arXiv subjects

Kimon P. Valavanis

Publications and source records attributed to Kimon P. Valavanis.

7 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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arXiv2024

A Comparative Study of Real-Time Implementable Cooperative Aerial Manipulation Systems

This survey paper focuses on quadrotor- and multirotor- based cooperative aerial manipulation. Emphasis is first given on comparing and evaluating prototype systems that have been implemented and tested in real-time in diverse application environments. Underlying modeling and control approaches are also discussed and compared. The outcome of the survey allows for understanding the motivation and rationale to develop such systems, their applicability and implementability in diverse applications and also challenges that need to be addressed and overcome. Moreover, the survey provides a guide to develop the next generation of prototype systems based on preferred characteristics, functionality, operability and application domain.

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arXiv2024

A Survey of Offline and Online Learning-Based Algorithms for Multirotor UAVs

Multirotor UAVs are used for a wide spectrum of civilian and public domain applications. Navigation controllers endowed with different attributes and onboard sensor suites enable multirotor autonomous or semi-autonomous, safe flight, operation, and functionality under nominal and detrimental conditions and external disturbances, even when flying in uncertain and dynamically changing environments. During the last decade, given the faster-than-exponential increase of available computational power, different learning-based algorithms have been derived, implemented, and tested to navigate and control, among other systems, multirotor UAVs. Learning algorithms have been, and are used to derive data-driven based models, to identify parameters, to track objects, to develop navigation controllers, and to learn the environment in which multirotors operate. Learning algorithms combined with model-based control techniques have been proven beneficial when applied to multirotors. This survey summarizes published research since 2015, dividing algorithms, techniques, and methodologies into offline and online learning categories, and then, further classifying them into machine learning, deep learning, and reinforcement learning sub-categories. An integral part and focus of this survey are on online learning algorithms as applied to multirotors with the aim to register the type of learning techniques that are either hard or almost hard real-time implementable, as well as to understand what information is learned, why, and how, and how fast. The outcome of the survey offers a clear understanding of the recent state-of-the-art and of the type and kind of learning-based algorithms that may be implemented, tested, and executed in real-time.

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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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arXiv2017

Learning-based Formal Synthesis of Cooperative Multi-agent Systems

We propose a formal design framework for synthesizing coordination and control policies for cooperative multi-agent systems to accomplish a global mission. The global performance requirements are specified as regular languages while dynamics of each agent as well as the shared environment are characterized by finite automata, upon on which a formal design approach is carried out via divide-and-conquer. Specifically, the global mission is decomposed into local tasks; and local mission supervisors are designed to accomplish these local tasks while maintaining the multi-agent performance by integrating supervisor synthesis with compositional verification techniques; finally, motion plans are automatically synthesized based on the obtained mission plans. We present three modifications of the L* learning algorithm such that they are adapted for the synthesis of the local mission supervisors, the compositional verification and the synthesis of local motion plans, to guarantee that the collective behavior of the agents will ensure the satisfaction of the global specification. Furthermore, the effectiveness of the proposed framework is demonstrated by a detailed experimental study based on the implementation of a multi-robot coordination scenario. The proposed hardware-software architecture, with each robot's communication and localization capabilities, is exploited to examine the automatic supervisor synthesis with inter-robot communication.

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