arXiv:2610.32248v1 Announce Type: new Abstract: This paper presents a guidance method that enables a quadrotor uncrewed aerial vehicle to perform inspection tasks along an elliptical boundary enclosing a structure of interest. The proposed guidance approach leverages a bifurcation theory-based framework that supports multiple inspection tasks, including convergence to a desired viewpoint, switching between viewpoints along the boundary, constant-speed elliptical circumnavigation, and circumnavigation with sectorial dwell-time constraint. Stability analysis of the proposed guidance dynamics establishes convergence of the generated reference trajectories to the desired behavior. The control parameters in the proposed method further allow the settling time of the reference trajectory to be specified for each task. The resulting reference velocity expressions are closed-form and algebraically simple, facilitating practical implementation. A qualitative comparison with existing guidance methods highlights the flexibility of the proposed approach in achieving different inspection tasks through a unified framework, while relying on simpler guidance computations. The proposed guidance method is validated through numerical simulations using a six-degree-of-freedom quadrotor model with model uncertainties, and a cascaded sliding-mode controller that tracks the generated reference trajectories under bounded disturbances.