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

Challenges in Controllers on UAV Aircraft: Theory and Practice

This review explores the theoretical foundations and experimental dynamics of modern tiltrotor aircraft. Emphasizing feedback linearization, the study delves into the distinctive constraints and angular velocity ranges shaping tiltrotor behavior. Experimental findings highlight challenges in tracking circular trajectories, with color-coded representations illustrating the impact of angular velocity. Practical implications for applications like unmanned aerial vehicles are discussed, alongside identified challenges and avenues for future research. This work contributes to both theoretical understanding and practical considerations in the evolving field of tiltrotor control

Quantum Circuit Design for Solving Linear Systems of Equations

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key aspects of the algorithm from the standpoint of finding its efficient quantum circuit implementation using only elementary quantum operations, which is important for determining the potential usefulness of the algorithm in practical settings. Then we present a small-scale quantum circuit that solves a 2x2 linear system. The quantum circuit uses only 4 qubits, implying a tempting possibility for experimental realization. Furthermore, the circuit is numerically simulated and its performance under different circuit parameter settings is demonstrated.Comment: 7 pages, 3 figures. The errors are corrected. For the general case, discussions are added to account for recent results. The 4x4 example is replaced by a 2x2 one due to recent experimental efforts. The 2x2 example was devised at the time of writing v1 but not included in v1 for brevit

Geometric and Feedback Linearization on UAV: Review

The pervasive integration of Unmanned Aerial Vehicles (UAVs) across multifarious domains necessitates a nuanced understanding of control methodologies to ensure their optimal functionality. This exhaustive review meticulously examines two pivotal control paradigms in the UAV landscape, Geometric Control and Feedback Linearization. Delving into the intricate theoretical underpinnings, practical applications, strengths, and challenges of these methodologies, the paper endeavors to provide a comprehensive overview. Geometric Control, grounded in the principles of differential geometry, offers an elegant and intuitive approach to trajectory tracking and mission execution. In contrast, Feedback Linearization employs nonlinear control techniques to linearize UAV dynamics, paving the way for enhanced controllability. This review not only dissects the theoretical foundations but also scrutinizes real-world applications, integration challenges, and the ongoing research trajectory of Geometric Control and Feedback Linearization in the realm of UAVs

Generalized Two Color Map Theorem -- Complete Theorem of Robust Gait Plan for a Tilt-rotor

Gait plan is a procedure that is typically applied on the ground robots, e.g., quadrupedal robots; the tilt-rotor, a novel type of quadrotor with eight inputs, is not one of them. While controlling the tilt-rotor relying on feedback linearization, the tilting angles (inputs) are expected to change over-intensively, which may not be expected in the application. To help suppress the intensive change in the tilting angles, a gait plan procedure is introduced to the tilt-rotor before feedback linearization. The tilting angles are specified with time in advance by users rather than given by the control rule. However, based on this scenario, the decoupling matrix in feedback linearization can be singular for some attitudes, combinations of roll angle and pitch angle. It hinders the further application of the feedback linearization. With this concern, Two Color Map Theorem is established to maximize the acceptable attitude region, where the combinations of roll and pitch will give an invertible decoupling matrix. That theorem, however, over-restricts the choice of the tilting angles, which can rule out some feasible robust gaits. This paper gives the generalized Two Color Map Theorem; all the robust gaits can be found based on this generalized theorem. The robustness of three gaits that satisfy this generalized Two Color Map Theorem (while violating Two Color Map Theorem) are analyzed. The results show that Generalized Two Color Map Theorem completes the search for the robust gaits for a tilt-rotor

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

MusiLingo: Bridging Music and Text with Pre-trained Language Models for Music Captioning and Query Response

Large Language Models (LLMs) have shown immense potential in multimodal applications, yet the convergence of textual and musical domains remains relatively unexplored. To address this gap, we present MusiLingo, a novel system for music caption generation and music-related query responses. MusiLingo employs a single projection layer to align music representations from the pre-trained frozen music audio model MERT with the frozen LLaMA language model, bridging the gap between music audio and textual contexts. We train it on an extensive music caption dataset and fine-tune it with instructional data. Due to the scarcity of high-quality music Q&A datasets, we created the MusicInstruct (MI) dataset from MusicCaps, tailored for open-ended music inquiries. Empirical evaluations demonstrate its competitive performance in generating music captions and composing music-related Q&A pairs. Our introduced dataset enables notable advancements beyond previous ones