arXiv subjects

Margareta Stefanovic

Publications and source records attributed to Margareta Stefanovic.

4 recordsLinked to original sources

arXiv2025

Dimensionality Reduction with Koopman Generalized Eigenfunctions

This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman formulation of rigid body dynamics, but it can be extended to any data-driven or analytically derived generalized eigenfunction set. It achieves a representation for which the number of Koopman observables matches the number of inputs allowing for Koopman linearization control solutions rather than resorting to the least squares approximation method adopted in high dimensional Koopman formulations. Through a linear combination of Koopman generalized eigenfunctions a new set of Koopman generalized eigenfunction is constructed so that the zero order truncation approximate a Koopman eigenfunction which can be used to design linear control strategies to steer the dynamics of the original nonlinear system. The proposed methodology is tested by designing a linear quadratic (LQ) flight controller for a quadrotor UAV. Numerical and Hardware-in-the-loop (HIL) simulations validate the applicability and real-time implementability of the proposed approach in the presence of noise and sensor delays. The main advantage of the proposed method is the realization of a fully actuated Koopman based model which, in the case of the underactuated quadrotor system, allows to achieve trajectory tracking through a single linear control loop.

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arXiv2025

Reinforcement Learning Based Prediction of PID Controller Gains for Quadrotor UAVs

A reinforcement learning (RL) based methodology is proposed and implemented for online fine-tuning of PID controller gains, thus, improving quadrotor effective and accurate trajectory tracking. The RL agent is first trained offline on a quadrotor PID attitude controller and then validated through simulations and experimental flights. RL exploits a Deep Deterministic Policy Gradient (DDPG) algorithm, which is an off-policy actor-critic method. Training and simulation studies are performed using Matlab/Simulink and the UAV Toolbox Support Package for PX4 Autopilots. Performance evaluation and comparison studies are performed between the hand-tuned and RL-based tuned approaches. The results show that the controller parameters based on RL are adjusted during flights, achieving the smallest attitude errors, thus significantly improving attitude tracking performance compared to the hand-tuned approach.

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arXiv2024

Koopman Analytical Modeling of Position and Attitude Dynamics: a Case Study for Quadrotor Control

This research presents a novel, analytical, Koopman Operator based formulation for position and attitude dynamics which can be used to derive control strategies for underactuated systems. Compared to data driven Koopman based techniques, the analytical approach presented in this work is model based and allows for an exact linear representation of the original nonlinear position and attitude dynamics. In fact, the resulting infinite dimensional model, defined in the lifted state space, is linear in the autonomous component and state dependent in the control. A boundary study is carried on to define the range of validity of the finite truncation of the Koopman based model followed by a controllability and stabilizability analysis to show the feasibility of employing the derived model for control system design. Compared to existing literature formulation, the presented model results in a better approximation of the original dyanmics using a more compact truncation of the lifted state space. Moreover, the model is derived using the Koopman approach on the entirety of the dynamics and does not require the need of angular velocity dynamic compensation. A case study involving an underactuated quadrotor unmanned aerial vehicle (UAV) is provided to show that, for practical use, a truncated subset of the infinite dimensional model, embeds most of the original nonlinear dynamics and can be used to design linear control strategies in the lifted space which results in nonlinear controllers in the original state space. The main advantages of the presented approach reside in the effective use of linear control strategies for nonlinear plats and the solution of the underactuation problem employing a single control loop.

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arXiv2023

Correction to Euler Lagrange Multirotor Model with Euler Angles Generalized Coordinates

This technical note proves analytically how the exact equivalence of the Newton-Euler and Euler-Lagrange modeling formulations as applied to multirotor UAVs is achieved. This is done by deriving a revised Euler-Lagrange multirotor attitude dynamics model. A review of the published literature reveals that the commonly adopted Euler-Lagrange multirotor dynamics model is equivalent to the Newton-Euler model only when it comes to the position dynamics, but not in the attitude dynamics. Step-by-step derivations and calculations are provided to show how modeling equivalence to the Newton-Euler formulation is proven. The modeling equivalence is then verified by obtaining identical results in numerical simulation studies. Simulation results also illustrate that when using the revised model for feedback linearization, controller stability at high gains is improved.

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