Review of PID Controller Applications for UAVs

Unmanned Aerial Vehicles (UAVs) have gained widespread recognition for their diverse applications, ranging from surveillance to delivery services. Among the various control algorithms employed to stabilize and navigate UAVs, the Proportional-Integral-Derivative (PID) controller stands out as a classical yet robust solution. This review provides a comprehensive examination of PID controller applications in the context of UAVs, addressing their fundamental principles, dynamics modeling, stability control, navigation tasks, parameter tuning methods, challenges, and future directions

Four-dimensional Gait Surfaces for A Tilt-rotor -- Two Color Map Theorem

This article presents the four-dimensional surfaces which instruct the gait plan for a tilt-rotor. The previous gaits analyzed in the tilt-rotor research are inspired by animals; no theoretical base backs the robustness of these gaits. This research deduces the gaits by diminishing the effect of the attitude of the tilt-rotor for the first time. Four-dimensional gait surfaces are subsequently found, on which the gaits are expected to be robust to the attitude. These surfaces provide the region where the gait is suggested to be planned. However, a discontinuous region may hinder the gait plan process while utilizing the proposal gait surfaces. A Two Color Map Theorem is then established to guarantee the continuity of each gait designed. The robustness of the typical gaits obeying the Two Color Map Theorem and on the gait surface is demonstrated by comparing the singular curve in attitude with the gaits not on the gait surface. The result shows that the acceptable attitudes enlarge for the gaits on the gait surface

Advanced Feedback Linearization Control for Tiltrotor UAVs: Gait Plan, Controller Design, and Stability Analysis

Three challenges, however, can hinder the application of Feedback Linearization: over-intensive control signals, singular decoupling matrix, and saturation. Activating any of these three issues can challenge the stability proof. To solve these three challenges, first, this research proposed the drone gait plan. The gait plan was initially used to figure out the control problems in quadruped (four-legged) robots; applying this approach, accompanied by Feedback Linearization, the quality of the control signals was enhanced. Then, we proposed the concept of unacceptable attitude curves, which are not allowed for the tiltrotor to travel to. The Two Color Map Theorem was subsequently established to enlarge the supported attitude for the tiltrotor. These theories were employed in the tiltrotor tracking problem with different references. Notable improvements in the control signals were witnessed in the tiltrotor simulator. Finally, we explored the control theory, the stability proof of the novel mobile robot (tilt vehicle) stabilized by Feedback Linearization with saturation. Instead of adopting the tiltrotor model, which is over-complicated, we designed a conceptual mobile robot (tilt-car) to analyze the stability proof. The stability proof (stable in the sense of Lyapunov) was found for a mobile robot (tilt vehicle) controlled by Feedback Linearization with saturation for the first time. The success tracking result with the promising control signals in the tiltrotor simulator demonstrates the advances of our control method. Also, the Lyapunov candidate and the tracking result in the mobile robot (tilt-car) simulator confirm our deductions of the stability proof. These results reveal that these three challenges in Feedback Linearization are solved, to some extents.Comment: Doctoral Thesis at The University of Toky

