Stability Analysis and Formally Guaranteed Tracking Control of Quadrotors

Abstract

Reach-avoid tasks are among the most common challenges in autonomous aerial vehicle (UAV) applications. Despite the significant progress made in the research of aerial vehicle control during recent decades, the task of efficiently generating feasible trajectories amidst complex surroundings while ensuring formal safety guarantees during trajectory tracking remains an ongoing challenge. In response to this challenge, we propose a comprehensive control framework specifically for quadrotor UAVs reach-avoid tasks with robust formal safety guarantees. Our approach integrates geometric control theory with advanced trajectory generation techniques, enabling the consideration of tracking errors during the trajectory planning phase.

Our framework leverages the well-established geometric tracking controller, analyzing its stability to demonstrate the local exponential stability of tracking error dynamics with any positive control gains. Additionally, we derive precise and tight uniform bounds for tracking errors, ensuring guaranteed safety of the system's behavior under certain conditions. In the trajectory generation phase, our approach incorporates these bounds into the planning process, employing sophisticated sampling-based planning algorithms and safe hyper-rectangular set computations to define robust safe tubes within the environment. These safe tubes serve as corridors within which trajectories can be constructed, with piecewise continuous Bezier curves employed to ensure smooth and continuous motion. Furthermore, to enhance the performance and adaptability of our framework, we formulate an optimization problem aimed at determining optimal control gains, thereby enabling the quadrotor UAV to navigate with optimal safety guarantees.

To demonstrate the validation of the proposed framework, we conduct comprehensive numerical simulations as well as real experiments, demonstrating its ability to successfully plan and execute reach-avoid maneuvers while maintaining a high degree of safety and precision. Through these simulations, we illustrate the practical effectiveness and versatility of our framework in addressing real-world challenges encountered in UAV navigation and trajectory planning.