Bifurcation-Based Quadrotor Guidance for Circular Inspection Modes

This paper presents a new guidance method for a quadrotor uncrewed aerial vehicle to perform standoff inspection from specific viewpoints arranged along a circular periphery surrounding a structure. The proposed approach leverages a bifurcation-theory-based framework to realize multiple inspection modes: reaching a specific viewpoint, switching between viewpoints along the inspection circle, and continuous circumnavigation, as the bifurcation parameter is varied. A stability analysis establishes that the quadrotor achieves the desired inspection mode. Analytical expressions relate the control parameters to the desired settling time for the inspection modes. A qualitative comparison with existing circumnavigation methods highlights the flexibility and computational feasibility of the proposed strategy. The efficacy of the guidance approach is demonstrated through numerical simulations using a six-degree-of-freedom quadrotor model.