Trajectory Generation for a Quadrotor Unmanned Aerial Vehicle

RÉSUMÉ Le domaine des véhicules aériens sans pilote de type multicoptères a connu une progression substantielle au cours de la dernière décennie. La génération et le contrôle des trajectoires ont été au centre des préoccupations de ce nouveau domaine, avec des méthodes qui permettent d’exécuter des manoeuvres complexes dans l’espace. Plusieurs efforts ont été faits pour exécuter ces manoeuvres en utilisant la commande non linéaire, notamment la commande par platitude différentielle. Cependant, l’absence de théorie pour l’estimation des dérivées d’ordre supérieur a empêché l’application expérimentale de plusieurs de ces techniques. Ce travail explore tout d’abord l’approche par composition séquentielle pour l’exécution de manoeuvres à travers des fenêtres étroites. Cette technique implique la combinaison de plusieurs contrôleurs théoriquement simples afin de produire un résultat complexe. Les résultats expérimentaux réalisés dans le Laboratoire de Robotique Mobile et de Systèmes Automatisés à Polytechnique Montréal démontrent la validité de cette approche, en produisant des manoeuvres précises et répétables. Cependant, on atteint rapidement les limites d’une telle méthode dans les applications du monde réel, du fait de son manque de précision initiale et l’absence d’évaluation de faisabilité. Ce mémoire se concentre ensuite sur le développement d’une architecture d’estimation d’état basée sur le filtre de Kalman linéaire afin de fournir en temps réel des estimés des 2e et 3e dérivées de la position d’un quadricoptère (appelées respectivement accélération, et àcoup ou jerk). Des filtres de complexités différentes sont développés afin d’incorporer toute l’information disponible sur le système pour améliorer l’estimé résultant. On obtient alors un estimateur d’état complet qui utilise les mesures de position et d’accélération, ainsi que les entrées de commande, et fournit des estimés pour la rétroaction. Un contrôleur du jerk augmenté basé sur la théorie de la commande optimale est ensuite développé afin de valider cet estimateur. Il est conçu de façon à utiliser le jerk, l’accélération, la vitesse et la position du drone ; sans rétroaction de chacun de ces termes, le système est alors instable. Des tests sont effectués afin d’examiner les performances de l’estimateur et du contrôleur. Tout d’abord, le quadricoptère est chargé de suivre diverses entrées de référence dans l’espace pour assurer sa stabilité. Le contrôleur permet de suivre au plus près ces références, comme réalisé en simulation. Le contrôleur doit ensuite suivre un changement de référence afin d’évaluer la précision de l’estimateur développé. Les résultats montrent que l’estimation en temps réel du jerk suit adéquatement les valeurs hors ligne. Pour autant que nous le sachions, c’est la première mise en oeuvre dans le monde réel du retour de jerk pour contrôler un multicoptère.----------ABSTRACT The field of multirotor unmanned aerial vehicles (UAVs) has seen substantial progression in the past decade. Trajectory generation and control has been a main focus in this domain, with methods that enable the performance of complex three-dimensional maneuvers through space. Efforts have been made to execute these maneuvers using concepts of nonlinear control and differential flatness. However, a lack of theory for the estimation of higher-order dérivatives of a multirotor UAV has prevented the experimental application of several of these techniques concentrated on trajectory control. This work firstly explores the existing control approach of sequential composition for the execution of quadrotor manoeuvres through narrow windows. This technique involves the combination of several theoretically simple controllers in sequence in order to produce a complex result. Experimental results conducted in the Mobile Robotics and Automated Systems Laboratory (MRASL) at Polytechnique demonstrate the validity of this approach, producing precise and repeatable manoeuvres through narrow windows. However, they also show the limitations of such a method in real world applications, notably its initial inaccuracy and lack of feasibility evaluation. This thesis then focuses on the development of a state-estimation architecture based on linear Kalman filter techniques in order to provide a real-time value of a quadrotor UAV’s second and third derivatives (referred to as acceleration and jerk, respectively). Filters of different complexities are developed with the goal of incorporating all available system information into the resulting estimate. A full-state estimator is produced that uses a quadrotor’s position and acceleration measurements as well as control inputs in order to be usable for feedback. A jerk-augmented controller based off of optimal control theory is then developed in order to validate this estimator. It is designed in such a way to use the UAV’s jerk, acceleration, velocity and position as design parameters and to be unstable without feedback in each of these terms. Tests are conducted in order to examine the performance of both the estimator and controller. Firstly, the quadrotor is commanded to track various reference inputs in 3D space to ensure its stability. The controller tracks these references very closely to simulated responses. The controller is then asked to follow a changing reference in order to evaluate the precision of the developed estimator. Results show that the real-time estimation of the jerk follows offline values adequately. To the best of our knowledge, this is the first application to implement the feedback of a multirotor UAV’s jerk in real-world experimentation

Global Chartwise Feedback Linearization of the Quadcopter With a Thrust Positivity Preserving Dynamic Extension

We propose a new dynamic extension of the thrust variable in the quadcopter dynamics that preserves the positive sign of the thrust. This extension not only eliminates the positive sign constraint on the thrust variable, but also leads to global chartwise feedback linearization of the quadcopter dynamics. For the latter, an atlas is first constructed on the entire state space of the quadcopter and then the dynamically extended quadcopter system is transformed to a 14-dimensional linear controllable system on each chart in the atlas. Based on the chartwise dynamic feedback linearization, a global tracking strategy is proposed for the quadcopter and its excellent performance is demonstrated with a simulation. © 1963-2012 IEEE.1