Modeling and Control of Multirotor UAVs: A Comprehensive Framework
Organizers and Lecturers
Kimon P. Valavanis, Matthew J. Rutherford Simone Martini[1], Serhat Sonmez, Laura Sopegno[2]
D. F. Ritchie School of Engineering and Computer Science
DU Unmanned Systems Research Institute (DU2SRI)
University of Denver – Denver, CO 80208
E-mail:
Tutorial Summary
The goal of the Tutorial is to provide a comprehensive framework that supports modeling, navigation, and control of multirotor UAVs with different onboard sensor modalities and endowed with different levels of autonomous functionality.
The first part of the tutorial centers around modeling. The two classical modeling formulations of Newton-Euler (N-E) and Euler-Largange (E-L) are described in detail and the equations of motion are derived. Gyroscopic effects are introduced and included in both models. In addition, different drag types (i.e., drag due to blade flapping, induced, translational, profile and parasitic) are explicitly derived and accounted for. However, to prove the exact mathematical equivalence of the N-E and E-L formulations, a revised multirotor attitude model is derived following the E-L formulation, r-E-L. When considering the N-E and the r-E-L formulations, either complete or simplified, obtained results for different types of multirotors (quadrotors, hexacopters) are identical. This part concludes by presenting a quaternion-based modeling alternative.
The second part of the tutorial focuses on the configuration of the multirotor navigation control architecture and on controller design, development, implementation, and testing, as well as performance evaluation and comparison. The overall navigation control architecture is hierarchical, hardware agnostic, and it follows a modular, component (i.e., sensors) plug in–plug out, design. It is fault tolerant in nature as it accounts for single and multiple failures, it includes an emergency landing component and allows for human–multirotor interaction. Controller design spans model-based, model-free, and combined data-driven and model-based approaches. Linear, linearized and fully nonlinear control approaches are presented first, followed by Fuzzy Logic and Artificial Neural Network based designs. Then, learning-based (machine learning, deep learning, reinforcement learning) control of multirotors is introduced along with advantages and disadvantages of online and offline techniques. Empasis is given in what is being learned, why, how, and how fast. Then, a new, novel, analytical controller design methodology is introduced, implemented, and tested, which takes advantage of the Koopman operator, and results in a fully controllable and stable (or stabilizable) system. Trajectory tracking performance is evaluated and compared by applying different controllers on multirotors functioning in 3-D uncertain environments. Chosen trajectories include non-aggressive and aggressive multirotor maneuvers, under nominal and detrimental conditions.
The third part of the tutorial presents a ‘simulation platform’ to serve as the ‘common denominator’ when conducting simulated experiments in diverse environments. The software tools that are used to develop this platform are MATLAB/Simulink, ROS/Gazebo, Simscape and the X-Plane Simulator. The aim is to acquire, through detailed studies, information about ‘how good’ a controller is, and under what conditions. Moreover, the developed software will be Open Source to be used by interested researchers and scientists.
Tutorial Objectives
The central objective of the Tutorial is to provide a foundational basis for accurate modeling and controller design for multirotors, facilitating at the same time implementation, testing and performance evaluation under realistic nominal and detrimental conditions.
Key Topics
The topics that will be addressed and discussed center around the conventional Newton-Euler and Euler-Lagrange modeling formulations, their similarities and differences and their exact equivalence, which, then, paves the way for accurate controller designs. Controller designs span model based, and data driven techniques, as well as a combination of both. Two key topics that will be detailed and addressed are the Koopman based framework for controller designs and learning based modeling and control for multirotor UAVs.
Tutorial Format
The Tutorial will include a series of detailed presentations what will include multimedia modules.
Target Audience
The Tutorial is suitable for graduate students conducting research in related areas, scientists, and engineers, as well as developers and manufacturers of UAVs.
Tentative Outcome
It is expected that participants will obtain a deep understanding of modeling challenges that need to be addressed and overcome to obtain ‘accurate models’ for a class of highly nonlinear and underactuated systems, and how such models may be used to derive and implement robust controllers with performance guarantees.
Material
Participants will be given comprehensive lecture notes along with a series of research papers.
[1] Simone Martini is also with Politecnico di Torino (PoliTo).
[2] Laura Sopegno is also with Universita degli Studi di Palermo (UniPa).