Formal verification of local-minimum avoidance under field superposition

Prove that superposing the convergent guiding vector field from Machado (2026) with the harmonic potential-flow obstacle-avoidance field preserves the absence of undesired local minima.

Background

The proposed LiDARFlow guidance strategy combines a nominal convergent guiding vector field with a harmonic potential-flow obstacle-avoidance field. Each component is individually free of local minima under its respective assumptions, but the combined guidance field is not formally established to retain this property. The paper only gives an intuitive argument that undesired local minima are unlikely to arise, leaving a formal verification of the combined field's behavior unresolved.