Date of Award
Summer 8-24-2024
Document Type
Dissertation
Degree Name
Ph.D.
Organizational Unit
Daniel Felix Ritchie School of Engineering and Computer Science, Electrical and Computer Engineering
First Advisor
Kimon P. Valavanis
Second Advisor
Margareta Stefanovic
Third Advisor
Alvaro Arias
Fourth Advisor
Matthew J. Rutherford
Fifth Advisor
Alessandro Rizzo
Copyright Statement / License for Reuse
All Rights Reserved.
Keywords
Koopman operator, Multirotor UAV, Nonlinear control
Abstract
This PhD dissertation focuses on adopting the emerging Koopman Operator theory for modeling and nonlinear control of multirotor UAVs, focusing specifically on quadrotors for proof-of-concept demonstration purposes.
The Koopman Operator theory is based on the foundation that nonlinear dynamics in the state space may be represented as a linear evolution of some functions in the state space. Thus, using appropriately defined and possibly nonlinear functions of the state variables, called observables, as a new and maybe infinite set of coordinates that are referred to as lifted space, the original nonlinear dynamics appear to be linear. The implications of this theory center around the promising trait of defining a systematic framework for generalizing linear system analysis to the underlying nonlinear dynamics of the system under consideration. However, a key and open challenge is to find sets of Koopman observables for which a finite truncation of the infinite dimensional system representation embeds most of the original nonlinear dynamics.
The first main contribution of this dissertation is the derivation of a novel and analytically derived Koopman Operator based linear model for rigid body position and attitude dynamics; the novel formulation is adapted to multirotor UAVs which constitute underactuated and highly nonlinear robot platform systems. The Koopman based model is then used for controller design purposes. Compared to limited existing literature research, the presented analytical model provides a better approximation of the nonlinear dynamics in a more compact truncated form.
The second important contribution and result of the presented formulation is that it allows for solving the underactuation problem by extracting the intrinsic dependencies between inputs and states, effectively controlling the multirotor using a single linear control loop.
A third main contribution is the design and testing of an attitude trajectory tracking Koopman reduced order multirotor controller that exploits a well-known Koopman operator eigenfunction, i.e., the Hamiltonian function, which allows for embedding the nonlinear dynamics in a lower dimensional space. The resulting attitude controller is able to achieve trajectory tracking by exploiting a single scalar function that drastically simplifies the controller design.
The fourth main set of contributions are the correction of the literature Euler-Lagrange multirotor model by providing a proof of equivalence to the Newton-Euler formulation, the derivation of a Euler-Lagrange model with detailed aerodynamics and gyroscopic effects used for dynamic compensation control, and a comparative study of linear and nonlinear quadrotor controllers.
Finally, additional contributions include a Mars simulation environment for testing hexacopter autonomous control and navigation strategies, real-time hardware in the loop design and implementation of an enhanced model reference adaptive controller, and deployment and testing of model-based controllers on real quadrotor platforms.
Copyright Date
8-2024
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Rights Holder
Simone Martini
Provenance
Received from Author
File Format
application/pdf
Language
English (eng)
Extent
211 pgs
File Size
38.9 MB
Recommended Citation
Martini, Simone, "Koopman-Based Modeling for Nonlinear Control of Multirotor UAVs" (2024). Electronic Theses and Dissertations. 2481.
https://digitalcommons.du.edu/etd/2481
Included in
Controls and Control Theory Commons, Navigation, Guidance, Control and Dynamics Commons, Robotics Commons
