method because continuous trajectories can be queried at any time, allowing for fusion of multiple asynchronous, high-frequency measurement sources. This dissertation investigates various continuous-time estimation algorithms and their application to a handful of mobile robot autonomy and sensor calibration problems. In particular, we begin by analyzing and comparing two prominent continuous-time trajectory representations from the literature: Gaussian processes and splines, both on vector spaces and Lie groups. Our comparisons show that the two methods give comparable results so long as the same measurements and motion model are used. We then apply spline-based estimation to the problem of calibrating the extrinsic parameters between a camera and a GNSS receiver by fusing measurements from these two sensors and an IMU in continuous-time. Next, we introduce a novel estimation technique that uses the differential flatness property of dynamic systems to model the continuous-time trajectory of a robot on its flat output space, and show that estimating in the flat output space can provide superior accuracy and computation time than estimating on the configuration manifold. We use this new flatness-based estimation technique to perform pose estimation for velocity-constrained vehicles using only GNSS and IMU and show that modeling on the flat output space renders the global heading of the system observable, even when the motion of the system is insufficient to observe attitude from the measurements alone. We then show how flatness-based estimation can be used to calibrate the transformation between the dynamics coordinate frame and the coordinate frame of a sensor, along with other sensor-to-dynamics parameters, and use this calibration to improve the performance of flatness-based estimation when six-degree-of-freedom measurements are involved. Our final contribution involves nonlinear control of a quadrotor aerial vehicle. We use Lie theoretic concepts to develop a geometric attitude controller that utilizes logarithmic rotation error and prove that this controller is globally-asymptotically stable. We then demonstrate the ability of this controller to track highly-aggressive quadrotor trajectories.

Degree

PhD

College and Department

Ira A. Fulton College of Engineering; Electrical and Computer Engineering

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2023-08-14

Document Type

Dissertation

Handle

http://hdl.lib.byu.edu/1877/etd12930

Keywords

trajectory estimation, sensor calibration, differential flatness, splines, Gaussian processes, Lie groups, geometric control

Language

english

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